Chapters five and six are invaluable to me as a future teacher. Again, I appreciate the manner in which this text presents the information to us. It is easy to read and easy to follow. As a person who has only recently developed an appreciation for mathematics this text allows me to learn ways to promote healthy and positive attitudes about mathematics to my students. This is something I need help with since my own attitudes were not that positive. The quotes utilized in the opening of the chapters were very inspirational to me, I am one of those people who loves to hear things stated eloquently- so they resonated clearly to me, “Assessment should be the servant of teaching and learning,” and, “It was a wise man who said that there is no greater inequality than the equal treatment of unequals.” These quotes will stay with me as I enter the classroom. I have heard before that treating all students equally is inherently unequal, and I appreciate the meaning still. You would not educate a blind student the same way you would a deaf student; accommodations and modifications must be made. I think that educators as a whole are starting to grasp at this concept because of the NCLB legislation; and that is one good change that NCLB has brought to education. About assessment; there is unfortunately a negative connotation tied to that word. Nearly everyone cringes when they hear it, and unfortunately many children have absorbed this natural tendency. However; using formative assessment as a tool to help us shape our lessons is life altering. Maybe I am romanticizing a bit, but not really. If formative assessment stops a child from enduring years of frustration caused by a simple misunderstanding then it is truly life altering. I think we all need to shake off our preconceived notions about assessment and embrace the positive outcomes we can see when we assess the right things in the right manner. I enjoyed the rubric presented in chapter 5, figure 5.2, and can easily see it being adapted to serve younger students. Also, I really enjoyed the suggestion of doing a ‘Giant Journal’ to tie in writing about math in lower grades. These are two things I will certainly do once in my own classroom. Teaching math equitably to all students is something that can be difficult for a great many of us. Unfortunately some of us didn’t have the greatest models for this principle in our own educations, so we must put out continual effort to analyze our own practices and ensure that we are making appropriate and equitable modifications and adjustments. I like that this chapter targeted not only students with disabilities, students who are CLD or ELL, or gifted students. This chapter embraced each set of students and offered specific ideas on how to properly target instruction for these groups. Again, I cannot say how great this text is at giving me hope for teaching mathematics. I truly enjoyed these readings.
Chapter five on assessment is a chapter that I have read in all my other method classes an in Curriculum and Assessment. Assessment as an educator is a big thing. The states "Traditional testing focused on what students do not know" and then in 1989 it was then shifted "toward what students do know." I feel it is extremely important for students to be taking assessments about items they know. Most students don't like taking test and have test anxiety, I am one of them still to this day. If you give a student a test about something they don't know it is not going to help the situation. It was nice seeing rubrics in this chapter that I have seen before and can relate to. In one of my other classes we talked about Anecdotal Notes and I feel that is something that will become useful in my classroom. I think that journal writing will be a nice thing to incorporate into the classroom.
Chapter six had information that i feel ties into the word diversity that we has future educators have had drilled into our heads thanks to the education department. Being sure that each student receives equal education isn't making sure they get the same education as others, it's giving them an education that fits their needs, while learning what others are learning. I don't feel this chapter should just be towards students with disabilities of any type. There are some students who just don't understand the material or are having a hard time grasping a concept. If that is the case you aren't going to give that child the same amount of work you are going to break it down for that child into smaller amounts. Ethnomathematics was a new word for me, I was not aware that it stood for the combination of culture, mathematics and education activities.
Over all I thought the chapters had a lot of information. Chapter five talked a lot about what I have heard before, but some of it was towards math and that made me understand assessment in a new way. Chapter six was new information in a way, but it was stated differently.
Adrianne, I a agree with you on formative assessments being a tool in shaping our lessons. Knowing how our students do on tests will let us know if they are ready to move on. It's also a good thing for the teacher in knowing how we can help our students to get better. I also enjoyed the rubric with the scale 4,3,2,1. It is one that I have become very familiar with over the years.
I found these two chapters to have valuable information in them. The anecdotal notes example on page 83 is a system I hope to use in the future. This is simply an observational tool for a teacher and I am afraid if I don't use something like this then I will forget information throughout my day. Thus, I will not be able to record information accurately. By using a clipboard with note cards attached I will be able to jot information randomly throughout the day. I have seen a teacher use this type of system but with a hardback notebook. She had tabs for each student and she would hang it on the side of the whiteboard so that she could grab it as she walked around the class and observed. I also like the idea of student self-assessment. I have found that students are usually overly easy on themselves or overly harsh on themselves. The types of questions associated with student self-assessments can be difficult for some students to answer. This is also something I would like to use in a future classroom. Let's face it, assessing students is not the funniest part of any teachers day, but it is a required task so I say, "Put on a happy face and just do it." I find the providing students with special needs the appropriate modifications should be a collaborative effort. Many times the special education teacher modifies work or assessments and many times the general education teacher modifies the work and hands it on to the special education teacher. Whichever is the case the appropriate modifications can make or break the success of a student. I have recently observed a teacher giving a clicker test and asking a student who needs their test modified to simply not do the last 5 questions. In my mind, this was the easy way out. The student needed more than just for a few questions to be deleted. The student needed the rest of the test read to them and given the option of few choices on multiple choice questions. The teacher could have modified this test and given this student the test at an alternative time or simply given then the written test and modified the hard copy. Consequently the student received low grade but knew them material. If given the adequate time and choices he could have preformed much better on the assessment. In my opinion, whatever the disability the student should have all the tools in his/her toolbelt to succeed. That may be through modifications, changing the language of the work, or even changing the environment where the work is performed. The same goes for those that are mathematically gifted. I feel these students are at times being left out because some teachers are teaching to the lowest level students rather than trying to add everyone to the mix and bring everyone into the instruction. I will be looking for ways to do this in my classroom.
Chapters 5 and 6 were full of lots of great information that will be helpful for me as a future teacher to know. Chapter 5 was all about building assessment into instruction throughout the classroom. I liked how the book explained the difference between summative and formative assessment which is helpful to know. I especially enjoyed looking at the figure 5.1 in the book that dealt with the four purposes of assessment and the results and it helped me to understand the concept better since I could see a picture of it. The book talked about never attempting to record data on every student in a single class period which is great advice. I liked how the chapter gave different types of formative and summative assessments that you can give your students which are helpful. Chapter 6 also contained great information dealing with teaching math equitably to all children. I liked how the book defined equity and stated that it is not every student should receive identical instruction but it demands reasonable accommodations be made as needed. RTI was a very hot topic presented in the chapter and the book did a great job of breaking down the process and explaining each of the tiers in detail. I liked the table 6.2 that gives teachers ideas and activities to do with a student who has moderate and severe disabilities. Overall both of the chapters were filled with great information and I was able to learn lots pertaining to these two different areas of math.
In response to Kayla R I also liked that chapter 5 had rubrics that I haven’t seen before as well. It was good to be able to see different types of rubrics so that as a future teacher I can vary my teaching and use different rubrics. I also like the idea of using journal writing in math as well and I feel that it is a great way to integrate across the curriculum when you are doing math. Chapter 6 was about diversity in the classroom and I liked the way that you stated equal education doesn’t mean that each student learns in the same way it means adjusting the instruction to meet the individual needs of each student. Lastly the word ethnomathematics was a new word for me as well but it nice to know what it means now.
In response to Kayla R I agree with you that we should be assessing students on what they know, and not trying to figure out what they don’t know. Assessment should be a tool with which we evaluate our own effectiveness in teaching a particular subject. Like you, Ethnomathematics stumped me. At first I thought it may have been a reference as to what not to say. Then- in reading on I too discovered what it was. I think it is finally time that we give credit to thinkers and mathematicians who have often been ignored.
Chapter 5 and 6 were full of great and useful information. Chapter 5 focused on assessment. We have gained a lot of information on assessment through out our college classes. Every teacher ed class seems to touch on it and the importance of it. I am glad that chapter five incorporated assessment in the text. I think that the best information I have read is on the importance of switching up the ways in which we assess. Dr. Stramel talked about this in class and we discussed ideas of different ways in which to assess students. Not everything needs to be sit down pencil and paper assessment. It is good to switch it up and cater to all students learning/testing styles. Chapter six was another subject in which we have learned a lot about...special ed accommodations. I think that it is important that we continue to learn about this because at some point in our careers we are going to have accommodate many different learning disabilities or handicaps. Sometimes, several in one year alone. It is obviously so important to be able to give every child an equal opportunity at an education. We have to be careful when accommodating a special ed student. You need to be able to cater to their IEP and also make it to where they still feel included in the class. Its a very fine and delicate balance. I am glad that chapter six discussed the importance and the ways in which we can do so!
Brooke M- I also liked how the text talked about the difference in formative and summative assessments. I think that as teachers we have to find ways to assess that best fits our students. Great post!
Brooke M I would like to view more types of formative tests. Evaluating students is something I have thought a lot about and would like to be creative in my approach and certainly do not want to plop down a written test every time I need to evaluate students. Keeping track of how students are progressing by keeping short notes is a way that I see myself staying focused. I also like table 6.2 and the activities it gives. I would like to utilize some type of file with ideas like these on my computer.
Chapter five was about assessments. I loved the paragraph under “What Is Assessment?” It defined the term assessment as a process of gathering evidence. In the following sentence it said “gathering evidence is not the same as giving a test or quiz.” As future teachers, we need to go beyond tests. We are no longer living in the era where we lecture, take notes, and test. Another point about assessments is the fact that we are not only assessing the students; we are assessing ourselves. I liked reading about all the different types of assessments and observations. Chapter six discussed mathematics for all children. It is important for every child to know how to do math and understand basic mathematical concepts. One of the ideas the book mentioned was peer-assisted learning. I know we learn about this all the time, but I think it is important to understand that there are some negatives about this. As a student, I hated when my peers helped me. I wanted to be the one with the answers. Also, girls hold grudges for a long time. How would a girl feel if her “worst enemy” was helping her solve a math problem? That would just be one more thing to throw in the other person’s face. I guess that is off the subject of special needs, but its really important to understand your students.
In response to Brooke: I liked learning about ethnomathematics. I never really thought about math in a cultural way. Figure 6.1 reminded me of the MTSS model they showed us during the MTSS conference on campus. I like how those types of things are brought together. If everything is different it would be so much harder to remember.
I agree with you that assessments should not always be sit down pencil and paper. I am one of those people who struggle under the pressure of taking tests like these. I have learned more, I think, throughout my education college classes through informal observation. By doing this you can see each student's strengths and weaknesses and it gives you an idea how to create different ways to help them more. Don't get me wrong, paper and pencil can be good to so that you can visually see but I think there should be other options available as well!
Chapters 5 and 6 are both very valuable chapters. Chapter 5 was all about assessments, but I liked how it focused on how to build them into assessments. One of the most important things about assessments is building them to actually assess your goals and objectives. The chapter also discussed the purpose of assessments. You can't just give an assessment and judge if the students do or do not understand. You have to use the assessment as a way to reflect on your teaching. Do you need to modify the program or improve instruction? I think some teachers might forget this. There are so many ways to assess your students, and I think you will have to find what works best for you and them. My mentor teacher for my math internship uses anecdotal notes while she observes students. This is something that I have been meaning to ask her about. I think anecdotal notes are a good way to informally assess students, but I think it might be hard to keep them organized. Chapter 6 was about teaching mathematics equitably to all children. When teaching for equity you try to attain equal outcomes for ALL students by being sensitive to differences. I feel like sometimes it is hard because you want to treat all students the same despite their differences, but sometimes you have to change instruction and adjust to children's needs to support learning because of their differences. This is my third internship, and really the first time there has been a student with a disability. There is a blind student in this classroom. I don't think I have been in there enough times yet to really see how my mentor teacher has to adjust to make sure she succeeds just like all the other students, but I am sure she does. I think that this internship will really show me how to create equitable instruction.
I also liked that the book described the importance of assessing to see how you are doing as a teacher. I think some teachers just assess and say oh well this student doesn't understand. Then there are teachers that will look at the assessment and say ok how can I change my instruction so this student can understand. That is so important! Teachers need to use assessments to reflect on themselves as well as the students.
You can never read enough about these two main topics discussed in chapters 5 and 6. Chapter 5 really makes a great statement about assessments when they list the two main ideas of the assessment principles. 1) Assessment should enhance student’s learning 2) Assessment is a valuable tool for making instructional decisions. I hope to really focus on these two components when I sit down to prepare my own lessons. I want to make sure I am using the results to help guide and direct what and how I instruct in my room.
A subject that caught my attention was when they mentioned grades and possible issues. I guess I had never really thought about this subject before but the more I focused on all the possibilities the more concerned I became. The main thing that calls to me is how grades impact the emotional stage of a child. That’s why I liked all the different types of assessments we discussed in class and read about. Those types of assessments I don’t think are taken too seriously by the child (even though they should) compared to an actually written out test. I have observed students when they get back papers and such. Those that did well are always more than willing to share and those who didn’t find a way to hide it or make fun of it. On the other hand I don’t want to assign things without giving them grades. Maybe I can find a way to substitute just classroom work grades with something else that is still valuable to them so they still feel rewarded without an actual grade. I don’t want to have a never ending grade book but I want them to see that each paper is worthwhile and important. I hated doing a paper and then getting it back with no grade. It made me feel like I didn’t accomplish anything or I did it all wrong so no grade. With that comes the idea of journals and interviews the chapter discussed. I like the idea of incorporating those items in my room. They provide a great way of assessment without the typical and are also a key social interaction between the student and teacher. I want them to feel comfortable and tell me on their level how they feel, what they know and what they don’t understand. Chapter 6 talks about being equitably. Grades tie in with this subject so well. My first semester I had to do some observation, I witnessed a teacher who should have not been a teacher. She had it in her mind before the year started who was on her good list. That’s one of the first things she talked about with me was who was good and who was bad and such and such. It was a little much considering I had no idea who she was. There was a student who was a direct result of her treatment in the room. His grades were also a reflection. This child had a “plan”, he was moved around from home to home. They often showered him at school, pretty much the worst setting a child could live in. With all that he was on medication and his actions were hard to control. She did everything to belittle this student while in school. He hated her and he hated school and had every right to.
In response to Elizabeth Sills,
I love taking notes so using anecdotal notes is probably going to be a pretty popular thing I use in my room. I want each child to have their own little folder or binder that I can store information for parent teachers conference. Notes will be everywhere! But like you mentioned you probably will have to be organized to make it work functionally and serve a true purpose.
Chapter 5 dealt with the assessment of students. Most of this chapter was a review for me because I learned quite a bit about assessment in my Curriculum and Assessment class. None-the-less, it was good to review the information because it gave me the mathematical view on the subject. I thought that this chapter gave me some good tips on how to assess my future students. One tip that they gave was to use preprinted cards that a teacher can fill out as they walk around the room. I think that this is a great way to assess students because it is up-to-date and in real time. A teacher can quickly change their lesson if they can see students struggling. Chapter 6 was very beneficial to me because it is about teaching ALL children. I think that some children get pushed to the wayside because they are having difficulties. One section in this chapter was about Response to Intervention. I feel lucky that Kansas has a personalized system for our state, and that, as a teacher candidate, I have been exposed to it. MTSS is currently used in my internship classroom. While I am there, I am with the 2nd tier of students who require extra help. It has been a great experience because I have seen that it works. It’s not the child’s fault that they are needing extra help. It is our duty as teachers to identify struggling students, and get them the help that they need.
In response to Deidre- I like that you bring up the point that we are no longer living in the area of lecture and test. Students today live in a different world than I did when I grew up. I know that this sounds like I’m an old man, but we grew up before the days of cell phones and computers in every home. Students have a wide range of technology that they can use to solve even the simplest problem. We as teachers have to adapt our lessons to cater to the lives of our fast paced students.
Automatically when I see the word “assessment” I think of how I will need to test students on the knowledge they have, or the knowledge they have gained, throughout a lesson or unit. There is so much more to assessing students, and even some of this assessment happens on a day-to-day basis. Observations made by the teacher are one-way assessments are made on a daily basis. As en educator it is key to know that assessments do not need to be in test form all of the time, and that a majority of assessments within the classroom should be informal.
I think one of the unique things about being a teacher is having the ability to create lessons that apply to every student, and all of those students typically have different abilities, strengths, and weaknesses. It may be one of the most important things to keep in mind when creating lessons. It may be time consuming to make a lesson fit the entire class, but in the end it is worth all the hard work.
I am also noticing a lot of what I am reading in the methods classes align with the information I have gotten from the Curriculum and Assessment course. It never hurts to have a review though, so I don’t mind it!
I aligned what was read in Chapter 6 to what I had learned in Educating Exceptional Students, being a peer tutor back in high school, and now what I am seeing in my mentor classroom. In the exceptional students course we were taught about all of the different disabilities that are covered under IDEA. We were also given great resources on how we can teach these students within the general classroom. Just because a student may not get the answer as quickly or as easily as others doesn’t make it okay for students to not be taught the curriculum.
I agree that when I think of assessment I automatically think of testing the students. It is so important to assess the students in what they know but we also need to be careful in not teaching for the tests.
Chapters 5 and 6 were really good chapters on assessment and teaching math equitably to all children. To me it is so important that we assess our students and ourselves, but we need to be careful to not teach for the tests. When I was a para I felt at times all we were doing was teaching the 3rd graders for their state assessment.
It is also important that we make sure that when we teach math that all students are understand. Me personally as a person who struggled with math would "pretend" I knew it so we could move on in class and I would not be the last to know it. Taking this Math Method's class has taught me that it doesn't matter how you got the answer, but you got it. If it requires taking a field trip to the football field and showing the 10 yard lines and counting by tens, then it works.
Chapter 5 and 6 were about teaching all children and assessing children. Since both of these are key components to being a good teacher, I thought these chapters were vital. Assessment is how a teacher tells how a student is doing with the information. Assessment does NOT have to be a test. I do think tests are necessary at some times, but not every single day. That just gets boring. The different types of assessment are very useful in this book. It describes what should be assessed and several different ways to assess. One way teachers assess a lot is observation. Observation is done daily. I do believe it is important that teachers take notes or have a rubric for observing, so they do not forget what they are watching. Also it keeps them on track and observing every student not just a few.
Since I am wanting to teach special education, I loved chapter 6. I think teaching to every student is not only the law, but also part of the job. I do not like singling children out, or making them do assignments that are obviously different. If that child is at a lower level I think they should do the same work just at different levels. I really like the section about modifications. It explains how many things a person might have to change just to modify for one student. Yes, it does take time, but it will be well worth it in the end. That student will learn so much more with his/her modifications.
Taking every child into consideration in every single lesson plan does take more effort, but in the long run its worth it. I believe that every child deserves the same chance at an education. I like the way you state that it is basically part of your job as a teacher. That says a lot about the kind of teacher you will be yourself also. :)
Chapter 5 on assessment was a great chapter because it did mention some things which I have learned from prior classes such as formative and summative assessment. What I liked is that it went a little deeper into the importance, types, and examples. I really like the examples, because I am a very visual person. Assessment is needed and is so important for us as teachers to be able to know where our students have been, where they are, and where they are headed. Assessment can be a simple check midway through a lesson for thumbs up if you are with me or more complex end of a chapter review/test. The chapter mentions journals and I had not really thought about journals as an assessment method, but I love it. This would be a way to get to know more about each student and the more we know the better we are able to teach them. Chapter 6 goes into detail about teaching math equitably to all children. When I began reading this I knew I had a lot to learn and I was eager to do so. I think this is one of the greatest challenges that I will face when it comes to teaching math. In my mentor classroom I see students every day who struggle and when I sit and try to help them – I struggle. I want to help them so badly, but I have yet to find that trigger that interests them or helps them to understand. Planning lessons in multiple ways will be tough but it is so important since students learn at different rates and levels. I also thought the section about tracking students was really interesting because initially I would have said this was a great idea. To me it just makes sense to keep kids together that learn and understand at the same rate so that you can better help all students. I now see that keeping the classroom heterogeneous helps the students more than splitting them would.
@Elizabeth Sills Wow! Teaching a child who is blind would be a real challenge. It would be very interesting to see how the lessons are adapted for the students disability. Math for me is very visual, so adapting the lesson would be very difficult I would think. I think this just goes to show you that teachers really do have a very tough job. Things are not getting any easier either. Some of the classrooms around this area have 26-29 kids per room. In my opinion that is just too many and the ones who are getting the short end are the students.
Chapter 5 and 6 are so valuable to future teachers. First of all assessments are so important in everyday classrooms. I really liked the section about indicators. Indicators help me so much that way I can see and know exactly what students need to know. I also like the idea about a journal. We had a journal in junior high math and it was called our UPAC book. We studied with it and it had tons of problem solving methods and tips and tricks in it. I like how chapter 6 was about teaching all children equitably. I think it is true that all student s learn differently and we need to be able to accommodate all our learners needs.
@ Cassandra S I agree with you Cassandra. So many teachers feel like they need to teach to the test and I can see why teachers are so worried about these. After all these high stakes tests are not just important for students but also the teachers who teach the students. I see a lot of teachers everyday teach to the test but if we do informal assessments on our students that we can see where they are at and what they need more.
From these chapters, what I took the most from was the parts about assessment. Of course, we have been learning about assessment in many of our education courses. I feel that assessment is such and important thing to focus on and it is apparent through the multiple learning experiences on the topic that we have had as future educators. For me, I have always been ok with test taking. I do know that there are htose that struggle with taking tests. They may know the material very well, but testing may be very difficult for them. Because of this, it is extremely important to have multiple forms of assessment. This way each aspect of evidence of knowledge is explored and a more accurate picture of what the students know can be shown. I enjoyed reading about the indicators for assessing purposes because this will help be to be able to pinpoint whether or not the students truly know what they need to know about the topic.
In reply to Shawna W.: I agree with you about journals. When I wrote journal entries as a student, I always thought of them as just writing about the topic as practice. I see now that it can be used as a great tool for assessment! I enjoyed reading your post!
The section in chapter 5 about “What Should Be Assessed” was very helpful for me. It gave me a very clear picture of what I should be looking for when I am trying to decide if my students understand the content I have taught. I also enjoyed all of the examples of performance-based tasks that will help me build math problems for my students. Until this chapter, I never had thought of using a rubric for math, but I would like to try the four-point rubric and see how it works for me. I also like the idea of using an observation rubric similar to figure 5.4 as I walk around the class to check for understanding. I feel that using math journals are a good idea because students can go back and look over previous lessons to help them. The example they gave for early learners seemed to be far more advanced than where the first graders in my school are. I would love to use journals that early, but I am not sure how to do it. Chapter 6 was valuable to me because my minor is in special education. I am always looking for ways to modify the work as needed for my students. I enjoyed reading about different activities I could use with mild to severe disabilities.
Chapter 5...Assessments! Ah, I know this word can make some cringe, but really, aren't assessments just seeing what students know? Anyway, what I got from this chapter is the way to assess without paper and pencil. Often times in my educational career, I have been up late at night studying for that big test. All that has caused is one anxious student and more coffee being consumed! As future teachers, we must be creative and think of ways to measure our student's knowledge than creating test after test. This textbook mentioned several ways to use formative testing such as journals, checklists, and rubrics.
Chapter 6 was significant to me because in my internship, the class is starting Math Groups, based off of the Response to Intervention pyramid. They will begin next month, so I'm not sure of what will be taught. I do know that the students are divided up into groups based off of achievement levels. Here in Kansas, we have adopted Multi-Tierred System of Supports or MTSS. It will be interesting to see if the students show significant growth in mathematics throughout my internship this semester.
Angela, If you look on page 86, the author shows how to use journal writing in Kindergarten. Here, the students produced a giant math journal where the teachers recorded the student responses. Maybe you could try that with your first graders.
I too like to use rubrics. The four point system seems fair and user friendly! In a previous internship, I made use of the smiley face rubric. It was a 2 point rubric. 2 points for a smiley, 1 point for a straight face, and 0 points for a frown. It was easy to use and the kindergartners understood it.
I love your post regarding chapter 6. Trying to make lesson plans for so many levels is hard. Last year when I was a para for special education trying to find that trigger that interests them or helps them understand the material was always the biggest challenge for me too, so you are not alone. You really have to build a relationship with that student so that you are able to understand them more. Don't give up, you will find that trigger! Good post!
In chapter 5 on page 78, the section on "What should be assessed" really caught my eye. The first subsection says "Concepts and Procedures". My first thought was, to insist that the students all learn a specific way of arriving to an answer is extremely difficult and, in my opinion, should not be assessed. However, as I read it, I discovered that that was not what the author meant. Van De Walle states that the student must understand the "why" which, again in my opinion, is essential if the student is to learn. How the student arrives to the answer is not as important as understanding why the correct answer is the correct answer.
An example of this is when I am presented with a problem of say "972 / 9, I understand the proper way of dividing this problem, however, it can be easier for me and faster if I understand that 9x100=900 and 9x8=72 and then add the 100 and 8 for an answer of 108. I understand that 9x100 is just a matter of 9x1 and add 2 zero's. The students need to understand the why if they are to understand the problem. I learned this in 5th grade when I asked my mom why 5x5 equaled 25 and she said because 5 fives is 25. Ohhhhhh, I get it, so 3x4 is 3 fours and 9x2 is 2 nines!
Lindsay I also liked the idea of the journal, I had never heard of a math journal until going to my math internship. At first I wondered why they would have a journal and when Mrs. D told the kids what to write, I thought what a wonderful idea!
This week we read chapters 5 & 6. The first chapter was over assessment. I think every teacher education professor has their own view and ideas on this subject along with every teacher in the field. I strongly believe that after completing my degree that (like most teachers) I will be professional and educated enough to make my own calls in the classroom. I know I wouldn’t be able to make an educated decision without all the different chapters over the different types of assessments and the best times to use each of them. It is important for every teacher to realize the variety and benefits of different types of assessments in math and all subjects. It is especially important in math to realize that paper and pencil is not the only way to assess and as teachers we need to think outside the box, we expect our students to. The next chapter is over teaching mathematics to all children. We as teachers don’t get to pick the students we teach (nor should we want to) so we need to be ready to teach students from all walks of life. I know many of us feel that we have read so much information and books of exceptionalities and English learners that we feel like experts on the subject but the idea is that we need to be prepared for everything. Even after all of these classes we will all still have a student walk into our classroom that makes us stop and take a step back because we don’t know what to do. My mother (7th grade teacher) was talking to me about an ELL student that she has (no names) and she says she has never came across with a student like this in her 10 years of teaching. She was at a loss, so I showed her some of my books and talked with her about possible reasons for his lack of comprehension in all subjects. Both of these chapters will affect how we teach our class and individual students, and I know for me makes me think more about my own teaching style and strategies.
In response to Linda McC I think you hit the nail on the head! I think students so often just follow the example problem and really have no idea of the actually reasoning behind the problem itself (the why). I hate going to a table and asking the student if that answer makes sense of if they will check their work and they respond with “but I followed the steps.” I would have done that problem completely different than you, but that’s ok because we still got the same answer. The part I disagree with you on is that the answer should be equally important. Never in the real world can you say I did all the steps right, shouldn’t that be good enough? On your taxes they don’t care if you added and subtracted right if you didn’t get the right number in the box.
Chapter five had great information on ways to integrate assessment into the classroom and lesson plans. I loved that it had a multitude of different ways to informally assess the students. I think one of the most important things that each of us needs to remember is that the students are not the only ones being assessed by the information. We are able to see for ourselves where we may be going wrong as instructors and the areas that must be re-taught and how to better prepare the lesson for the next time around. I think one of my favorite ways that I have seen my mentor teacher assess the students is by having them use whiteboards. It avoids students being embarrassed or feeling as if they are being put on the spot. However, it gives the teacher a good understanding of where each student is. Also, the students love using them so they pay more attention and participate.
Chapter six really caught my attention right off the bat. Our entire lives we have been taught to treat people equally and fairly. However, this chapter starts off by saying how students shouldn’t be treated equally in the classroom. And that is because we all learn differently and need to be taught differently. We also need to be assessed differently. One of the most surprising areas to me was saying how girls should be given more social ways of working on the lesson whenever possible because they are often times very social beings.
In response to Rebecca B... I am also looking forward to the day that I can make my own judgement calls on how to assess my students. It amazes me how many different ways my mentor teacher assesses her students every week. Often times it can be very subtle but she gains a lot of information by asking the right types of questions. I think it is very important to remember that different assessment strategies can work better for different lessons and different students.
Carissa K. I totally agree with what you said about the students are not the only ones being assessed. In reality the assessment is a test for the teacher as well. If students are struggling maybe the teacher needs to reconsider how they are presenting the information.
Chapters 5 and 6 were very informational about assessment and teaching math equitably to all children. In all of my classes we talk about how important assessment is, I like how every think keeps going back to not all children learn the same way. We are now in the time where paper tests are not the only way to asses the students. These chapters tie together well because accommodating to your students is what teachers have to do. I have seen in my internships that teachers make accommodation for students who may need more help and also have students who are working faster extend their learning. Teaching to ALL the students is what we really need to work on, with students learning different ways we need to make sure that we help them so they don't get left in the dust.
To Andrew D: I currently am in curriculum and assessment. These chapters were a review but I didn't mind because its just showing me how important assessment is. I thought that the note cards were a great way to asses the students. I think that you are right it's so important that we teach to ALL students. Accommodating to each student to help them is just part of our job.
To Rebecca: I agree with you that after all the classes we have taken, we should be prepared for any classroom. However, I still have a knot in my stomach as I think about meeting the needs of all my students. In my internship class there are 27 students. It is a mixture of all academic abilities. I worry about those students who seem like they may slipping through the crack. The budget cuts have forced schools to put more children in classrooms and how is one teacher able to meet the needs of so many students?
Oh!!!! assessments. A fancy word for test. It doesn't matter how old we are, no one likes to take a test. Chapter 5-6 discussed assessments. We learned about what an assessment should cover. I think as teachers we need to remember why we are giving our students an assessment. In addition, we need to let go of our egos and accept the responsibility if the assessment scores are inadequate. This could be a sign that the teacher needs to reteach the information. Since I am a stressful test taker the test taking strategies were particularly interesting to me. Additionally, I am one who believes that there is not an one fit all test. For instances, I would much rather take an essay test rather than an multiple choice test. My brain get all rattled and I can not make a decision because sometimes I can see how one than one answer could be correct. An essay test allows me to show what I know. In chapter 6 they talked about providing for students with special needs. Teachers need to be flexible when assessing students with special needs. As a special education para I have learned that what works with one student will not necessary be appropriate for another. For instance, we might provide a word bank for a student, while another student may not even need that accommodation. Students who have IEP's are going to be taken care by the special education department. I have been a para long enough to see that the regular education teacher needs to understand that their some students who do not get identified and it is their job to meet the needs of that struggling student. These are the students who wind up falling through the cracks.
Chapter 5 was over assessments. It was somewhat of a review for me from Curriculum and Assessment this past summer. As a student, I always thought that tests/assessments were given only at the end of lessons over what was learned in the lesson. Now, as a pre-service teacher, I am learning that assessment should be done throughout the teaching/learning process. I liked the circle model with the four purposes of assessment. Assessing is NOT simply for putting a grade in the grade book. It was not until I started taking classes, that I learned that teachers should assess for different reasons and that there are different types of assessments, such as diagnostic, formative and summative. I think it is important for teachers to assess student understanding during the lessons and not just at the end. Not all students are going to “get it” the first time through.
Chapter 6 was over equity and diverse learners. I particularly liked the three principles from the authors of Adding It Up: 1) Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas; 2) Learning builds on what students already know; and 3) Instruction in school should take advantage of the student’s informal knowledge of mathematics. Lessons need to be created to meet the needs of different learning styles, different learning abilities and students with learning disabilities or ESOL. This requires teachers to use different lessons, create adaptations or modifications and enrichment for students who do not need additional practice or instruction.
Special education is not the only area of education in which what works for one student may not work for another student. Every student is different and will look at the same thing just a little differently. As a teacher we need to make sure that we understand that.
I think that students who have test anxiety issues, like you, will be helped by the inclusion of less formal assessments that are gathered at times when they are not thinking about being tested.
As I first looked at these two chapters I could not understand why we were looking at them as part of the same blog. After reading them I think I see the point. Assessment is one area that must be adjusted for students who have special needs.
When we create assessment as teachers we are not looking to find out who failed, we do not want any of our students to fail. We need to create assessments that allow the things that each student is best at to be looked at in turn.
Lesson plans need to consider the individual needs of our students. Our lessons and tests should teach to both the student who is behind the rest of the class and the student who is ahead of the rest of the class.
As I read these two chapters I realized that I tend to only think of the one way to test math skills; I tend to think of math as based on finding the correct answer. As a teacher I need to understand that how they get there is just as important, if not more important. At the same time as long as it gets them to the answer how they get to is does not really matter. It all seems like a circle without a solution.
Assessment is the best way to monitor how we are doing as teachers, how children are are progressing, where the student started at and where they are headed as well as how fast. Assessments can tell us any problems physical and mentally that children may be dealing with. Assessments allow us to adjust to each child’s individual needs. Performance-based assessments can allow us to assess each student’s on a regular or daily basis in the classroom. It allows us to adjust an activity. Mental math is great and we do it daily mental math is great and we do it daily on their white boards. The four-point rubric could be used with the daily assessments. I liked anecdotal notes, because it allows you to make a quick note of something about a child that you would want to reflect to at a later time. I’m one of those types that need to keep notes because I’ll forget in 10 minutes. Checklists for full class might take a little while to make up a standard, and a few minutes to change or adapt it, but it would save time in the long run. I’m glad the book goes over test-taking strategies. I am horrible at tests so I know how much some kids may struggle while taking a test. Since I have been working with children I have learned to use those test taking strategies on my own tests. I think one of the more difficult parts of teaching mathematics is keeping equity. There are so many different learning styles and abilities that it puts a lot on the plate to teach. I think that my experience working with children in special education will allow me to be a better classroom teacher that might have a child with a disability. I like the fact that many of the new programs have a section in them to help adjust the curriculum to help every student. I had never heard the term ethnomathematics. Learning to count in other languages, I have seen some teachers that actually do that with the children. Telling the students the objectives for the lesson is something I’m seeing in many classrooms, especially at the 3rd, 4th, and 5th grade level. Chapter after chapter keeps taking us back to getting the families involved and how important it is. Motivating students to want to do math through games, activities, and the concept or behavior we show is very important for building up those students. I was really impressed with the section on gifted students because my child is in the gifted mathematics class and she really loves math. I don’t ever want to know that a teacher was the main reason she stopped liking math.
In response to Kim M. I really agree with what you had to say. It doesn't help if we grade the students at the end. It's over and done and we don't have time to make corrections and help them where they need it. It's good to find problems early. I also think it is very important to teach to everyone and with our society so amazingly different it does take a juggling act and lots of neat ideas to keep the kids engaged in what they are learning.Great post.
KatieC~ I felt very sad when I read your post. It reminded me of what Dr. Walizer read at the end of the semester last year, "Letters from Teddy" I think it was. I think we all have to fight that tendency not to fall into that trap. But I hope I will not single out a student to belittle or humiliate and I hope I will remember how it felt when I was that kid.
I liked reading this section because it talked about many different types of assessment. Not every assessment needs to be a test! I like how the book talked about using observation as an assessment tool. This is great because it is quick and easy for the teacher and, as a teacher, you can see if a student needs extra help or if the class is understanding or not. I like the use of observation because it isn't a test. Tests do not need to be the only assessment in the class. Some students freeze on tests and do not perform as good as they should because of the "test" label put on the assignment. Students deserve the best opportunity to succeed and test are sometimes not the best way.
I liked how chapter 6 talked about teaching to every students. This is great because as a teacher you are teaching the whole class, but you need to be able to teach to each student as they need it. All of your students are going to learn in a different way and as a teacher you need to be able to find that and try your best to teach them to the best of your ability.
I like how you talked about the quotes. The quote "equal treatment of unequals is unequal" is a great quote. Plus, it is so true. One student may need more help than another, and this is completely fair. All students are different and learn in different ways. Some need more help than others and deserve as much help as they need!
Chapter 5 and 6 are very good chapters. Ch. 5 focuses a lot on assessments which is what we talked about in class the other day. Assessments can be done in MANY different ways. I think it depends on your students the way you have to decipher which assessments work best. Assessing is one way to test your students knowledge as well as your competence as a teacher. Assessments should also enhance the students learning in ways that they may not even know that what they are going through is an assessments. Ch. 6 was about accommodations for special education students. This chapter is great for any teacher, you never know when you will have to work with students who struggle with certain things. One thing that stuck out to me was to treat each child equally- this may not be the same but it is as much as each child needs. Every child is different with the things they need in a teacher. The main goal is to get the students to understand and know how to do basic math skills. Plan ahead for the students and prepare them for what they need help with the most!
In response to Tammy M:
I agree with what you said about assessments being very good. Assessments are one way to see how you as a teacher are doing and also see how your students are doing under your instruction. If we don't assess students we will have a hard time figuring out where to take them next.
Chapter Five is a great source of information on assessments and how they help teachers help students. I think sometimes assessment can be viewed negatively, even though the goal of assessments is to find out what has been learned and what needs to be improved (which is actually positive). The information gained from assessment can be invaluable to teachers, because it helps them know what and how to teach. Assessment is valuable to students because it gives them feedback, and also allows their teacher to teach to plan instruction to meet their needs. I really enjoyed the section on “observational tools” because I think that so much valuable information can be gained about what students actually know by observing them problem solve or work out problems during class time. While I had heard of a few of the tools, such as anecdotal notes or journals, I hadn’t heard of checklists or exit slips. I can see myself using many of these strategies in my classroom someday and look forward to being able to use the information to positively impact my teaching. Chapter 6 discussed something very important, “teaching mathematics equitably to all children.” To me this means giving all children equal opportunity to learn through equal instruction (by making necessary accommodations and adaptations). I love that the text gave strategies that will work will all learners’ regardless of disability, background, giftedness, or gender. Before reading, I hadn’t really thought of gender as a factor in mathematics education, but after reading now understand that this is something I must take in to consideration as well. I will definitely be reviewing and using some of the adaptations listed in this chapter in my internship, lesson plan, and future classroom. I also enjoyed the in class discussion on “dyscalculia.” I have seen this many times as a para, and appreciate the strategies that were given in class. Overall, I think I will be able to use many of the strategies given to ensure all students are actively engaged in learning mathematics.
I agree that it is important to meet the students needs, so that every student has equal opportunity to learn. This includes special education students, but also includes ELL students and gifted students as well. I also agree it is important to plan ahead. It isn't fair to students if you are unprepared to meet their needs.
Chapter five and six discussed two extremely important topics. Assessment plays a huge role in educational success. I’m pretty familiar with assessment, how important it is, and how to implement it but I still learned a lot through chapter five. Lately, through this course and others, I’ve been learning of the true importance of journals in the classroom. Many students are more likely to write down their own thoughts in their journal than they are to tell the whole class about them and this is where a teacher can truly see their real feeling and thoughts on topics. Through journals teachers can assess how a student is really doing in the class. The text talks about writing being a unique window to students true perceptions, thoughts, and ideas and this is so true. In chapter six the importance of providing all students with a quality education was addressed. I’m worried about how I will be able to do this as a professional educator though. In my mentor teachers classroom there are two special needs students who spend less than half the day in her classroom. I know they are learning the information they need elsewhere with another qualified educator but I feel like they should be included more in their homeroom classroom with their fellow students. The part in this chapter about providing for students with special needs stood out to me because of my current observations in the field. I think peer-assisted learning and student think-alouds are great tools that can be used for all students in education. These tools cater to students with special needs but also can be extremely helpful to all of their piers as well. I was trying to think of ways to make it possible for special needs students to remain in their homeroom more often than not. I think by using teaching tools that cater to them but work great for all students as well is one way to do this.
I also liked learning about gifted students. You don’t want to give students work that is to easy for them, you want to challenge them without pushing them to their frustration level. The book also listed some great strategies to incorporate in teaching a gifted student. I really liked the idea of allowing students to pace their own learning, this way they won’t be pushed beyond their means or bored with easy content. There is so much work and specifics that go into making sure every student is catered to. It’s nerve racking but I’m hopeful I can do it.
I agree with the fact that the type of assessments used in your classroom have to work well with the students. I think the community of students in a classroom will learn to work together and will get in a learning groove that works best for all of them as a whole. It will be our job as educators to adhere to their needs and groove. I also liked how you made the statement that assessment not only assessing students knowledge but the teachers competence as well. This is so true, if the teacher is not aware of his or her students needs and how to properly serve those needs the students won’t be able to learn easily.
Chapter 5 is all about assessment. It gives a lot of different ideas about how to assess and why we assess. We talk constantly about assessing students in order to find out how they are doing in class. This chapter also addresses what to assess and gives different ideas about testing. One idea that I like is anecdotal notes. The other idea I really like is using rubrics. Rubrics help the teacher and the student. If teachers give the students the rubric ahead of time, the student knows what is expected of them. Teachers have an easier time grading because they know what they are looking for. I think that rubrics should be clear and not muddled. The book gave good examples. I think that rubrics work as well as the teacher planning them. I had a bad experience last semester with a mentor teacher who told me that no one “greatly exceeds expectations” and she gave me all “acceptable” marks because she told me that everyone has room for improvement. The mentor teacher made a note on the paper saying that she doesn’t give anyone “greatly exceeds” when they are in her class. What I learned through this was that I will want to develop a clear rubric so that I know what I am looking for and the students also know what is expected of them and I can choose the score accordingly. Page 90 in the text describes nicely how a rubric should work. It states that when papers are returned with less than perfect scores, a detailed rubric will point out what the student needs to do to achieve a higher score. Rubrics provide students with feedback as to what they did correctly and what they can improve on. Personally, I value this type of feedback and learn the most from assignments graded on a rubric. Chapter 6 starts out stating that “excellence in mathematics education requires equity—high expectations and strong support for all students.” It goes on to state that all students should be held to a high standard and expected to do well and that an equal opportunity to learn does not mean that all students receive the exact same instruction: “… this does not mean the instruction for every child should be equal.” The section titled “Creating Equitable Instruction” lays the responsibility squarely on the shoulders of the teacher and on page 94 it states that “many achievement gaps are actually instructional gaps or expectation gaps.” At the end of the section there is a statement by NCTM that gives teachers a standard to live by in their classrooms and defines equity as “high expectations, respect, understanding, and strong support for all students.” The book goes on the say that teachers who equip themselves with a lot of strategies are the ones who succeed in supporting each child in their classroom. I was surprised to read in the text that all children essentially learn in the same way. Once I read farther though, I realize that within those three principles are a lot of differences. Principle 2 states that learning builds on what students already know. So this varies greatly and accessing prior knowledge and building on it will be different for many students. The school I am interning in this semester is structured very differently than the school I worked in and interned in last year. My mentor teacher was not familiar with Kansas’ Multi-tiered Systems of Support, or RTI. But the more we talked about it, we both realized that she uses a tier system. Her 6th grade students are learning division, she looks at her grades and the rubric they are based on and sees that 4 students are struggling, so she pulls them out for some small group instruction. If that is not adequate, she will add the individual instructional time or ask for help beyond your classroom. I was surprised that she was not inundated with MTSS information because it is flooding our state and the school I was at last year uses that terminology all the time, but I see that her students are getting tiered support in her class.
Jeanette~ do you think that assessment really means test? or is that old school thinking? I think the chapter gave good ways to assess without testing as well some things discussed in class last week. One way we can assess is through games. This gives us an understanding of where students are at without the dreaded test! I think tests will always be around and are actually a necessary part of education, but they are only one part of assessment!
After reading chapter five, I was able to pick up a little more on assessment, and why it is so important. I also liked the different ideas the chapter gave on assessing that didn't involve testing. I liked how the chapter mentioned keeping a journal for the students so they can express their thoughts and feelings about math. You could also use these journals with parents at conferences. Chapter six focused on teaching math to students with different diversities. I really enjoyed reading the information on teaching math to students with disabilities. I think that would be a great challenge for me. I'm pretty sure that don't have a child with a disability in the classroom that I'm observing. I think this chapter helped me out a lot though with different ideas on how to approach it.
Jordan O, I also liked reading that there are different methods of assessing. I don't want to be the teacher that tests students over and over again. Knowing that I can assess the students by simply observing will be a great thing. I liked how you mentioned that some students "freeze" on tests. I completely agree with you. Just because the student did poorly on a test, doesn't necessarily mean they don't understand the material. This is why it's awesome that their are different ways of assessing!
As a virtual student I have the opportunity to watch the classes before I read. I must say that I love doing it this way. It's somewhat of a backward approach, but for me it works great. I have always had a hard time reading nonfiction and don't really retain or comprehend a lot of what I read. However, having the ability to learn auditory and then visually is a great combination for me.
As far as assessment I think the most challenging step for me will be designing the assessment. I want to have a non-traditional approach to this step and be able to have out-of the textbook, fun, creative assessments - especially for math. Test taking strategies on page 90 was a great review. Nearly every lesson my mentor teacher covers strategies for problem solving - Reread, find key words, etc.
Another challenge for me when writing lesson plans is adapting lessons. The example in the book was great, it takes a simple approach - change the manipulative and change the numbers to be >10. I think I typically try to complicate modifications and adaptations. My question is - IS there a way to not make it obvious to the rest of the class that adaptations are being made? I don't ever want the student/s left out or like an outcast.
@Lindsay S I too love the idea of using exit slips. Sometimes I get so frustrated with my own children asking them what they learned. I never get any details. I would love to be able to review my children's exit slips. It is also a great activity to incorporate writing.
Chapter five and six of the textbook “Elementary and Middle School Mathematics: Teaching Developmentally (2010) by J.A. Van De Walle, K.S. Karp and J.M. Bay-Williams discussed assessment and “equitably”. In these chapters I learned many interesting facts that made me think of matters differently, information that made me look at my own experience, and made me question the text. An important and interesting fact in chapter five of the textbook by Van De Walle et al. was on page 76 when the textbook mentions “The Assessment Principle in Principals and Standards stresses two main ideas: (1) Assessment should enhance students’ learning, and (2) assessment is a valuable tool for making instruction decisions.(Van De Walle et al.,76). Assessments are not just to see where the students are in their ability but it is there to help the teacher improve what they are teaching to the students. Something that I learned in chapter five of the Van De Walle et al. text book that made me think differently was on page and I will use in my own classroom is the section on “Scoring with a Four-Point Rubric” (Van De Walle et al.,81). According to Van De Walle et al. textbook “A rubric and its performance indicators should focus you and your students on the objectives and away from the self-limiting question ‘How many can you miss and still get an A?’” (Van De Walle et al.,81). There are many different kinds of rubrics available for teachers to look at when assessing students. The more rubrics I know about the better able I will be to judge which one works better for me. Something that I learned in chapter five that I can use in the future is the “anecdotal notes” (Van De Walle et al.,83). I think this is a great ways to keep tabs on my students and record their observations. As the textbook mentions I can observe a limited amount of students and write down what I observe when they are at school. Something that was mentioned in chapter 6 of Van De Walle et al. text book was that “Many achievement gaps are actually instructional gaps or expectation gaps” (Van De Walle et al., 94). This is something that I have experiences many times in classrooms that I have worked in and teachers that I had when I was younger. Teachers will teach students a certain way that they feel are “easiest” for them to understand, but just because the teacher feel s this way does not always make it so. Teachers should teach materials in a variety of ways so that all the students can figure out what works best for them. I also believe that teachers should think that the student can do something until proven otherwise. I don’t believe letting the student sit there and struggle but just give him/her a chance to complete the work. Something out of Chapter 6 that I would like to use in my classroom is the “STAR” problem solving technique on page 99 of Van De Walle et al. text book (Van De Walle et al., 99). The text mentions that “STAR is a mnemonic for problem solving; Search the word problem for important information; Translate the words into models, pictures, or symbols; Answer the problem; Review your solution for reasonableness (Van De Walle et al., 99). This is defiantly something that I could have in my classroom for students to use if they are having trouble. A question that I had for chapter six was how everyone feels about giving students that excel extra work. I have meet students that find the work easy but go slow because they know if they go too fast they will have to do extra. References: Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Jennifer Pen Reply to Matthew, You mentioned how you liked that the textbook talked about different ways to asses the students. Assessing is very important because it will not only let the teacher see when the student is at but what the teacher can do to improve. I think that teachers at time rely too much on tests and when they want to see how a student is doing they just have them take a test. Some students are just not very good test takers. I know when I take tests I feel pressured because of the time limit and I think many other students feel this way. I think that a teachers should assess students in a variety of ways so that they can better understand the students ability.
Chapter five gives a lot of great ideas on assessing students. I love the idea of making reusable and peel-and-stick rubrics for assessing the students. I think that would make keeping records of the students’ progress much easier. Much of what was covered in this chapter, such as what assessments should be used for, is information we have been learning in our teacher education classes. One new thing, to me anyway, is writing in math. In my math history I have never had to write more than a short answer. I love the idea of math journals because it gets the kids writing, it helps them think through the math processes, and it gives us an excellent way to assess what they know and how they do things. The overall idea presented in chapter six is individualized instruction. Different children learn in different ways. It will be our job as teachers to figure out how to teach each child to ensure that every one of them reaches the goals we set. Ethnomathematics was a new word for me. I have never thought about math differing from culture to culture other than perhaps its value. I am glad I read about this because I now know to consider math culture when planning lessons.
Jennifer P, I agree with the textbook in that giving extra work to gifted students is a bad idea. Why reward a student's talent with more work? I feel instead that they should be given tasks that are more meaningful to them that will keep them engaged for a longer period of time, and allow them to gain an even deeper understanding of the concepts and materials they are working on.
Chapters 5 & 6 were both a lot of review for me, but I’m always happy to have a refresher and build on me previous knowledge. Chapter 5 was all about assessments. Assessments are extremely important as we have learned many many times throughout the education program. Assessments tell teachers what they need to change, tell students if they have more work to do, and help teachers drive their instruction. I liked the break down of the NCTM assessments standards in Table 5.1. We had discussed these standards briefly, but this table made it easy to understand each standard. I also liked the examples of the different types of assessment tools. It always nice to have a visual to go with the description.
Chapter 6 dealt with teaching mathematics to students with special needs. This includes gifted, ELL, learning disabled, intellectual disabled, etc. I am currently taking my final course for my special education minor, so I have learned a lot about teaching students of all exceptionalities. However, it was nice to get some specific strategies for the mathematics area. I am really hoping to teach middle school math, so all of the information I can get tailored to math I soak up!
Agreed, reusable and peel-and-stick rubrics are a great idea. It is always helpful for teachers to have something quick and easy to use. Those are definitely ideas to keep in mind for future use. I also like the idea of math journals. When students write about math they may discover something knew, or realize they don’t fully understand a concept. Its also a great way to integrate.
The chapter about assessment made it very clear that teachers need to be aware that the word assessment is not synonymous to the words test and quiz. Assessment is something that teachers should be doing everyday in order to improve their level of instruction as well as increase their students’ learning. There are many ways that teachers can assess their students, whether they are using formative or summative assessments. I was surprised to find out that teachers should consider assessing their students’ confidence and believes about mathematics and if they like it or dislike it as well as why. This would be a great way for teachers to better understand their students and why they may be struggling with a certain mathematics concept or why they don’t even like mathematics at all. I thought that the examples given in the text of performance based tasks would definitely be useful in evaluating a students’ understanding and would allow for more discussion than a “naked number” problem that was already given to them.
Using rubrics is a great way for teachers to evaluate their students, especially because the students will know exactly what is expected of them. I liked that the text stated about observation, “Do not attempt to record data on every student in a single class period.” Observation is a very useful tool for teachers to use but it can also be a long process in order to get all of the necessary information for all students. By writing anecdotal notes, teachers can gather tons of useful information that can be beneficial during parent-teacher conferences, gathering data to help improve lesson plans and instruction as well as gathering feedback to help students. I’m glad to see that the text states how important writing is in the mathematics classroom and not only in the English classroom. Journals are a great way for students to share their thoughts about a certain concept and show their understanding. During my kindergarten mathematics internship class, the students write in their journals and draw a picture of something that represents the number they are working on in class that day. Whether it be writing the number five in words or drawing five dogs, the students show that they understand the concept of the number. I thought the concept of giving students tests that where they can actually show what they know instead of only answering multiple choice questions is a great idea. Continued...
I love the quote at the beginning of Chapter 6 that states, “It was a wise man who said that there is no greater inequality than the equal treatment of unequals.” All students should be treated fairly but mathematics can’t be taught in the same way for students who are struggling as for students who already understand it. There are going to be many different types of diverse learners in our classrooms including students with learning disabilities, English language learners, students from different cultural backgrounds and even students who are gifted in mathematics. Although accommodations and modifications will need to be made in order to better educate them, all teachers should have high expectations for their students regardless of their learning status. If students who aren’t exactly excelling at mathematics are put on the lower-level track with low expectations, they will not be challenged to improve and probably won’t be motivated to even try. Small group instruction, peer-assisted learning and student think-alouds are only a few ways that teachers can better serve the needs of their students with special needs.
Ethnomathematics sounds like a great way to better educate students while also catering to the special needs of some students. Not only would ELL benefit from this type of instruction but all of the students will become more culturally aware because of it. Teachers need to make sure students are motivated and are enjoying mathematics and they will be more likely to succeed. Playing mathematics games that involve all of the students is a great way to do this. As for the students that are mathematically gifted, I agree with Dr. Stramel in that it’s not fair to give them more of the same problems to solve if they finish early. Giving them an enrichment activity that allows them to think deeper about a problem will definitely be more beneficial.
I had never heard the term ethnomathematics either before reading this chapter and I found it to be very interesting. I think that since you have already worked with children with special needs you definitely have an advantage. I’m glad to see that although you have trouble taking tests that you are using some of the test taking strategies that are offered in the text as well as the ones you’ve seen being used in the classroom. I hope that your daughter continues to love math.
Chapter 5 and 6 were about assessment. Most children hate assessment time at school, especially math assessments. I think for students to feel better about taking assessments, they need to know great test taking strategies. They also need to know the material they are being tested over or what they should know. This chapter talked a lot about anecdotal notes and I think it is something I am going to use a lot as I become a teacher. Journal writing will be something the students will enjoy to do as an activity. They may not understand they are writing something about themselves or what they learned and can later go back and see what they wrote. For the other chapter, making sure that the teachers cover those that have special needs is very important too. I have a child in kindergarten that has developmental delays. It is a learning experience for all of us, even me. He has been in a preschool classroom for three years and now moved onto a different environment. I have to help the new teachers and paras figure him out better. He is of course adapting real well and getting used to the changes he is enduring. This chapter taught me a lot about how he is assessed and how to work with him at home on his school work. He had never had homework before so I never knew how to deal with that aspect. Learning a new word such as Ethnomathematics was quite interesting. Very weird word, but I feel I have learned a lot already even on dyscalculia. I think that is what I have as math has always been a struggle for me.
In response to SarahRob--- I loved the quote at the beginning of chapter 6 as well. All students should be treated fairly and taught fairly, just maybe in a different manner. Not all students learn at the same rate or same speed. We have to slow down for those that don’t quite gain the concept. We can’t just assume since a majority of them are catching on that we are able to move on to the next concept and leave a few behind to figure it out for themselves. My son is in the 8th grade and his math teacher is the type that just does each consecutive page in the book. He has an assignment every night. If it is a review section then they have a test within the next few days. Then she goes on to the next concept before they have taken the test. I think that confuses students because they are trying to remember what they just learned and now she is bringing in new concepts.
Chapter 5 covered a lot of material over assessments. The chapter included information on what an assessment is, the purpose of assessments, and different types of assessments. Like other people mentioned in their blogs, I always thought that assessments were what our teachers gave us to see what we did and did not know. I now know how important it is to assess your students throughout the whole learning process and not just at the end. This does not mean that you have to have quizzes all the time, it just means that you should see if your students are comprehending what you are trying to teach them. If they are not learning the information your are giving them what is the point of moving on? You are just setting the students up for failure. Growing up, I don't really remember ever having my teachers assess the class at any time other than at the end of a lesson. I think that a lot of students would do so much better and be much more confident in themselves if you checked on their comprehension throughout the lesson.
Teaching Mathematics Equitably to All Children is the title of chapter 6. This chapter included information on how to modify your lesson to accommodate all your students, the students with special needs, students that are gifted, and students who are English Language Learners. Being a special ed minor I really found this chapter helpful. It gave some strategies on how to accommodate those students that need to be taught in a different way. I also liked this chapter because I was an ELL. I grew up speaking only Spanish but when I started pre-k and had to learn English. It was hard for me because at school I would have to speak English and at home I would speak Spanish because that's what my parents knew. I know how difficult it can be to learn for a student who's first language is not English. There were some great strategies mentioned and I definitely learned a lot from this chapter.
In response to Carissa K I completely agree with your comment about treating the students equally. Growing up we all learned that in order to be fair we must treat everyone equally. How is it fair for students with special needs to be treated the same and given the same work as students who do not have special needs? Another thing that I always heard growing up was that I was an individual and that no one else was the same as me. Well if we are all different then don’t we all have different needs? Are we not all going to learn in a different way? This is one situation when it’s okay to give some students more resources or help. By not providing those students with what they need to learn we are not being fair to them.
Chapter 5-I think it's always important to allow for all aspects of teaching to have a great balance. With assessment, this is equally true. After reading chapter 5, I realize why it's more important that we assess. This includes the steps of monitoring student progress, making instructional decisions, evaluating student achievement, and evaluating programs. While making sure that this steps are made, I also feel it's important to make it has fun as possible, while still being productive and learning, of course. I know from past experiences, and even still, I am not the most comfortable test taker. Making the atmosphere for students comfortable, I feel will help with their overall feelings towards assessment (not that assessment HAS to be tests). I feel that the performance based tasks can be fun and productive. You can even turn the performance based tasks into some type of small group or classroom game. Out of the three steps of the mathematical process, I feel that communication is crucial! That last step sums up the task. Without communication, how can one learn? Or teach? Also, within chapter 5, it discusses rubrics. I am familiar with rubrics from college, but I understand that there are so many types of rubrics out there. I think as a future teacher, whether I call it rubric or not, it's important that ALL students understand and know what is expected of them. While in practicums, I have had "my students" create their own personal journal entries. This can be used with all subjects. I have used it with reading before and we as a group would have "read alouds" and then respond in our journals. Students would be presented a question and have to respond in their journal with at least three complete sentences with their response. I would go through weekly and grade their work. The journal was neat and organized. It was easy for me to see and grade and fun for the students to decorate and look forward to. This was also a bonus because it allowed writing to be incorporated with lessons. Chapter 6-I really enjoyed this chapter. I have worked with several students with special needs within practicums/internships. I have also worked with adults with disabilities outside of school. Both have given me a good balance of experience and I am more and more interested into working with students in the future with special needs. I want to potentially go into Special Education as a Masters Degree. I thin it's important to always recognize and keep the tiers in mind. This helps the teachers, as well as the students feel comfortable and to learn/teach. After reading chapter 6, I overall gather that one-on-one attention is almost always needed with special needs (whether it's mild or not). It's important that I understand that everyone has different needs and to cater to their needs when they need them. CLARITY is very important for all students, but especially those with special needs. I also fund that a lot of things you should do for special needs students, can also be applied just as equally to classroom students without special needs. As an "extra", I have been told that using read alongs and technology can help special needs students learning experience.
I also feel it's important that all students know the strategies to take in order to do well on assessments. I think we, as future teachers, must understand and apply all options to students. Just as we talked about in class the other day, everyone learns differently, but it's important I feel to give as many options as possible. Some students may learn a certain way or use a certain mathematics strategy to get an answer to a problem, and some may use a complete different way to get there. The most important thing is that ALL students get there. I feel this is the exact same attitude towards strategies for assessment.
I was never a good test-taker in school. I always struggled with the test no matter how much or little I studied. I often would get a similar grade on a test that I studied on then those that I didn't. It is really difficult for me to pinpoint an area that causes me to have this problem. I do not want my students to have the same problem that I did. I do not want to give them the answers to the test but I want to give them strategies and procedures in taking a test. I think one of the reasons I have trouble taking tests is because of anxiety. I think finding ways to cope with this are allowing the student to take sections of a test at a time throughout the day, if they want to with the proper guidelines that are fair to their peers. I also think that putting them in "stressful" situations outside of the test can help them when they do take a test. Much like an athlete does in sports. They are sometimes pushed harder in practice than they are in games. Some coaches choose to do this but not all. This allows the athlete to experience the stress greater than a game so he/she is able to conquer the opposing team. Same way in school. We can put them in a time restraint or something that causes them to push hard and then when it comes time for the test they have "all the time in the world." The book gave several other great suggestions that I liked.
Chapter 5 addresses the extreme need to assess our students…continuously. In order for us to adjust our teaching strategies and meet student needs, we must constantly assess how our students are handling the material we have given them. Performance-based assessments allow all students to show knowledge, skills, or understanding. They often involve real-world problems, and the justifications for answers often provide more information than the answers would have, if given alone. My questions have often been, “How are we to document that we have assessed our students? Does there need to be a written worksheet/quiz/etc. for every assessment?” I know that I constantly walk around to observe and make mental notes of each student’s performance and understanding, but understanding how important it is to document that information for reference makes this chapter very relevant. I love the simple rubrics shown in this chapter, and the observation tools are exactly what I needed to read about. I had forgotten about the anecdotal notes that we had learned about in Reading and Language Arts Methods, too. I also thought the section on assessing grades was interesting. It is very true that, if given a low number of points possible, on a rubric, test, or otherwise, there is a reasonable chance of a low grade for the student. This is discouraging – instead of providing the encouragement that our students need. My daughter had a math teacher in 7th grade that gave a “completion grade”. As long as the students made an effort to work the problems and do their very best to try to understand and ask for help when needed, the teacher rewarded that effort. I thought this was a very positive way to promote learning in her math class, and it provided a very safe environment for the students to learn in.
Chapter 6 was a very interesting chapter. The title might initially make you believe that it is about teaching all students “equally”. In fact, the chapter addresses how important it is to NOT treat children exactly the same as we instruct them. “…teaching for equity attempts to attain equal outcomes for all students by being sensitive to individual differences.” (page 93) Teaching at a high-risk school has shown me just how diverse one classroom can be, and I can honestly say that in a classroom of 23 students, none of them learns the same or is at the same level – in any content area. This creates a real challenge when trying to “attain equal outcomes”. I am so thankful for the suggestions provided in this chapter that will help me to focus my instruction strategies. The “Before, During, and After” suggestions are very helpful. I know that I will be referring back to this chapter a great deal, but one thing that really made me feel good about my existing teaching approach was on page 107 under the Demonstrate an Ethic of Caring category, “It is obvious that children will work harder and do things – even things like adding fractions – for people they love and trust.” I have always truly believed that it is SO important for your students to know that you truly care about their well-being and success. They need to know that we believe in them, and I do believe that they work harder for me because I show that I genuinely care about their ability to succeed. It sounds a little crazy, but I have seen a number of teachers that don’t display this attitude toward their students, and it does make a world of difference in their students’ willingness to try.
In response to Jenna (Chapter 5)…I am in complete agreement on the need to take anecdotal notes! I also worry that I will observe and then forget what I have observed. I like the idea of the teacher you observed (notebook attached to whiteboard), but I would worry about confidentiality issues. That could easily be resolved, though, by keeping the notebook in a closed desk drawer. Thanks for sharing!
In response to Brooke (Chapter 6): I liked how this chapter broke down RTI, too. This tiered system of support really makes sense. I wish that I had been able to be in an internship in Russell to experience MTSS. That would have been wonderful to see a tiered system of support that is already up and running!
Chapters 5-6 were quite informative. Both chapters made me reflect on what I already know and realize I still have a lot to learn when it comes to teaching math. For example I have never heard of the word Ethnomathematics therefore I had no idea what it meant! Chapter 5 gave a lot of information on the correct ways to assess students and of course assessment is very important as it is what drives our instruction. As stated on page 78 in our text it is very important to provide numerous ways to assess students on their abilities to do math problems due to the fact that there may be numerous ways in which to complete the work. On page 80 it was interesting to learn the defined difference of scoring and grading. I will always think about this now when I am “grading” papers! I like the quote “student should always see the possibility to excel.” (pg 81) I really like the idea of how to keep anecdotal notes on page 83 by having cards or pieces of paper with each student’s name on them stuck to a clip board and the teacher can then just write down records of what they see the student dong each day. I had never thought of writing and keeping journals in Math but I can see where it would be a good idea for some students, but necessarily for all students. I am very big on teaching hands-on methods especially when it comes to Math. I am a very visual person and I feel hands-on and visual activities are of the greatest importance when it comes to teaching Math. It was interesting to read about RTI or what we call MTSS in Kansas. I have had experience with MTSS in reading but just this year we are implementing it into our interventions for Math also. Cooperative learning is a huge part of our curriculum at the school where I work and this is a great strategy to use especially when working with student with special needs. When working with “gifted” students I agree with the quote out of the book on page 108 that states “another way not to capitalize on student’s talents is allowing then to have free time if they finish faster than the others.” I do not feel giving a student free time for getting their work accomplished quickly is great use of the students time.
I thought that Chapters 5-6 were very informative and explained a lot about assessments that I did not know. I found it interesting that the text listed reasons for having assessments was that the NCTM requires an appropriate assessment reflect a full range of different math concepts. I really liked the section on Writing and Journals. I have never had a journal in a math class and after thinking about it for a while I thought it could be a great tool to get students to open up about their concerns and struggles with math. In response to Joel- I like the idea of breaking up tests into sections to help the students that may struggle.
In response to Elizabeth: I also like the idea of peal and sick rubrics and this is a concept I plan on using in my own classroom. While I had never thought of using writing in Math either, I think this could be a very good strategy to use with certain students in the classroom. I believe it could help students with higher reasoning thinking skills in relation to the work they are doing. Ethnomathematics was also new to me! I guess we often take for granted the idea that even in Math the learning that takes place across cultures can be very different.
Chapter 5 and 6 are very important to think about and use in the classroom. Ch. 5 talks about assessments and how to build them into instruction. I liked how it gave examples of performance-based tasks and how to assess the students on them. Assessments are ways for teachers to see what a student knows, how they learn and what they have trouble on. Rubrics and performance indicators are just a couple of tools to use to mark the information we find out on a student so a teacher knows what to help them with. I personally liked the checklists for individual students. Ch. 6 talked about how to teach math to all the students and not just some of them. The three principles the book talked about were organizing knowledge around big conceptual ideas, learning builds on what students already know and instruction in school should take advantage of the children’s informal knowledge of mathematics. These principles I will have to refer back to when I begin teaching in the classroom.
In response to Tammi Whi – I also would agree that having a journal in a math class would be a great way to have the students reflect and also a way for the teacher to assess the students. I don’t remember having a journal for math when I was in elementary school, so this would be something that I could see myself having the students do.
What caught my eye right off the bat in Chapter 5 was the subtitle “Why Do We Assess?” The reason it jumped at me so quick is because we have been discussing that very topic and reading about it in another class. I thought that this book broke it down perfectly in the little chart on page 77. It lists all four purposes of assessment which are: evaluation programs, monitoring student progress, evaluating student achievement, and making instructional decisions. Then it had and arrow from each one of those reason pointing to what the results led to. Evaluating programs led to modifying programs because in order to get better you have to evaluate where you are struggling and make changes in order to get better. Monitoring student progress led resulted in promoting growth which is what we want to do with our students. Making instructional decisions led to improving instructions. I found this one important because ever student learns in a different way so we have to be willing to modify and improve our instructions so that all students get the benefit of an education. Lastly, evaluation student achievement results in recognizing student accomplishments. You won’t always be able to tell by a test whether or not a student understands the information. But by discussions and activities in class you can gain a better understanding of where a student is strongest and where that student still needs some work.
Ashley L You said it perfectly about Chapter 6 when you said that it talks about how to teach to all students and not just some of them. As educators we have to be willing to teach in a wide variety of ways. Math, in my opinion, is probably the easiest subject to use a variety of different strategies to teach different areas. You can use whiteboards, stories, blocks, money, the list just goes on and on. It is one of the subjects I am looking forward to most to teaching just because of all of the different approaches you can take to teaching it.
I found chapter 5 and 6 to be very informative. Chapter 5 talked in depth about the important of assessments. I completely agree with this, I believe for here on our of our educator profession we are going to be seeing many assessments. Assessments are a great thing for many different reasons, for instance checking for understanding, checking to see what they have learned and what you as a teacher may need to reteach. They can also be evaluating yourself and you may not even know it. Judging by the children's score will show how well you introduced the lesson and that you may need to take a step backwards to some more basic steps. Assessments are something all new teachers are going to have to know about so I think it is a great idea that it talks about it in our textbook. I also really enjoyed this section because I would eventually like to get my MS in Special Education so this section was very interesting to me. I got so much out of this section that I can take with me. I am a paraprofessional for special education so I constantly found myself referring one of my students to an example in the text.
In response to Ashley L--Ashley, I also agree with you. One thing I enjoyed about this section was it did talk about how to teach all students. Whether they are gifted or have a severe special need they deserve to all be taught but they may have to be taught the materials differently or different materials all together. This section was extremely interesting to me because of my previous work experience. I think this section is something all new teachers should read because during some point in their teaching career they are going to have a child with a special need in their classroom. Great post!
Chapters five and six are invaluable to me as a future teacher. Again, I appreciate the manner in which this text presents the information to us. It is easy to read and easy to follow. As a person who has only recently developed an appreciation for mathematics this text allows me to learn ways to promote healthy and positive attitudes about mathematics to my students. This is something I need help with since my own attitudes were not that positive.
ReplyDeleteThe quotes utilized in the opening of the chapters were very inspirational to me, I am one of those people who loves to hear things stated eloquently- so they resonated clearly to me, “Assessment should be the servant of teaching and learning,” and, “It was a wise man who said that there is no greater inequality than the equal treatment of unequals.” These quotes will stay with me as I enter the classroom. I have heard before that treating all students equally is inherently unequal, and I appreciate the meaning still. You would not educate a blind student the same way you would a deaf student; accommodations and modifications must be made. I think that educators as a whole are starting to grasp at this concept because of the NCLB legislation; and that is one good change that NCLB has brought to education.
About assessment; there is unfortunately a negative connotation tied to that word. Nearly everyone cringes when they hear it, and unfortunately many children have absorbed this natural tendency. However; using formative assessment as a tool to help us shape our lessons is life altering. Maybe I am romanticizing a bit, but not really. If formative assessment stops a child from enduring years of frustration caused by a simple misunderstanding then it is truly life altering. I think we all need to shake off our preconceived notions about assessment and embrace the positive outcomes we can see when we assess the right things in the right manner. I enjoyed the rubric presented in chapter 5, figure 5.2, and can easily see it being adapted to serve younger students. Also, I really enjoyed the suggestion of doing a ‘Giant Journal’ to tie in writing about math in lower grades. These are two things I will certainly do once in my own classroom.
Teaching math equitably to all students is something that can be difficult for a great many of us. Unfortunately some of us didn’t have the greatest models for this principle in our own educations, so we must put out continual effort to analyze our own practices and ensure that we are making appropriate and equitable modifications and adjustments. I like that this chapter targeted not only students with disabilities, students who are CLD or ELL, or gifted students. This chapter embraced each set of students and offered specific ideas on how to properly target instruction for these groups. Again, I cannot say how great this text is at giving me hope for teaching mathematics. I truly enjoyed these readings.
Chapter five on assessment is a chapter that I have read in all my other method classes an in Curriculum and Assessment. Assessment as an educator is a big thing. The states "Traditional testing focused on what students do not know" and then in 1989 it was then shifted "toward what students do know." I feel it is extremely important for students to be taking assessments about items they know. Most students don't like taking test and have test anxiety, I am one of them still to this day. If you give a student a test about something they don't know it is not going to help the situation. It was nice seeing rubrics in this chapter that I have seen before and can relate to. In one of my other classes we talked about Anecdotal Notes and I feel that is something that will become useful in my classroom. I think that journal writing will be a nice thing to incorporate into the classroom.
ReplyDeleteChapter six had information that i feel ties into the word diversity that we has future educators have had drilled into our heads thanks to the education department. Being sure that each student receives equal education isn't making sure they get the same education as others, it's giving them an education that fits their needs, while learning what others are learning. I don't feel this chapter should just be towards students with disabilities of any type. There are some students who just don't understand the material or are having a hard time grasping a concept. If that is the case you aren't going to give that child the same amount of work you are going to break it down for that child into smaller amounts. Ethnomathematics was a new word for me, I was not aware that it stood for the combination of culture, mathematics and education activities.
Over all I thought the chapters had a lot of information. Chapter five talked a lot about what I have heard before, but some of it was towards math and that made me understand assessment in a new way. Chapter six was new information in a way, but it was stated differently.
Adrianne,
ReplyDeleteI a agree with you on formative assessments being a tool in shaping our lessons. Knowing how our students do on tests will let us know if they are ready to move on. It's also a good thing for the teacher in knowing how we can help our students to get better. I also enjoyed the rubric with the scale 4,3,2,1. It is one that I have become very familiar with over the years.
I found these two chapters to have valuable information in them. The anecdotal notes example on page 83 is a system I hope to use in the future. This is simply an observational tool for a teacher and I am afraid if I don't use something like this then I will forget information throughout my day. Thus, I will not be able to record information accurately. By using a clipboard with note cards attached I will be able to jot information randomly throughout the day. I have seen a teacher use this type of system but with a hardback notebook. She had tabs for each student and she would hang it on the side of the whiteboard so that she could grab it as she walked around the class and observed. I also like the idea of student self-assessment. I have found that students are usually overly easy on themselves or overly harsh on themselves. The types of questions associated with student self-assessments can be difficult for some students to answer. This is also something I would like to use in a future classroom. Let's face it, assessing students is not the funniest part of any teachers day, but it is a required task so I say, "Put on a happy face and just do it."
ReplyDeleteI find the providing students with special needs the appropriate modifications should be a collaborative effort. Many times the special education teacher modifies work or assessments and many times the general education teacher modifies the work and hands it on to the special education teacher. Whichever is the case the appropriate modifications can make or break the success of a student. I have recently observed a teacher giving a clicker test and asking a student who needs their test modified to simply not do the last 5 questions. In my mind, this was the easy way out. The student needed more than just for a few questions to be deleted. The student needed the rest of the test read to them and given the option of few choices on multiple choice questions. The teacher could have modified this test and given this student the test at an alternative time or simply given then the written test and modified the hard copy. Consequently the student received low grade but knew them material. If given the adequate time and choices he could have preformed much better on the assessment.
In my opinion, whatever the disability the student should have all the tools in his/her toolbelt to succeed. That may be through modifications, changing the language of the work, or even changing the environment where the work is performed. The same goes for those that are mathematically gifted. I feel these students are at times being left out because some teachers are teaching to the lowest level students rather than trying to add everyone to the mix and bring everyone into the instruction. I will be looking for ways to do this in my classroom.
Chapters 5 and 6 were full of lots of great information that will be helpful for me as a future teacher to know. Chapter 5 was all about building assessment into instruction throughout the classroom. I liked how the book explained the difference between summative and formative assessment which is helpful to know. I especially enjoyed looking at the figure 5.1 in the book that dealt with the four purposes of assessment and the results and it helped me to understand the concept better since I could see a picture of it. The book talked about never attempting to record data on every student in a single class period which is great advice. I liked how the chapter gave different types of formative and summative assessments that you can give your students which are helpful.
ReplyDeleteChapter 6 also contained great information dealing with teaching math equitably to all children. I liked how the book defined equity and stated that it is not every student should receive identical instruction but it demands reasonable accommodations be made as needed. RTI was a very hot topic presented in the chapter and the book did a great job of breaking down the process and explaining each of the tiers in detail. I liked the table 6.2 that gives teachers ideas and activities to do with a student who has moderate and severe disabilities. Overall both of the chapters were filled with great information and I was able to learn lots pertaining to these two different areas of math.
In response to Kayla R
ReplyDeleteI also liked that chapter 5 had rubrics that I haven’t seen before as well. It was good to be able to see different types of rubrics so that as a future teacher I can vary my teaching and use different rubrics. I also like the idea of using journal writing in math as well and I feel that it is a great way to integrate across the curriculum when you are doing math. Chapter 6 was about diversity in the classroom and I liked the way that you stated equal education doesn’t mean that each student learns in the same way it means adjusting the instruction to meet the individual needs of each student. Lastly the word ethnomathematics was a new word for me as well but it nice to know what it means now.
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ReplyDeleteIn response to Kayla R
ReplyDeleteI agree with you that we should be assessing students on what they know, and not trying to figure out what they don’t know. Assessment should be a tool with which we evaluate our own effectiveness in teaching a particular subject. Like you, Ethnomathematics stumped me. At first I thought it may have been a reference as to what not to say. Then- in reading on I too discovered what it was. I think it is finally time that we give credit to thinkers and mathematicians who have often been ignored.
Chapter 5 and 6 were full of great and useful information. Chapter 5 focused on assessment. We have gained a lot of information on assessment through out our college classes. Every teacher ed class seems to touch on it and the importance of it. I am glad that chapter five incorporated assessment in the text. I think that the best information I have read is on the importance of switching up the ways in which we assess. Dr. Stramel talked about this in class and we discussed ideas of different ways in which to assess students. Not everything needs to be sit down pencil and paper assessment. It is good to switch it up and cater to all students learning/testing styles. Chapter six was another subject in which we have learned a lot about...special ed accommodations. I think that it is important that we continue to learn about this because at some point in our careers we are going to have accommodate many different learning disabilities or handicaps. Sometimes, several in one year alone. It is obviously so important to be able to give every child an equal opportunity at an education. We have to be careful when accommodating a special ed student. You need to be able to cater to their IEP and also make it to where they still feel included in the class. Its a very fine and delicate balance. I am glad that chapter six discussed the importance and the ways in which we can do so!
ReplyDeleteBrooke M- I also liked how the text talked about the difference in formative and summative assessments. I think that as teachers we have to find ways to assess that best fits our students. Great post!
ReplyDeleteBrooke M
ReplyDeleteI would like to view more types of formative tests. Evaluating students is something I have thought a lot about and would like to be creative in my approach and certainly do not want to plop down a written test every time I need to evaluate students. Keeping track of how students are progressing by keeping short notes is a way that I see myself staying focused.
I also like table 6.2 and the activities it gives. I would like to utilize some type of file with ideas like these on my computer.
Chapter five was about assessments. I loved the paragraph under “What Is Assessment?” It defined the term assessment as a process of gathering evidence. In the following sentence it said “gathering evidence is not the same as giving a test or quiz.” As future teachers, we need to go beyond tests. We are no longer living in the era where we lecture, take notes, and test. Another point about assessments is the fact that we are not only assessing the students; we are assessing ourselves. I liked reading about all the different types of assessments and observations. Chapter six discussed mathematics for all children. It is important for every child to know how to do math and understand basic mathematical concepts. One of the ideas the book mentioned was peer-assisted learning. I know we learn about this all the time, but I think it is important to understand that there are some negatives about this. As a student, I hated when my peers helped me. I wanted to be the one with the answers. Also, girls hold grudges for a long time. How would a girl feel if her “worst enemy” was helping her solve a math problem? That would just be one more thing to throw in the other person’s face. I guess that is off the subject of special needs, but its really important to understand your students.
ReplyDeleteIn response to Brooke: I liked learning about ethnomathematics. I never really thought about math in a cultural way. Figure 6.1 reminded me of the MTSS model they showed us during the MTSS conference on campus. I like how those types of things are brought together. If everything is different it would be so much harder to remember.
ReplyDeleteIn response to Kristie C,
ReplyDeleteI agree with you that assessments should not always be sit down pencil and paper. I am one of those people who struggle under the pressure of taking tests like these. I have learned more, I think, throughout my education college classes through informal observation. By doing this you can see each student's strengths and weaknesses and it gives you an idea how to create different ways to help them more. Don't get me wrong, paper and pencil can be good to so that you can visually see but I think there should be other options available as well!
Chapters 5 and 6 are both very valuable chapters. Chapter 5 was all about assessments, but I liked how it focused on how to build them into assessments. One of the most important things about assessments is building them to actually assess your goals and objectives. The chapter also discussed the purpose of assessments. You can't just give an assessment and judge if the students do or do not understand. You have to use the assessment as a way to reflect on your teaching. Do you need to modify the program or improve instruction? I think some teachers might forget this. There are so many ways to assess your students, and I think you will have to find what works best for you and them. My mentor teacher for my math internship uses anecdotal notes while she observes students. This is something that I have been meaning to ask her about. I think anecdotal notes are a good way to informally assess students, but I think it might be hard to keep them organized.
ReplyDeleteChapter 6 was about teaching mathematics equitably to all children. When teaching for equity you try to attain equal outcomes for ALL students by being sensitive to differences. I feel like sometimes it is hard because you want to treat all students the same despite their differences, but sometimes you have to change instruction and adjust to children's needs to support learning because of their differences. This is my third internship, and really the first time there has been a student with a disability. There is a blind student in this classroom. I don't think I have been in there enough times yet to really see how my mentor teacher has to adjust to make sure she succeeds just like all the other students, but I am sure she does. I think that this internship will really show me how to create equitable instruction.
In response to DeidreJ,
ReplyDeleteI also liked that the book described the importance of assessing to see how you are doing as a teacher. I think some teachers just assess and say oh well this student doesn't understand. Then there are teachers that will look at the assessment and say ok how can I change my instruction so this student can understand. That is so important! Teachers need to use assessments to reflect on themselves as well as the students.
Katie Coulter
ReplyDeleteChapters 5&6
Math
You can never read enough about these two main topics discussed in chapters 5 and 6. Chapter 5 really makes a great statement about assessments when they list the two main ideas of the assessment principles. 1) Assessment should enhance student’s learning 2) Assessment is a valuable tool for making instructional decisions. I hope to really focus on these two components when I sit down to prepare my own lessons. I want to make sure I am using the results to help guide and direct what and how I instruct in my room.
A subject that caught my attention was when they mentioned grades and possible issues. I guess I had never really thought about this subject before but the more I focused on all the possibilities the more concerned I became. The main thing that calls to me is how grades impact the emotional stage of a child. That’s why I liked all the different types of assessments we discussed in class and read about. Those types of assessments I don’t think are taken too seriously by the child (even though they should) compared to an actually written out test. I have observed students when they get back papers and such. Those that did well are always more than willing to share and those who didn’t find a way to hide it or make fun of it. On the other hand I don’t want to assign things without giving them grades. Maybe I can find a way to substitute just classroom work grades with something else that is still valuable to them so they still feel rewarded without an actual grade. I don’t want to have a never ending grade book but I want them to see that each paper is worthwhile and important. I hated doing a paper and then getting it back with no grade. It made me feel like I didn’t accomplish anything or I did it all wrong so no grade. With that comes the idea of journals and interviews the chapter discussed. I like the idea of incorporating those items in my room. They provide a great way of assessment without the typical and are also a key social interaction between the student and teacher. I want them to feel comfortable and tell me on their level how they feel, what they know and what they don’t understand. Chapter 6 talks about being equitably. Grades tie in with this subject so well. My first semester I had to do some observation, I witnessed a teacher who should have not been a teacher. She had it in her mind before the year started who was on her good list. That’s one of the first things she talked about with me was who was good and who was bad and such and such. It was a little much considering I had no idea who she was. There was a student who was a direct result of her treatment in the room. His grades were also a reflection. This child had a “plan”, he was moved around from home to home. They often showered him at school, pretty much the worst setting a child could live in. With all that he was on medication and his actions were hard to control. She did everything to belittle this student while in school. He hated her and he hated school and had every right to.
In response to Elizabeth Sills,
I love taking notes so using anecdotal notes is probably going to be a pretty popular thing I use in my room. I want each child to have their own little folder or binder that I can store information for parent teachers conference. Notes will be everywhere! But like you mentioned you probably will have to be organized to make it work functionally and serve a true purpose.
Chapter 5 dealt with the assessment of students. Most of this chapter was a review for me because I learned quite a bit about assessment in my Curriculum and Assessment class. None-the-less, it was good to review the information because it gave me the mathematical view on the subject. I thought that this chapter gave me some good tips on how to assess my future students. One tip that they gave was to use preprinted cards that a teacher can fill out as they walk around the room. I think that this is a great way to assess students because it is up-to-date and in real time. A teacher can quickly change their lesson if they can see students struggling.
ReplyDeleteChapter 6 was very beneficial to me because it is about teaching ALL children. I think that some children get pushed to the wayside because they are having difficulties. One section in this chapter was about Response to Intervention. I feel lucky that Kansas has a personalized system for our state, and that, as a teacher candidate, I have been exposed to it. MTSS is currently used in my internship classroom. While I am there, I am with the 2nd tier of students who require extra help. It has been a great experience because I have seen that it works. It’s not the child’s fault that they are needing extra help. It is our duty as teachers to identify struggling students, and get them the help that they need.
In response to Deidre-
ReplyDeleteI like that you bring up the point that we are no longer living in the area of lecture and test. Students today live in a different world than I did when I grew up. I know that this sounds like I’m an old man, but we grew up before the days of cell phones and computers in every home. Students have a wide range of technology that they can use to solve even the simplest problem. We as teachers have to adapt our lessons to cater to the lives of our fast paced students.
Automatically when I see the word “assessment” I think of how I will need to test students on the knowledge they have, or the knowledge they have gained, throughout a lesson or unit. There is so much more to assessing students, and even some of this assessment happens on a day-to-day basis. Observations made by the teacher are one-way assessments are made on a daily basis. As en educator it is key to know that assessments do not need to be in test form all of the time, and that a majority of assessments within the classroom should be informal.
ReplyDeleteI think one of the unique things about being a teacher is having the ability to create lessons that apply to every student, and all of those students typically have different abilities, strengths, and weaknesses. It may be one of the most important things to keep in mind when creating lessons. It may be time consuming to make a lesson fit the entire class, but in the end it is worth all the hard work.
@ Andrew Dempewolf
ReplyDeleteI am also noticing a lot of what I am reading in the methods classes align with the information I have gotten from the Curriculum and Assessment course. It never hurts to have a review though, so I don’t mind it!
I aligned what was read in Chapter 6 to what I had learned in Educating Exceptional Students, being a peer tutor back in high school, and now what I am seeing in my mentor classroom. In the exceptional students course we were taught about all of the different disabilities that are covered under IDEA. We were also given great resources on how we can teach these students within the general classroom. Just because a student may not get the answer as quickly or as easily as others doesn’t make it okay for students to not be taught the curriculum.
@ Emily M.
ReplyDeleteI agree that when I think of assessment I automatically think of testing the students. It is so important to assess the students in what they know but we also need to be careful in not teaching for the tests.
Chapters 5 and 6 were really good chapters on assessment and teaching math equitably to all children. To me it is so important that we assess our students and ourselves, but we need to be careful to not teach for the tests. When I was a para I felt at times all we were doing was teaching the 3rd graders for their state assessment.
ReplyDeleteIt is also important that we make sure that when we teach math that all students are understand. Me personally as a person who struggled with math would "pretend" I knew it so we could move on in class and I would not be the last to know it. Taking this Math Method's class has taught me that it doesn't matter how you got the answer, but you got it. If it requires taking a field trip to the football field and showing the 10 yard lines and counting by tens, then it works.
Chapter 5 and 6 were about teaching all children and assessing children. Since both of these are key components to being a good teacher, I thought these chapters were vital. Assessment is how a teacher tells how a student is doing with the information. Assessment does NOT have to be a test. I do think tests are necessary at some times, but not every single day. That just gets boring. The different types of assessment are very useful in this book. It describes what should be assessed and several different ways to assess. One way teachers assess a lot is observation. Observation is done daily. I do believe it is important that teachers take notes or have a rubric for observing, so they do not forget what they are watching. Also it keeps them on track and observing every student not just a few.
ReplyDeleteSince I am wanting to teach special education, I loved chapter 6. I think teaching to every student is not only the law, but also part of the job. I do not like singling children out, or making them do assignments that are obviously different. If that child is at a lower level I think they should do the same work just at different levels. I really like the section about modifications. It explains how many things a person might have to change just to modify for one student. Yes, it does take time, but it will be well worth it in the end. That student will learn so much more with his/her modifications.
In response to Emily M.
ReplyDeleteTaking every child into consideration in every single lesson plan does take more effort, but in the long run its worth it. I believe that every child deserves the same chance at an education. I like the way you state that it is basically part of your job as a teacher. That says a lot about the kind of teacher you will be yourself also. :)
Chapter 5 on assessment was a great chapter because it did mention some things which I have learned from prior classes such as formative and summative assessment. What I liked is that it went a little deeper into the importance, types, and examples. I really like the examples, because I am a very visual person. Assessment is needed and is so important for us as teachers to be able to know where our students have been, where they are, and where they are headed. Assessment can be a simple check midway through a lesson for thumbs up if you are with me or more complex end of a chapter review/test. The chapter mentions journals and I had not really thought about journals as an assessment method, but I love it. This would be a way to get to know more about each student and the more we know the better we are able to teach them.
ReplyDeleteChapter 6 goes into detail about teaching math equitably to all children. When I began reading this I knew I had a lot to learn and I was eager to do so. I think this is one of the greatest challenges that I will face when it comes to teaching math. In my mentor classroom I see students every day who struggle and when I sit and try to help them – I struggle. I want to help them so badly, but I have yet to find that trigger that interests them or helps them to understand. Planning lessons in multiple ways will be tough but it is so important since students learn at different rates and levels. I also thought the section about tracking students was really interesting because initially I would have said this was a great idea. To me it just makes sense to keep kids together that learn and understand at the same rate so that you can better help all students. I now see that keeping the classroom heterogeneous helps the students more than splitting them would.
@Elizabeth Sills
ReplyDeleteWow! Teaching a child who is blind would be a real challenge. It would be very interesting to see how the lessons are adapted for the students disability. Math for me is very visual, so adapting the lesson would be very difficult I would think. I think this just goes to show you that teachers really do have a very tough job. Things are not getting any easier either. Some of the classrooms around this area have 26-29 kids per room. In my opinion that is just too many and the ones who are getting the short end are the students.
Chapter 5 and 6 are so valuable to future teachers. First of all assessments are so important in everyday classrooms. I really liked the section about indicators. Indicators help me so much that way I can see and know exactly what students need to know. I also like the idea about a journal. We had a journal in junior high math and it was called our UPAC book. We studied with it and it had tons of problem solving methods and tips and tricks in it. I like how chapter 6 was about teaching all children equitably. I think it is true that all student s learn differently and we need to be able to accommodate all our learners needs.
ReplyDelete@ Cassandra S
I agree with you Cassandra. So many teachers feel like they need to teach to the test and I can see why teachers are so worried about these. After all these high stakes tests are not just important for students but also the teachers who teach the students. I see a lot of teachers everyday teach to the test but if we do informal assessments on our students that we can see where they are at and what they need more.
From these chapters, what I took the most from was the parts about assessment. Of course, we have been learning about assessment in many of our education courses. I feel that assessment is such and important thing to focus on and it is apparent through the multiple learning experiences on the topic that we have had as future educators. For me, I have always been ok with test taking. I do know that there are htose that struggle with taking tests. They may know the material very well, but testing may be very difficult for them. Because of this, it is extremely important to have multiple forms of assessment. This way each aspect of evidence of knowledge is explored and a more accurate picture of what the students know can be shown. I enjoyed reading about the indicators for assessing purposes because this will help be to be able to pinpoint whether or not the students truly know what they need to know about the topic.
ReplyDeleteIn reply to Shawna W.:
ReplyDeleteI agree with you about journals. When I wrote journal entries as a student, I always thought of them as just writing about the topic as practice. I see now that it can be used as a great tool for assessment! I enjoyed reading your post!
The section in chapter 5 about “What Should Be Assessed” was very helpful for me. It gave me a very clear picture of what I should be looking for when I am trying to decide if my students understand the content I have taught. I also enjoyed all of the examples of performance-based tasks that will help me build math problems for my students. Until this chapter, I never had thought of using a rubric for math, but I would like to try the four-point rubric and see how it works for me. I also like the idea of using an observation rubric similar to figure 5.4 as I walk around the class to check for understanding. I feel that using math journals are a good idea because students can go back and look over previous lessons to help them. The example they gave for early learners seemed to be far more advanced than where the first graders in my school are. I would love to use journals that early, but I am not sure how to do it. Chapter 6 was valuable to me because my minor is in special education. I am always looking for ways to modify the work as needed for my students. I enjoyed reading about different activities I could use with mild to severe disabilities.
ReplyDeleteLacey Keller
ReplyDeleteChapter 5...Assessments! Ah, I know this word can make some cringe, but really, aren't assessments just seeing what students know? Anyway, what I got from this chapter is the way to assess without paper and pencil. Often times in my educational career, I have been up late at night studying for that big test. All that has caused is one anxious student and more coffee being consumed! As future teachers, we must be creative and think of ways to measure our student's knowledge than creating test after test. This textbook mentioned several ways to use formative testing such as journals, checklists, and rubrics.
Chapter 6 was significant to me because in my internship, the class is starting Math Groups, based off of the Response to Intervention pyramid. They will begin next month, so I'm not sure of what will be taught. I do know that the students are divided up into groups based off of achievement levels. Here in Kansas, we have adopted Multi-Tierred System of Supports or MTSS. It will be interesting to see if the students show significant growth in mathematics throughout my internship this semester.
Lacey Keller
ReplyDeleteAngela,
If you look on page 86, the author shows how to use journal writing in Kindergarten. Here, the students produced a giant math journal where the teachers recorded the student responses. Maybe you could try that with your first graders.
I too like to use rubrics. The four point system seems fair and user friendly! In a previous internship, I made use of the smiley face rubric. It was a 2 point rubric. 2 points for a smiley, 1 point for a straight face, and 0 points for a frown. It was easy to use and the kindergartners understood it.
In response to Shawna W.,
ReplyDeleteI love your post regarding chapter 6. Trying to make lesson plans for so many levels is hard. Last year when I was a para for special education trying to find that trigger that interests them or helps them understand the material was always the biggest challenge for me too, so you are not alone. You really have to build a relationship with that student so that you are able to understand them more. Don't give up, you will find that trigger! Good post!
In chapter 5 on page 78, the section on "What should be assessed" really caught my eye. The first subsection says "Concepts and Procedures". My first thought was, to insist that the students all learn a specific way of arriving to an answer is extremely difficult and, in my opinion, should not be assessed. However, as I read it, I discovered that that was not what the author meant.
ReplyDeleteVan De Walle states that the student must understand the "why" which, again in my opinion, is essential if the student is to learn. How the student arrives to the answer is not as important as understanding why the correct answer is the correct answer.
An example of this is when I am presented with a problem of say "972 / 9, I understand the proper way of dividing this problem, however, it can be easier for me and faster if I understand that 9x100=900 and 9x8=72 and then add the 100 and 8 for an answer of 108.
I understand that 9x100 is just a matter of 9x1 and add 2 zero's.
The students need to understand the why if they are to understand the problem.
I learned this in 5th grade when I asked my mom why 5x5 equaled 25 and she said because 5 fives is 25. Ohhhhhh, I get it, so 3x4 is 3 fours and 9x2 is 2 nines!
Lindsay
ReplyDeleteI also liked the idea of the journal, I had never heard of a math journal until going to my math internship. At first I wondered why they would have a journal and when Mrs. D told the kids what to write, I thought what a wonderful idea!
This week we read chapters 5 & 6. The first chapter was over assessment. I think every teacher education professor has their own view and ideas on this subject along with every teacher in the field. I strongly believe that after completing my degree that (like most teachers) I will be professional and educated enough to make my own calls in the classroom. I know I wouldn’t be able to make an educated decision without all the different chapters over the different types of assessments and the best times to use each of them. It is important for every teacher to realize the variety and benefits of different types of assessments in math and all subjects. It is especially important in math to realize that paper and pencil is not the only way to assess and as teachers we need to think outside the box, we expect our students to. The next chapter is over teaching mathematics to all children. We as teachers don’t get to pick the students we teach (nor should we want to) so we need to be ready to teach students from all walks of life. I know many of us feel that we have read so much information and books of exceptionalities and English learners that we feel like experts on the subject but the idea is that we need to be prepared for everything. Even after all of these classes we will all still have a student walk into our classroom that makes us stop and take a step back because we don’t know what to do. My mother (7th grade teacher) was talking to me about an ELL student that she has (no names) and she says she has never came across with a student like this in her 10 years of teaching. She was at a loss, so I showed her some of my books and talked with her about possible reasons for his lack of comprehension in all subjects. Both of these chapters will affect how we teach our class and individual students, and I know for me makes me think more about my own teaching style and strategies.
ReplyDeleteIn response to Linda McC
ReplyDeleteI think you hit the nail on the head! I think students so often just follow the example problem and really have no idea of the actually reasoning behind the problem itself (the why). I hate going to a table and asking the student if that answer makes sense of if they will check their work and they respond with “but I followed the steps.” I would have done that problem completely different than you, but that’s ok because we still got the same answer. The part I disagree with you on is that the answer should be equally important. Never in the real world can you say I did all the steps right, shouldn’t that be good enough? On your taxes they don’t care if you added and subtracted right if you didn’t get the right number in the box.
Carissa Kruse
ReplyDeleteChapter 5-6 BLOG-
Chapter five had great information on ways to integrate assessment into the classroom and lesson plans. I loved that it had a multitude of different ways to informally assess the students. I think one of the most important things that each of us needs to remember is that the students are not the only ones being assessed by the information. We are able to see for ourselves where we may be going wrong as instructors and the areas that must be re-taught and how to better prepare the lesson for the next time around. I think one of my favorite ways that I have seen my mentor teacher assess the students is by having them use whiteboards. It avoids students being embarrassed or feeling as if they are being put on the spot. However, it gives the teacher a good understanding of where each student is. Also, the students love using them so they pay more attention and participate.
Chapter six really caught my attention right off the bat. Our entire lives we have been taught to treat people equally and fairly. However, this chapter starts off by saying how students shouldn’t be treated equally in the classroom. And that is because we all learn differently and need to be taught differently. We also need to be assessed differently. One of the most surprising areas to me was saying how girls should be given more social ways of working on the lesson whenever possible because they are often times very social beings.
In response to Rebecca B...
ReplyDeleteI am also looking forward to the day that I can make my own judgement calls on how to assess my students. It amazes me how many different ways my mentor teacher assesses her students every week. Often times it can be very subtle but she gains a lot of information by asking the right types of questions. I think it is very important to remember that different assessment strategies can work better for different lessons and different students.
Carissa K. I totally agree with what you said about the students are not the only ones being assessed. In reality the assessment is a test for the teacher as well. If students are struggling maybe the teacher needs to reconsider how they are presenting the information.
ReplyDeleteChapters 5 and 6 were very informational about assessment and teaching math equitably to all children. In all of my classes we talk about how important assessment is, I like how every think keeps going back to not all children learn the same way. We are now in the time where paper tests are not the only way to asses the students. These chapters tie together well because accommodating to your students is what teachers have to do. I have seen in my internships that teachers make accommodation for students who may need more help and also have students who are working faster extend their learning. Teaching to ALL the students is what we really need to work on, with students learning different ways we need to make sure that we help them so they don't get left in the dust.
ReplyDeleteTo Andrew D:
ReplyDeleteI currently am in curriculum and assessment. These chapters were a review but I didn't mind because its just showing me how important assessment is. I thought that the note cards were a great way to asses the students. I think that you are right it's so important that we teach to ALL students. Accommodating to each student to help them is just part of our job.
To Rebecca: I agree with you that after all the classes we have taken, we should be prepared for any classroom. However, I still have a knot in my stomach as I think about meeting the needs of all my students. In my internship class there are 27 students. It is a mixture of all academic abilities. I worry about those students who seem like they may slipping through the crack. The budget cuts have forced schools to put more children in classrooms and how is one teacher able to meet the needs of so many students?
ReplyDeleteOh!!!! assessments. A fancy word for test. It doesn't matter how old we are, no one likes to take a test. Chapter 5-6 discussed assessments. We learned about what an assessment should cover. I think as teachers we need to remember why we are giving our students an assessment. In addition, we need to let go of our egos and accept the responsibility if the assessment scores are inadequate. This could be a sign that the teacher needs to reteach the information. Since I am a stressful test taker the test taking strategies were particularly interesting to me. Additionally, I am one who believes that there is not an one fit all test. For instances, I would much rather take an essay test rather than an multiple choice test. My brain get all rattled and I can not make a decision because sometimes I can see how one than one answer could be correct. An essay test allows me to show what I know. In chapter 6 they talked about providing for students with special needs. Teachers need to be flexible when assessing students with special needs. As a special education para I have learned that what works with one student will not necessary be appropriate for another. For instance, we might provide a word bank for a student, while another student may not even need that accommodation. Students who have IEP's are going to be taken care by the special education department. I have been a para long enough to see that the regular education teacher needs to understand that their some students who do not get identified and it is their job to meet the needs of that struggling student. These are the students who wind up falling through the cracks.
ReplyDeleteChapter 5 was over assessments. It was somewhat of a review for me from Curriculum and Assessment this past summer. As a student, I always thought that tests/assessments were given only at the end of lessons over what was learned in the lesson. Now, as a pre-service teacher, I am learning that assessment should be done throughout the teaching/learning process. I liked the circle model with the four purposes of assessment. Assessing is NOT simply for putting a grade in the grade book. It was not until I started taking classes, that I learned that teachers should assess for different reasons and that there are different types of assessments, such as diagnostic, formative and summative. I think it is important for teachers to assess student understanding during the lessons and not just at the end. Not all students are going to “get it” the first time through.
ReplyDeleteChapter 6 was over equity and diverse learners. I particularly liked the three principles from the authors of Adding It Up: 1) Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas; 2) Learning builds on what students already know; and 3) Instruction in school should take advantage of the student’s informal knowledge of mathematics. Lessons need to be created to meet the needs of different learning styles, different learning abilities and students with learning disabilities or ESOL. This requires teachers to use different lessons, create adaptations or modifications and enrichment for students who do not need additional practice or instruction.
In response to Jeanette
ReplyDeleteSpecial education is not the only area of education in which what works for one student may not work for another student. Every student is different and will look at the same thing just a little differently. As a teacher we need to make sure that we understand that.
I think that students who have test anxiety issues, like you, will be helped by the inclusion of less formal assessments that are gathered at times when they are not thinking about being tested.
As I first looked at these two chapters I could not understand why we were looking at them as part of the same blog. After reading them I think I see the point. Assessment is one area that must be adjusted for students who have special needs.
ReplyDeleteWhen we create assessment as teachers we are not looking to find out who failed, we do not want any of our students to fail. We need to create assessments that allow the things that each student is best at to be looked at in turn.
Lesson plans need to consider the individual needs of our students. Our lessons and tests should teach to both the student who is behind the rest of the class and the student who is ahead of the rest of the class.
As I read these two chapters I realized that I tend to only think of the one way to test math skills; I tend to think of math as based on finding the correct answer. As a teacher I need to understand that how they get there is just as important, if not more important. At the same time as long as it gets them to the answer how they get to is does not really matter. It all seems like a circle without a solution.
Assessment is the best way to monitor how we are doing as teachers, how children are are progressing, where the student started at and where they are headed as well as how fast. Assessments can tell us any problems physical and mentally that children may be dealing with. Assessments allow us to adjust to each child’s individual needs. Performance-based assessments can allow us to assess each student’s on a regular or daily basis in the classroom. It allows us to adjust an activity. Mental math is great and we do it daily mental math is great and we do it daily on their white boards. The four-point rubric could be used with the daily assessments. I liked anecdotal notes, because it allows you to make a quick note of something about a child that you would want to reflect to at a later time. I’m one of those types that need to keep notes because I’ll forget in 10 minutes. Checklists for full class might take a little while to make up a standard, and a few minutes to change or adapt it, but it would save time in the long run. I’m glad the book goes over test-taking strategies. I am horrible at tests so I know how much some kids may struggle while taking a test. Since I have been working with children I have learned to use those test taking strategies on my own tests. I think one of the more difficult parts of teaching mathematics is keeping equity. There are so many different learning styles and abilities that it puts a lot on the plate to teach. I think that my experience working with children in special education will allow me to be a better classroom teacher that might have a child with a disability. I like the fact that many of the new programs have a section in them to help adjust the curriculum to help every student. I had never heard the term ethnomathematics. Learning to count in other languages, I have seen some teachers that actually do that with the children. Telling the students the objectives for the lesson is something I’m seeing in many classrooms, especially at the 3rd, 4th, and 5th grade level. Chapter after chapter keeps taking us back to getting the families involved and how important it is. Motivating students to want to do math through games, activities, and the concept or behavior we show is very important for building up those students. I was really impressed with the section on gifted students because my child is in the gifted mathematics class and she really loves math. I don’t ever want to know that a teacher was the main reason she stopped liking math.
ReplyDeleteIn response to Kim M. I really agree with what you had to say. It doesn't help if we grade the students at the end. It's over and done and we don't have time to make corrections and help them where they need it. It's good to find problems early. I also think it is very important to teach to everyone and with our society so amazingly different it does take a juggling act and lots of neat ideas to keep the kids engaged in what they are learning.Great post.
ReplyDeleteKatieC~
ReplyDeleteI felt very sad when I read your post. It reminded me of what Dr. Walizer read at the end of the semester last year, "Letters from Teddy" I think it was. I think we all have to fight that tendency not to fall into that trap. But I hope I will not single out a student to belittle or humiliate and I hope I will remember how it felt when I was that kid.
I liked reading this section because it talked about many different types of assessment. Not every assessment needs to be a test! I like how the book talked about using observation as an assessment tool. This is great because it is quick and easy for the teacher and, as a teacher, you can see if a student needs extra help or if the class is understanding or not. I like the use of observation because it isn't a test. Tests do not need to be the only assessment in the class. Some students freeze on tests and do not perform as good as they should because of the "test" label put on the assignment. Students deserve the best opportunity to succeed and test are sometimes not the best way.
ReplyDeleteI liked how chapter 6 talked about teaching to every students. This is great because as a teacher you are teaching the whole class, but you need to be able to teach to each student as they need it. All of your students are going to learn in a different way and as a teacher you need to be able to find that and try your best to teach them to the best of your ability.
Adrianne Hoefler,
ReplyDeleteI like how you talked about the quotes. The quote "equal treatment of unequals is unequal" is a great quote. Plus, it is so true. One student may need more help than another, and this is completely fair. All students are different and learn in different ways. Some need more help than others and deserve as much help as they need!
Chapter 5 and 6 are very good chapters. Ch. 5 focuses a lot on assessments which is what we talked about in class the other day. Assessments can be done in MANY different ways. I think it depends on your students the way you have to decipher which assessments work best. Assessing is one way to test your students knowledge as well as your competence as a teacher. Assessments should also enhance the students learning in ways that they may not even know that what they are going through is an assessments.
ReplyDeleteCh. 6 was about accommodations for special education students. This chapter is great for any teacher, you never know when you will have to work with students who struggle with certain things. One thing that stuck out to me was to treat each child equally- this may not be the same but it is as much as each child needs. Every child is different with the things they need in a teacher. The main goal is to get the students to understand and know how to do basic math skills. Plan ahead for the students and prepare them for what they need help with the most!
In response to Tammy M:
I agree with what you said about assessments being very good. Assessments are one way to see how you as a teacher are doing and also see how your students are doing under your instruction. If we don't assess students we will have a hard time figuring out where to take them next.
Chapter Five is a great source of information on assessments and how they help teachers help students. I think sometimes assessment can be viewed negatively, even though the goal of assessments is to find out what has been learned and what needs to be improved (which is actually positive). The information gained from assessment can be invaluable to teachers, because it helps them know what and how to teach. Assessment is valuable to students because it gives them feedback, and also allows their teacher to teach to plan instruction to meet their needs. I really enjoyed the section on “observational tools” because I think that so much valuable information can be gained about what students actually know by observing them problem solve or work out problems during class time. While I had heard of a few of the tools, such as anecdotal notes or journals, I hadn’t heard of checklists or exit slips. I can see myself using many of these strategies in my classroom someday and look forward to being able to use the information to positively impact my teaching.
ReplyDeleteChapter 6 discussed something very important, “teaching mathematics equitably to all children.” To me this means giving all children equal opportunity to learn through equal instruction (by making necessary accommodations and adaptations). I love that the text gave strategies that will work will all learners’ regardless of disability, background, giftedness, or gender. Before reading, I hadn’t really thought of gender as a factor in mathematics education, but after reading now understand that this is something I must take in to consideration as well. I will definitely be reviewing and using some of the adaptations listed in this chapter in my internship, lesson plan, and future classroom. I also enjoyed the in class discussion on “dyscalculia.” I have seen this many times as a para, and appreciate the strategies that were given in class. Overall, I think I will be able to use many of the strategies given to ensure all students are actively engaged in learning mathematics.
@ Tessa W
ReplyDeleteI agree that it is important to meet the students needs, so that every student has equal opportunity to learn. This includes special education students, but also includes ELL students and gifted students as well. I also agree it is important to plan ahead. It isn't fair to students if you are unprepared to meet their needs.
Chapter five and six discussed two extremely important topics. Assessment plays a huge role in educational success. I’m pretty familiar with assessment, how important it is, and how to implement it but I still learned a lot through chapter five. Lately, through this course and others, I’ve been learning of the true importance of journals in the classroom. Many students are more likely to write down their own thoughts in their journal than they are to tell the whole class about them and this is where a teacher can truly see their real feeling and thoughts on topics. Through journals teachers can assess how a student is really doing in the class. The text talks about writing being a unique window to students true perceptions, thoughts, and ideas and this is so true.
ReplyDeleteIn chapter six the importance of providing all students with a quality education was addressed. I’m worried about how I will be able to do this as a professional educator though. In my mentor teachers classroom there are two special needs students who spend less than half the day in her classroom. I know they are learning the information they need elsewhere with another qualified educator but I feel like they should be included more in their homeroom classroom with their fellow students. The part in this chapter about providing for students with special needs stood out to me because of my current observations in the field. I think peer-assisted learning and student think-alouds are great tools that can be used for all students in education. These tools cater to students with special needs but also can be extremely helpful to all of their piers as well. I was trying to think of ways to make it possible for special needs students to remain in their homeroom more often than not. I think by using teaching tools that cater to them but work great for all students as well is one way to do this.
I also liked learning about gifted students. You don’t want to give students work that is to easy for them, you want to challenge them without pushing them to their frustration level. The book also listed some great strategies to incorporate in teaching a gifted student. I really liked the idea of allowing students to pace their own learning, this way they won’t be pushed beyond their means or bored with easy content. There is so much work and specifics that go into making sure every student is catered to. It’s nerve racking but I’m hopeful I can do it.
Tessa,
ReplyDeleteI agree with the fact that the type of assessments used in your classroom have to work well with the students. I think the community of students in a classroom will learn to work together and will get in a learning groove that works best for all of them as a whole. It will be our job as educators to adhere to their needs and groove. I also liked how you made the statement that assessment not only assessing students knowledge but the teachers competence as well. This is so true, if the teacher is not aware of his or her students needs and how to properly serve those needs the students won’t be able to learn easily.
Chapter 5 is all about assessment. It gives a lot of different ideas about how to assess and why we assess. We talk constantly about assessing students in order to find out how they are doing in class. This chapter also addresses what to assess and gives different ideas about testing. One idea that I like is anecdotal notes. The other idea I really like is using rubrics. Rubrics help the teacher and the student. If teachers give the students the rubric ahead of time, the student knows what is expected of them. Teachers have an easier time grading because they know what they are looking for. I think that rubrics should be clear and not muddled. The book gave good examples. I think that rubrics work as well as the teacher planning them. I had a bad experience last semester with a mentor teacher who told me that no one “greatly exceeds expectations” and she gave me all “acceptable” marks because she told me that everyone has room for improvement. The mentor teacher made a note on the paper saying that she doesn’t give anyone “greatly exceeds” when they are in her class. What I learned through this was that I will want to develop a clear rubric so that I know what I am looking for and the students also know what is expected of them and I can choose the score accordingly. Page 90 in the text describes nicely how a rubric should work. It states that when papers are returned with less than perfect scores, a detailed rubric will point out what the student needs to do to achieve a higher score. Rubrics provide students with feedback as to what they did correctly and what they can improve on. Personally, I value this type of feedback and learn the most from assignments graded on a rubric.
ReplyDeleteChapter 6 starts out stating that “excellence in mathematics education requires equity—high expectations and strong support for all students.” It goes on to state that all students should be held to a high standard and expected to do well and that an equal opportunity to learn does not mean that all students receive the exact same instruction: “… this does not mean the instruction for every child should be equal.” The section titled “Creating Equitable Instruction” lays the responsibility squarely on the shoulders of the teacher and on page 94 it states that “many achievement gaps are actually instructional gaps or expectation gaps.” At the end of the section there is a statement by NCTM that gives teachers a standard to live by in their classrooms and defines equity as “high expectations, respect, understanding, and strong support for all students.” The book goes on the say that teachers who equip themselves with a lot of strategies are the ones who succeed in supporting each child in their classroom. I was surprised to read in the text that all children essentially learn in the same way. Once I read farther though, I realize that within those three principles are a lot of differences. Principle 2 states that learning builds on what students already know. So this varies greatly and accessing prior knowledge and building on it will be different for many students. The school I am interning in this semester is structured very differently than the school I worked in and interned in last year. My mentor teacher was not familiar with Kansas’ Multi-tiered Systems of Support, or RTI. But the more we talked about it, we both realized that she uses a tier system. Her 6th grade students are learning division, she looks at her grades and the rubric they are based on and sees that 4 students are struggling, so she pulls them out for some small group instruction. If that is not adequate, she will add the individual instructional time or ask for help beyond your classroom. I was surprised that she was not inundated with MTSS information because it is flooding our state and the school I was at last year uses that terminology all the time, but I see that her students are getting tiered support in her class.
Jeanette~ do you think that assessment really means test? or is that old school thinking? I think the chapter gave good ways to assess without testing as well some things discussed in class last week. One way we can assess is through games. This gives us an understanding of where students are at without the dreaded test! I think tests will always be around and are actually a necessary part of education, but they are only one part of assessment!
ReplyDeleteAfter reading chapter five, I was able to pick up a little more on assessment, and why it is so important. I also liked the different ideas the chapter gave on assessing that didn't involve testing. I liked how the chapter mentioned keeping a journal for the students so they can express their thoughts and feelings about math. You could also use these journals with parents at conferences. Chapter six focused on teaching math to students with different diversities. I really enjoyed reading the information on teaching math to students with disabilities. I think that would be a great challenge for me. I'm pretty sure that don't have a child with a disability in the classroom that I'm observing. I think this chapter helped me out a lot though with different ideas on how to approach it.
ReplyDeleteJordan O,
ReplyDeleteI also liked reading that there are different methods of assessing. I don't want to be the teacher that tests students over and over again. Knowing that I can assess the students by simply observing will be a great thing. I liked how you mentioned that some students "freeze" on tests. I completely agree with you. Just because the student did poorly on a test, doesn't necessarily mean they don't understand the material. This is why it's awesome that their are different ways of assessing!
As a virtual student I have the opportunity to watch the classes before I read. I must say that I love doing it this way. It's somewhat of a backward approach, but for me it works great. I have always had a hard time reading nonfiction and don't really retain or comprehend a lot of what I read. However, having the ability to learn auditory and then visually is a great combination for me.
ReplyDeleteAs far as assessment I think the most challenging step for me will be designing the assessment. I want to have a non-traditional approach to this step and be able to have out-of the textbook, fun, creative assessments - especially for math. Test taking strategies on page 90 was a great review. Nearly every lesson my mentor teacher covers strategies for problem solving - Reread, find key words, etc.
Another challenge for me when writing lesson plans is adapting lessons. The example in the book was great, it takes a simple approach - change the manipulative and change the numbers to be >10. I think I typically try to complicate modifications and adaptations. My question is - IS there a way to not make it obvious to the rest of the class that adaptations are being made? I don't ever want the student/s left out or like an outcast.
@Lindsay S
I too love the idea of using exit slips. Sometimes I get so frustrated with my own children asking them what they learned. I never get any details. I would love to be able to review my children's exit slips. It is also a great activity to incorporate writing.
Chapter five and six of the textbook “Elementary and Middle School Mathematics: Teaching Developmentally (2010) by J.A. Van De Walle, K.S. Karp and J.M. Bay-Williams discussed assessment and “equitably”. In these chapters I learned many interesting facts that made me think of matters differently, information that made me look at my own experience, and made me question the text.
ReplyDeleteAn important and interesting fact in chapter five of the textbook by Van De Walle et al. was on page 76 when the textbook mentions “The Assessment Principle in Principals and Standards stresses two main ideas: (1) Assessment should enhance students’ learning, and (2) assessment is a valuable tool for making instruction decisions.(Van De Walle et al.,76). Assessments are not just to see where the students are in their ability but it is there to help the teacher improve what they are teaching to the students.
Something that I learned in chapter five of the Van De Walle et al. text book that made me think differently was on page and I will use in my own classroom is the section on “Scoring with a Four-Point Rubric” (Van De Walle et al.,81). According to Van De Walle et al. textbook “A rubric and its performance indicators should focus you and your students on the objectives and away from the self-limiting question ‘How many can you miss and still get an A?’” (Van De Walle et al.,81). There are many different kinds of rubrics available for teachers to look at when assessing students. The more rubrics I know about the better able I will be to judge which one works better for me.
Something that I learned in chapter five that I can use in the future is the “anecdotal notes” (Van De Walle et al.,83). I think this is a great ways to keep tabs on my students and record their observations. As the textbook mentions I can observe a limited amount of students and write down what I observe when they are at school.
Something that was mentioned in chapter 6 of Van De Walle et al. text book was that “Many achievement gaps are actually instructional gaps or expectation gaps” (Van De Walle et al., 94). This is something that I have experiences many times in classrooms that I have worked in and teachers that I had when I was younger. Teachers will teach students a certain way that they feel are “easiest” for them to understand, but just because the teacher feel s this way does not always make it so. Teachers should teach materials in a variety of ways so that all the students can figure out what works best for them. I also believe that teachers should think that the student can do something until proven otherwise. I don’t believe letting the student sit there and struggle but just give him/her a chance to complete the work.
Something out of Chapter 6 that I would like to use in my classroom is the “STAR” problem solving technique on page 99 of Van De Walle et al. text book (Van De Walle et al., 99). The text mentions that “STAR is a mnemonic for problem solving; Search the word problem for important information; Translate the words into models, pictures, or symbols; Answer the problem; Review your solution for reasonableness (Van De Walle et al., 99). This is defiantly something that I could have in my classroom for students to use if they are having trouble.
A question that I had for chapter six was how everyone feels about giving students that excel extra work. I have meet students that find the work easy but go slow because they know if they go too fast they will have to do extra.
References:
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Jennifer Pen Reply to
ReplyDeleteMatthew,
You mentioned how you liked that the textbook talked about different ways to asses the students. Assessing is very important because it will not only let the teacher see when the student is at but what the teacher can do to improve. I think that teachers at time rely too much on tests and when they want to see how a student is doing they just have them take a test. Some students are just not very good test takers. I know when I take tests I feel pressured because of the time limit and I think many other students feel this way.
I think that a teachers should assess students in a variety of ways so that they can better understand the students ability.
Chapter five gives a lot of great ideas on assessing students. I love the idea of making reusable and peel-and-stick rubrics for assessing the students. I think that would make keeping records of the students’ progress much easier. Much of what was covered in this chapter, such as what assessments should be used for, is information we have been learning in our teacher education classes. One new thing, to me anyway, is writing in math. In my math history I have never had to write more than a short answer. I love the idea of math journals because it gets the kids writing, it helps them think through the math processes, and it gives us an excellent way to assess what they know and how they do things. The overall idea presented in chapter six is individualized instruction. Different children learn in different ways. It will be our job as teachers to figure out how to teach each child to ensure that every one of them reaches the goals we set. Ethnomathematics was a new word for me. I have never thought about math differing from culture to culture other than perhaps its value. I am glad I read about this because I now know to consider math culture when planning lessons.
ReplyDeleteJennifer P, I agree with the textbook in that giving extra work to gifted students is a bad idea. Why reward a student's talent with more work? I feel instead that they should be given tasks that are more meaningful to them that will keep them engaged for a longer period of time, and allow them to gain an even deeper understanding of the concepts and materials they are working on.
ReplyDeleteChapters 5 & 6 were both a lot of review for me, but I’m always happy to have a refresher and build on me previous knowledge. Chapter 5 was all about assessments. Assessments are extremely important as we have learned many many times throughout the education program. Assessments tell teachers what they need to change, tell students if they have more work to do, and help teachers drive their instruction. I liked the break down of the NCTM assessments standards in Table 5.1. We had discussed these standards briefly, but this table made it easy to understand each standard. I also liked the examples of the different types of assessment tools. It always nice to have a visual to go with the description.
ReplyDeleteChapter 6 dealt with teaching mathematics to students with special needs. This includes gifted, ELL, learning disabled, intellectual disabled, etc. I am currently taking my final course for my special education minor, so I have learned a lot about teaching students of all exceptionalities. However, it was nice to get some specific strategies for the mathematics area. I am really hoping to teach middle school math, so all of the information I can get tailored to math I soak up!
Elizabeth –
ReplyDeleteAgreed, reusable and peel-and-stick rubrics are a great idea. It is always helpful for teachers to have something quick and easy to use. Those are definitely ideas to keep in mind for future use. I also like the idea of math journals. When students write about math they may discover something knew, or realize they don’t fully understand a concept. Its also a great way to integrate.
The chapter about assessment made it very clear that teachers need to be aware that the word assessment is not synonymous to the words test and quiz. Assessment is something that teachers should be doing everyday in order to improve their level of instruction as well as increase their students’ learning. There are many ways that teachers can assess their students, whether they are using formative or summative assessments. I was surprised to find out that teachers should consider assessing their students’ confidence and believes about mathematics and if they like it or dislike it as well as why. This would be a great way for teachers to better understand their students and why they may be struggling with a certain mathematics concept or why they don’t even like mathematics at all. I thought that the examples given in the text of performance based tasks would definitely be useful in evaluating a students’ understanding and would allow for more discussion than a “naked number” problem that was already given to them.
ReplyDeleteUsing rubrics is a great way for teachers to evaluate their students, especially because the students will know exactly what is expected of them. I liked that the text stated about observation, “Do not attempt to record data on every student in a single class period.” Observation is a very useful tool for teachers to use but it can also be a long process in order to get all of the necessary information for all students. By writing anecdotal notes, teachers can gather tons of useful information that can be beneficial during parent-teacher conferences, gathering data to help improve lesson plans and instruction as well as gathering feedback to help students. I’m glad to see that the text states how important writing is in the mathematics classroom and not only in the English classroom. Journals are a great way for students to share their thoughts about a certain concept and show their understanding. During my kindergarten mathematics internship class, the students write in their journals and draw a picture of something that represents the number they are working on in class that day. Whether it be writing the number five in words or drawing five dogs, the students show that they understand the concept of the number. I thought the concept of giving students tests that where they can actually show what they know instead of only answering multiple choice questions is a great idea.
Continued...
I love the quote at the beginning of Chapter 6 that states, “It was a wise man who said that there is no greater inequality than the equal treatment of unequals.” All students should be treated fairly but mathematics can’t be taught in the same way for students who are struggling as for students who already understand it. There are going to be many different types of diverse learners in our classrooms including students with learning disabilities, English language learners, students from different cultural backgrounds and even students who are gifted in mathematics. Although accommodations and modifications will need to be made in order to better educate them, all teachers should have high expectations for their students regardless of their learning status. If students who aren’t exactly excelling at mathematics are put on the lower-level track with low expectations, they will not be challenged to improve and probably won’t be motivated to even try. Small group instruction, peer-assisted learning and student think-alouds are only a few ways that teachers can better serve the needs of their students with special needs.
ReplyDeleteEthnomathematics sounds like a great way to better educate students while also catering to the special needs of some students. Not only would ELL benefit from this type of instruction but all of the students will become more culturally aware because of it. Teachers need to make sure students are motivated and are enjoying mathematics and they will be more likely to succeed. Playing mathematics games that involve all of the students is a great way to do this. As for the students that are mathematically gifted, I agree with Dr. Stramel in that it’s not fair to give them more of the same problems to solve if they finish early. Giving them an enrichment activity that allows them to think deeper about a problem will definitely be more beneficial.
In response to Tammy M:
ReplyDeleteI had never heard the term ethnomathematics either before reading this chapter and I found it to be very interesting. I think that since you have already worked with children with special needs you definitely have an advantage. I’m glad to see that although you have trouble taking tests that you are using some of the test taking strategies that are offered in the text as well as the ones you’ve seen being used in the classroom. I hope that your daughter continues to love math.
Chapter 5 and 6 were about assessment. Most children hate assessment time at school, especially math assessments. I think for students to feel better about taking assessments, they need to know great test taking strategies. They also need to know the material they are being tested over or what they should know. This chapter talked a lot about anecdotal notes and I think it is something I am going to use a lot as I become a teacher. Journal writing will be something the students will enjoy to do as an activity. They may not understand they are writing something about themselves or what they learned and can later go back and see what they wrote. For the other chapter, making sure that the teachers cover those that have special needs is very important too. I have a child in kindergarten that has developmental delays. It is a learning experience for all of us, even me. He has been in a preschool classroom for three years and now moved onto a different environment. I have to help the new teachers and paras figure him out better. He is of course adapting real well and getting used to the changes he is enduring. This chapter taught me a lot about how he is assessed and how to work with him at home on his school work. He had never had homework before so I never knew how to deal with that aspect. Learning a new word such as Ethnomathematics was quite interesting. Very weird word, but I feel I have learned a lot already even on dyscalculia. I think that is what I have as math has always been a struggle for me.
ReplyDeleteIn response to SarahRob---
ReplyDeleteI loved the quote at the beginning of chapter 6 as well. All students should be treated fairly and taught fairly, just maybe in a different manner. Not all students learn at the same rate or same speed. We have to slow down for those that don’t quite gain the concept. We can’t just assume since a majority of them are catching on that we are able to move on to the next concept and leave a few behind to figure it out for themselves. My son is in the 8th grade and his math teacher is the type that just does each consecutive page in the book. He has an assignment every night. If it is a review section then they have a test within the next few days. Then she goes on to the next concept before they have taken the test. I think that confuses students because they are trying to remember what they just learned and now she is bringing in new concepts.
Chapter 5 covered a lot of material over assessments. The chapter included
ReplyDeleteinformation on what an assessment is, the purpose of assessments, and
different types of assessments. Like other people mentioned in their
blogs, I always thought that assessments were what our teachers gave us to
see what we did and did not know. I now know how important it is to assess
your students throughout the whole learning process and not just at the
end. This does not mean that you have to have quizzes all the time, it
just means that you should see if your students are comprehending what you
are trying to teach them. If they are not learning the information your
are giving them what is the point of moving on? You are just setting the
students up for failure. Growing up, I don't really remember ever having
my teachers assess the class at any time other than at the end of a
lesson. I think that a lot of students would do so much better and be much
more confident in themselves if you checked on their comprehension
throughout the lesson.
Teaching Mathematics Equitably to All Children is the title of chapter 6.
This chapter included information on how to modify your lesson to
accommodate all your students, the students with special needs, students
that are gifted, and students who are English Language Learners. Being a
special ed minor I really found this chapter helpful. It gave some
strategies on how to accommodate those students that need to be taught in
a different way. I also liked this chapter because I was an ELL. I grew up
speaking only Spanish but when I started pre-k and had to learn English.
It was hard for me because at school I would have to speak English and at
home I would speak Spanish because that's what my parents knew. I know how
difficult it can be to learn for a student who's first language is not
English. There were some great strategies mentioned and I definitely
learned a lot from this chapter.
In response to Carissa K
ReplyDeleteI completely agree with your comment about treating the students equally. Growing up we all learned that in order to be fair we must treat everyone equally. How is it fair for students with special needs to be treated the same and given the same work as students who do not have special needs? Another thing that I always heard growing up was that I was an individual and that no one else was the same as me. Well if we are all different then don’t we all have different needs? Are we not all going to learn in a different way? This is one situation when it’s okay to give some students more resources or help. By not providing those students with what they need to learn we are not being fair to them.
Chapter 5-I think it's always important to allow for all aspects of teaching to have a great balance. With assessment, this is equally true. After reading chapter 5, I realize why it's more important that we assess. This includes the steps of monitoring student progress, making instructional decisions, evaluating student achievement, and evaluating programs. While making sure that this steps are made, I also feel it's important to make it has fun as possible, while still being productive and learning, of course. I know from past experiences, and even still, I am not the most comfortable test taker. Making the atmosphere for students comfortable, I feel will help with their overall feelings towards assessment (not that assessment HAS to be tests). I feel that the performance based tasks can be fun and productive. You can even turn the performance based tasks into some type of small group or classroom game. Out of the three steps of the mathematical process, I feel that communication is crucial! That last step sums up the task. Without communication, how can one learn? Or teach? Also, within chapter 5, it discusses rubrics. I am familiar with rubrics from college, but I understand that there are so many types of rubrics out there. I think as a future teacher, whether I call it rubric or not, it's important that ALL students understand and know what is expected of them. While in practicums, I have had "my students" create their own personal journal entries. This can be used with all subjects. I have used it with reading before and we as a group would have "read alouds" and then respond in our journals. Students would be presented a question and have to respond in their journal with at least three complete sentences with their response. I would go through weekly and grade their work. The journal was neat and organized. It was easy for me to see and grade and fun for the students to decorate and look forward to. This was also a bonus because it allowed writing to be incorporated with lessons.
ReplyDeleteChapter 6-I really enjoyed this chapter. I have worked with several students with special needs within practicums/internships. I have also worked with adults with disabilities outside of school. Both have given me a good balance of experience and I am more and more interested into working with students in the future with special needs. I want to potentially go into Special Education as a Masters Degree. I thin it's important to always recognize and keep the tiers in mind. This helps the teachers, as well as the students feel comfortable and to learn/teach. After reading chapter 6, I overall gather that one-on-one attention is almost always needed with special needs (whether it's mild or not). It's important that I understand that everyone has different needs and to cater to their needs when they need them. CLARITY is very important for all students, but especially those with special needs. I also fund that a lot of things you should do for special needs students, can also be applied just as equally to classroom students without special needs. As an "extra", I have been told that using read alongs and technology can help special needs students learning experience.
In response to April-
ReplyDeleteI also feel it's important that all students know the strategies to take in order to do well on assessments. I think we, as future teachers, must understand and apply all options to students. Just as we talked about in class the other day, everyone learns differently, but it's important I feel to give as many options as possible. Some students may learn a certain way or use a certain mathematics strategy to get an answer to a problem, and some may use a complete different way to get there. The most important thing is that ALL students get there. I feel this is the exact same attitude towards strategies for assessment.
I was never a good test-taker in school. I always struggled with the test no matter how much or little I studied. I often would get a similar grade on a test that I studied on then those that I didn't. It is really difficult for me to pinpoint an area that causes me to have this problem. I do not want my students to have the same problem that I did. I do not want to give them the answers to the test but I want to give them strategies and procedures in taking a test. I think one of the reasons I have trouble taking tests is because of anxiety. I think finding ways to cope with this are allowing the student to take sections of a test at a time throughout the day, if they want to with the proper guidelines that are fair to their peers. I also think that putting them in "stressful" situations outside of the test can help them when they do take a test. Much like an athlete does in sports. They are sometimes pushed harder in practice than they are in games. Some coaches choose to do this but not all. This allows the athlete to experience the stress greater than a game so he/she is able to conquer the opposing team. Same way in school. We can put them in a time restraint or something that causes them to push hard and then when it comes time for the test they have "all the time in the world." The book gave several other great suggestions that I liked.
ReplyDeleteRachel,
ReplyDeleteThat is it! Teaching students to have fun in the classroom and creating that environment is extremely important.
Chapter 5 addresses the extreme need to assess our students…continuously. In order for us to adjust our teaching strategies and meet student needs, we must constantly assess how our students are handling the material we have given them. Performance-based assessments allow all students to show knowledge, skills, or understanding. They often involve real-world problems, and the justifications for answers often provide more information than the answers would have, if given alone. My questions have often been, “How are we to document that we have assessed our students? Does there need to be a written worksheet/quiz/etc. for every assessment?” I know that I constantly walk around to observe and make mental notes of each student’s performance and understanding, but understanding how important it is to document that information for reference makes this chapter very relevant. I love the simple rubrics shown in this chapter, and the observation tools are exactly what I needed to read about. I had forgotten about the anecdotal notes that we had learned about in Reading and Language Arts Methods, too. I also thought the section on assessing grades was interesting. It is very true that, if given a low number of points possible, on a rubric, test, or otherwise, there is a reasonable chance of a low grade for the student. This is discouraging – instead of providing the encouragement that our students need. My daughter had a math teacher in 7th grade that gave a “completion grade”. As long as the students made an effort to work the problems and do their very best to try to understand and ask for help when needed, the teacher rewarded that effort. I thought this was a very positive way to promote learning in her math class, and it provided a very safe environment for the students to learn in.
ReplyDeleteChapter 6 was a very interesting chapter. The title might initially make you believe that it is about teaching all students “equally”. In fact, the chapter addresses how important it is to NOT treat children exactly the same as we instruct them. “…teaching for equity attempts to attain equal outcomes for all students by being sensitive to individual differences.” (page 93) Teaching at a high-risk school has shown me just how diverse one classroom can be, and I can honestly say that in a classroom of 23 students, none of them learns the same or is at the same level – in any content area. This creates a real challenge when trying to “attain equal outcomes”. I am so thankful for the suggestions provided in this chapter that will help me to focus my instruction strategies. The “Before, During, and After” suggestions are very helpful. I know that I will be referring back to this chapter a great deal, but one thing that really made me feel good about my existing teaching approach was on page 107 under the Demonstrate an Ethic of Caring category, “It is obvious that children will work harder and do things – even things like adding fractions – for people they love and trust.” I have always truly believed that it is SO important for your students to know that you truly care about their well-being and success. They need to know that we believe in them, and I do believe that they work harder for me because I show that I genuinely care about their ability to succeed. It sounds a little crazy, but I have seen a number of teachers that don’t display this attitude toward their students, and it does make a world of difference in their students’ willingness to try.
In response to Jenna (Chapter 5)…I am in complete agreement on the need to take anecdotal notes! I also worry that I will observe and then forget what I have observed. I like the idea of the teacher you observed (notebook attached to whiteboard), but I would worry about confidentiality issues. That could easily be resolved, though, by keeping the notebook in a closed desk drawer. Thanks for sharing!
ReplyDeleteIn response to Brooke (Chapter 6): I liked how this chapter broke down RTI, too. This tiered system of support really makes sense. I wish that I had been able to be in an internship in Russell to experience MTSS. That would have been wonderful to see a tiered system of support that is already up and running!
Chapters 5-6 were quite informative. Both chapters made me reflect on what I already know and realize I still have a lot to learn when it comes to teaching math. For example I have never heard of the word Ethnomathematics therefore I had no idea what it meant! Chapter 5 gave a lot of information on the correct ways to assess students and of course assessment is very important as it is what drives our instruction. As stated on page 78 in our text it is very important to provide numerous ways to assess students on their abilities to do math problems due to the fact that there may be numerous ways in which to complete the work. On page 80 it was interesting to learn the defined difference of scoring and grading. I will always think about this now when I am “grading” papers! I like the quote “student should always see the possibility to excel.” (pg 81) I really like the idea of how to keep anecdotal notes on page 83 by having cards or pieces of paper with each student’s name on them stuck to a clip board and the teacher can then just write down records of what they see the student dong each day. I had never thought of writing and keeping journals in Math but I can see where it would be a good idea for some students, but necessarily for all students. I am very big on teaching hands-on methods especially when it comes to Math. I am a very visual person and I feel hands-on and visual activities are of the greatest importance when it comes to teaching Math. It was interesting to read about RTI or what we call MTSS in Kansas. I have had experience with MTSS in reading but just this year we are implementing it into our interventions for Math also. Cooperative learning is a huge part of our curriculum at the school where I work and this is a great strategy to use especially when working with student with special needs. When working with “gifted” students I agree with the quote out of the book on page 108 that states “another way not to capitalize on student’s talents is allowing then to have free time if they finish faster than the others.” I do not feel giving a student free time for getting their work accomplished quickly is great use of the students time.
ReplyDeleteI thought that Chapters 5-6 were very informative and explained a lot about assessments that I did not know. I found it interesting that the text listed reasons for having assessments was that the NCTM requires an appropriate assessment reflect a full range of different math concepts. I really liked the section on Writing and Journals. I have never had a journal in a math class and after thinking about it for a while I thought it could be a great tool to get students to open up about their concerns and struggles with math.
ReplyDeleteIn response to Joel-
I like the idea of breaking up tests into sections to help the students that may struggle.
In response to Elizabeth:
ReplyDeleteI also like the idea of peal and sick rubrics and this is a concept I plan on using in my own classroom. While I had never thought of using writing in Math either, I think this could be a very good strategy to use with certain students in the classroom. I believe it could help students with higher reasoning thinking skills in relation to the work they are doing. Ethnomathematics was also new to me! I guess we often take for granted the idea that even in Math the learning that takes place across cultures can be very different.
Chapter 5 and 6 are very important to think about and use in the classroom. Ch. 5 talks about assessments and how to build them into instruction. I liked how it gave examples of performance-based tasks and how to assess the students on them. Assessments are ways for teachers to see what a student knows, how they learn and what they have trouble on. Rubrics and performance indicators are just a couple of tools to use to mark the information we find out on a student so a teacher knows what to help them with. I personally liked the checklists for individual students. Ch. 6 talked about how to teach math to all the students and not just some of them. The three principles the book talked about were organizing knowledge around big conceptual ideas, learning builds on what students already know and instruction in school should take advantage of the children’s informal knowledge of mathematics. These principles I will have to refer back to when I begin teaching in the classroom.
ReplyDeleteIn response to Tammi Whi –
ReplyDeleteI also would agree that having a journal in a math class would be a great way to have the students reflect and also a way for the teacher to assess the students. I don’t remember having a journal for math when I was in elementary school, so this would be something that I could see myself having the students do.
What caught my eye right off the bat in Chapter 5 was the subtitle “Why Do We Assess?” The reason it jumped at me so quick is because we have been discussing that very topic and reading about it in another class. I thought that this book broke it down perfectly in the little chart on page 77. It lists all four purposes of assessment which are: evaluation programs, monitoring student progress, evaluating student achievement, and making instructional decisions. Then it had and arrow from each one of those reason pointing to what the results led to. Evaluating programs led to modifying programs because in order to get better you have to evaluate where you are struggling and make changes in order to get better. Monitoring student progress led resulted in promoting growth which is what we want to do with our students. Making instructional decisions led to improving instructions. I found this one important because ever student learns in a different way so we have to be willing to modify and improve our instructions so that all students get the benefit of an education. Lastly, evaluation student achievement results in recognizing student accomplishments. You won’t always be able to tell by a test whether or not a student understands the information. But by discussions and activities in class you can gain a better understanding of where a student is strongest and where that student still needs some work.
ReplyDeleteAshley L
ReplyDeleteYou said it perfectly about Chapter 6 when you said that it talks about how to teach to all students and not just some of them. As educators we have to be willing to teach in a wide variety of ways. Math, in my opinion, is probably the easiest subject to use a variety of different strategies to teach different areas. You can use whiteboards, stories, blocks, money, the list just goes on and on. It is one of the subjects I am looking forward to most to teaching just because of all of the different approaches you can take to teaching it.
I found chapter 5 and 6 to be very informative. Chapter 5 talked in depth about the important of assessments. I completely agree with this, I believe for here on our of our educator profession we are going to be seeing many assessments. Assessments are a great thing for many different reasons, for instance checking for understanding, checking to see what they have learned and what you as a teacher may need to reteach. They can also be evaluating yourself and you may not even know it. Judging by the children's score will show how well you introduced the lesson and that you may need to take a step backwards to some more basic steps. Assessments are something all new teachers are going to have to know about so I think it is a great idea that it talks about it in our textbook. I also really enjoyed this section because I would eventually like to get my MS in Special Education so this section was very interesting to me. I got so much out of this section that I can take with me. I am a paraprofessional for special education so I constantly found myself referring one of my students to an example in the text.
ReplyDeleteIn response to Ashley L--Ashley, I also agree with you. One thing I enjoyed about this section was it did talk about how to teach all students. Whether they are gifted or have a severe special need they deserve to all be taught but they may have to be taught the materials differently or different materials all together. This section was extremely interesting to me because of my previous work experience. I think this section is something all new teachers should read because during some point in their teaching career they are going to have a child with a special need in their classroom. Great post!
ReplyDelete