Moskowitz post

My students draw some amazing pictures to represent fractions. They use shapes, colors, shading, and numbers in their pictures. Nonetheless, however many times I say that the shape they draw must be divided into equal parts, some students do not do this. Maybe they do not know how to divide a shape into equal parts, or maybe they do not know why. I have said that they need to, I have demonstrated how to draw pictures and divide it equally, and I have told them the reasons why. When they do not do this, their depiction of the fraction is wrong and the equation or problem that incorporates the picture, they will do it wrong. I wish I had focused more on the division of shapes to represent fractions earlier in the lesson or during homework. Now I know that the basics must not be overlooked for future lessons

Week 10 Bode

          Here is the work of one of my low level students whom I have worked with very much in the classroom. This student struggles to pay attention on the rug when I, or my MT, am teaching which is why I wanted to check his work for this blog. When I checked on his work, in every example he had 5 pennies circled and wrote one N in the “show with fewer coins” section. He explained to me that he was done—he had not filled out the total number of cents or the left over pennies he forgot to represent in the “fewer coins” section. I had asked him to look at the first example and tell me what he might be missing in this problem. Immediately he was able to tell me that he had forgotten to put the coins. He proceeded to count all the coins, the correct amount might I add, and then wrote in the answer. After that he felt he was done. We counted together the 7 cents in the first example, I told him to look at the 5 pennies he circled and made a nickel with. I asked if there were anymore coins left over—he took a minute to think and then I could tell he had an aha moment. He continued to count the remaining 2 pennies and say I have two pennies left over. He wasn’t aware that he had to then draw that next to the N he wrote in the “fewer coins” section. He completed number 1 and moved onto the next example, which I asked him to think about the problem and look for his unfinished work. With some prompting he was able to complete the rest of the problem (how much cents total and represent the left over pennies). By the third problem he could almost do it on his own, what concerns me is that the other pages my teacher asked me to assign to the children, he had not even completed or attempted to complete. He was only able to do this worksheet because I was sitting with him making sure he completed it. This student can understand how to exchange pennies for nickels but forgets to complete the problem with the remaining coins. He also fails to read all directions and complete all that’s asked of him mathematically in a problem. How can he get any work done if the only work he can do is one-on-one teaching?

            This student needs more work with counting all the coins in a problem and focusing on exchanging then counting the remaining. But above that this child needs serious help focusing and doing work even when not directed to. One way I would advance his thinking is by having him work with a partner, someone who will keep him on task and make sure he completes the whole worksheet but also doesn’t just give him the answers. I have a couple students in mind who I feel would be good fits at this job and can help this student stay on task. During the lessons he is normally not paying attention and gets distracted easily. I think what would be helpful is not just to have I’m sit in front but also have him participate as much as he can in answering questions or demonstrating his thinking, etc. This way he can stay engaged in the math content and lesson and maybe that will help him feel more motivated to pay attention to the worksheets when he gets back to his seat because he actually understands what he’s working on. I feel he’s not able to stay concentrated because he’s not quite sure what to do and doesn’t have confidence in his math skills. Helping him focus on the mathematics at the lessons time will help him understand the individual work being assigned.

Maria Ricchio-student work blog

After giving students their place value test, I noticed that many students did very well with the material. They were able to represent and classify different numbers using the base 10 blocks. However, I did notice many students still struggled with addition. When students were asked to find the number from looking at 10 base blocks they were usually able to do so, but when asked to add 100, subtract 100, and add 10…that’s when we lost some students. We were getting all sorts of different answers, which made it seem like students were just putting random numbers down. After analyzing their responses, I could see many of them were lost, so that tells me I need to go back and make sure students understand before we go forward. I believe my students really do better when they have visual representations. As I continue into GLT, I want to give my students opportunities to use manipulatives, as much as possible. Turning the math tasks into games seems to be working really well, because students don’t feel like they are doing “ real work”. I think through practice, students will gain more knowledge and how to perform shortcuts. Luckily, the next unit students will be learning is Addition and Subtraction, so this gives us the perfect opportunity to clear up those misconceptions and errors, so students can gain confidence in their responses.

Montague

Student Work Analysis Blog

            Thursday we taught a lesson on addition with the kindergarteners. We started the lesson with me modeling how to do the first 3 problems of the ladybug addition worksheet. Then, the next three were for students to work in partners with. Each pair of students had a die with numbers 1-6 on it. The first student would roll the die, they would identify the number and draw spots on one side of the ladybug that matched the number. Then, the next student would roll the die and do the same thing. After the spots were drawn, they would write the number sentence underneath (i.e 5+2=7) and they would also have to read the number sentence from left to write, so that they not only added the total number of spots but so that they had experience with number sentences and naming the + and = signs. Then, the last 3 problems on the page were for students to do independently if there was time, however, there was not enough time. 9 problems for kindergarten was probably way too many therefore, I would change this to about 5 or 6 if I were to teach the lesson. I also think that it would have been beneficial to ensure that there was time for students to work independently after the teacher modeled and after they had time to work with partners so that we could have gone around to get a better idea on who had a good idea on what to do and who did not. I do realize that this was the first time addition was taught and they are only in kindergarten therefore, they will get ample opportunities to do more addition problems that we can assess them in a better way.

            Looking at one students worksheet, it shows that they were able to follow along during the first three problems when I modeled it for the class but when they were released to work with their partners, this group was not ready! They did not do anything correct for the remainder of the worksheet. I think that this worksheet does reveal much about the student’s current mathematical understanding aside from the fact that they weren’t ready to work on their own because they don’t understand addition or they did not understand the directions of the worksheet. Also, the die could have been confusing to some students because when we were modeling it, we used a die that had dots, not numbers. But when we released them on their own, we gave them dice that had numbers, which seemed to confuse students.

            One way that I would re- do this would be to only give about 4 or 5 problems. 2 would be done as a class, 2 in groups and have students do 1 on their own. This way, I think that it would not be as overwhelming to have so many problems on one worksheet for kindergarten. Also, I think that I am going to make sheets of the lady bug with just 1 big lady bug, put them in slip covers so that this could be used as a center to further students’ understanding. Students will be able to use dry erase markers on the slipcovers. 

Quick Check- Patterns of Multiples

This week I reintroduced multiplication to my students and the patterns for the multiples of 2, 5, and 9. In the beginning a lot of the students had a difficult time really being able to show me that they understood the pattern by using it to explain their answer.

For example I would prompt them with this question: "Using the pattern for multiples of 5 how do you know 5 x 4 is NOT 24." That was a multiplication fact they all knew and they all knew the proper product was 20 not 24. However, because these students have never had to use reasoning for math it was hard to answer the question by using the pattern to explain. One of my students answers was the following,

"I know it is not 24 because it is 20. I know this because the fives count up by 5s and that has a 4."

Although this student is correct in the fact that the multiples of 5 count up by 5, you could say that for any multiple of any number however, the distinct pattern for the multiples of 5 that we discussed and they wrote down was that the number in the ones place of the product always ends in a zero or a five. This student was able to tell me this pattern, write this pattern down, explain the pattern to me however, when it came time to applying the pattern they could not do it. I think this is because they have not fully internalized the pattern and do not fully understand how they can explain their mathematical thinking using the facts and patterns they know.

Student Work Sample

This week as part of my Guided Lead Teaching, one of my last lessons was introducing addition.  First I used everyday language and relevant examples using my students' lives and our classroom culture to represent simple addition problems.  Next, we developed problems together using a story board of a bunk bed and animal math manipulatives about "bears having a slumber party (the meanipulatives on the top bunk) who called their friends to come over (the manipulatives on the bottom bunk) and showing this "number story" as a math equation.

I then released my students into independent practice, so that they had their own bunk bed story board and animal manipulatives.  Walking around, I noticed that some of my students weren't understanding that in for a simple addition equation, we need three numbers- the two numbers we're adding together and the sum.  In particular, I noticed that Jamir was simply counting two groups of manipulatives- his animals on the top bunk, continuing onto his animals on the bottom bunk.  Next week, when I teach number stories again, I want to think of a way to really show two distinct number entities and representations joining but also how numbers relate and decompose into each other.

Student Work: Week 9

Student Work #1

          This is a piece of student work (a formative assessment given mid-week) completed this week during my guided lead teaching. The first three days we spent talking about what place value is, how to represent it, and how to write numbers. This question asked the student to write out the number 5, 059 in word form. Shown above, instead of writing out "five thousand fifty-nine," the student wrote out the place value for each number. Although these are related, I think the student looked at the number and thought about what each digit represents.

          The next steps for this would be to practice writing numbers in a more authentic way. For example, the day I taught this, I was supposed to teach my students how to write checks. Although this would have been the ideal plan, it was hard to jump into writing checks when the students had no background knowledge on this. I would ask the students: What does 5 tens represent? Do we have to say zero hundreds when there are not any? The next step would to practice writing numbers more authentically. Although checks are becoming less popular, it is still an important life skill for students to have.

Student Work #2

          This is part of a summative assessment given from the last unit on beginning multiplication. During this unit, we talked about grouping items, adding the same number together multiple times, and writing multiplication sentences. I chose this piece of student work because I was most impressed with how the student showed how the student made a multiplication sentence. As you can see, this student first drew 31 boxes, then she broke them up into five each. I liked the way the student wrote this problem out and drew the boxes to write a multiplication sentence. 

          The next steps for this student would be to practice writing multiplication sentences in a more authentic way. For example, I would like the student to begin to create and respond to multiplication problems without addition. I would ask my students: What does 5+5+5+5+5+5=? What's another way to write this out? Create one multiplication problem for your classmates.