DMI chapter 5

This chapter was very interesting and it opened my eyes to how important it is to understand how your students think about and understand multiplcation. One thing that I have learned so far throughout this course is providing your students with opportunities to show you what they know and or understand. In the first case Eleanor gives her student a homework page and has them go home and solve the problem in two different ways. It was interesting that she did not give them any ideas on how to solve them, but rather left it up to them in order to see what they know, understand, or dont know. While reading this I started reflecting on my own strategies and the one thing that I realized I need to work on is allowing my students to solve the problem how they think they should or how they understand. I feel as though when I am teaching math I try and teach the students ways in which I learned or understand math. I understand by reading this chapter that in order for me as a teacher to really learn about how my students think about and understand math I need to let go of the leash and allow them to explore different methods and understandings. One thing that concerned me while reading this chapter was that I did not always understand how students thought or solved the problem. For instance, I did not understand how the students used arrays to solve 23 x 4. This method seemed confusing and like I said, I did not understand it. Also I was a bit confused with what was behind Michael's thinking when he tried to solve 25 x 9. While reading this chapter, my biggest concern was the fact that I did not always understand the logic behind students thinking and it made me worried that when I have my students solve a math problem the best way they know how or understand, I won't be able to understand their thinking and be able to guide them in the right direction. I know that I shouldn't have all of these answers right now, but they are thoughts that were going through my mind while reading this chapter. All in all I really enjoyed this chapter and thought it was really interesting.

DMI chapter 5

DMI Chapter 5

One thing I got from Eleanor's case in chapter 5 of the DMI book is how important it is to have an understanding of where the children are in their learning. Taking notes and work samples are one way to keep track of how their thinking has progressed (or not progressed). It is important to analyze your own teaching, what the children are learning, and how you can better support them in their development. The question I have is how you support all the children in their learning so the information being taught is not to hard or to easy for one particular child.

Also, with the DMI Chapter I really thought about how the type of problems that are given to students need to be well thought out. In Lauren's case when she gave the problems:

2 x 4
3 x 4
2 x 40
20 x 4
23 x 4

She allowed for her students to think through the problems and analyze how a problem they already know can help them with a "harder" problem. The other thing I liked about this case is how the children were excited about learning and instead of the learning process being a struggle it became a game as to how big of a multiplication problem they children could solve.

Overall, I really liked this chapter because I feel that many of the ideas that were in the text could be pulled out and be useful in other circumstances or grade levels. Also, being able to read the case studies allows for a context which a certain idea was used. This gives me more of an understanding of how it could be used in my future classroom.

DMI Chapter 5: Interesting Ways to Multiply

Chapter 5 shows some very diverse thinking when it comes to multiplication. When reading Eleanor’s case I found it interesting than none of the children used the standard algorithm to multiply 27x4. A lot of the strategies are very conducive to mental math. I thought it was interesting how Mark changed the problem into an addition problem by adding all of the 20’s and then four 7’s. I also thought Mika’s interpretation of 4x25=100; 2x4=8; 100+8=108. She is basically using the distributive property by solving this way. These strategies as well as using the arrays in Lauren’s case study were much easier to understand for student than using the standard algorithm as seen in Susannah’s case. Some students tried to follow a procedure rather than really understanding the math behind multiplication. An example of this is:

1

49

x 2

108

In this case the student “carried” then 1 and added 4+1 to get 5 and multiplied 5 by 2. This use of a familiar procedure proved detrimental because she made a small mistake that lead to an incorrect answer.

When reading Lauren’s case an issue came up for me. She was troubled by the language students were using when they multiplied by a multiple of 10 (4x20=60). The students would have explained that 4x2=6 and you “add a zero.” I find this language to be a bit troubling as well. I think the concept is very important, especially to doing mental math, but I wonder if there is a better way to describe the mathematical processes that are actually occurring.

Robert’s At Risk Article

The article I read was “Problem Solving and At Risk Students” by Roberts. The teacher explains how difficult it was moving to an urban school where the students were angry and underprivileged. Her teaching methods just didn’t seem to work. One thing this teacher did was to activities that integrated team building. This article discusses that children “think as a byproduct of the activities, assignments, and so on we ask them to do.” She decided that she needed to create activities that allowed the students to feel successful so they do not become angry with failure and give up. She also started by using problems that had only one answer so students didn’t feel like they were taking a risk to make a claim. Roberts learned to model many ways of solving problems to reach the wide variety of student thinking. With her guidance, students became more accepting of the different solutions for one problem. She also build up student confidence because she gave rubrics in class and had students do reflections of their work to show progress, even though their report cards may not have been the reflection of the progress they were indeed making. Her strategy here was student centered assessments such as dialogue journals between her and the students. All of these strategies helped to foster positive thinking from students about mathematics and they serve as great practical suggestions for classrooms with at risk students.

A concern that I have after reading this article is that if I have at risk students I won’t have the answers about what to do to help them. Children are so diverse in their needs that I worry I may not find a way to connect with and help at risk students. I think what I can take from this article is to never give up trying and to always use my resources to seek help with at risk students.

Meeting the Needs of All Children

One of the most interesting long term experiences I am able have in my field placement is the ability to see the progression of the GLCEs and also note how the skills are introduced, worked on, and mastered. This may be due to my knowledge of the kindergarten math GCLEs, but it may also be because the curriculum at the elementary school where I do my field placement is based on the GLCEs. With that said, I also see teacher support for children who are struggling in particular curriculum areas. Assessment is very important to this school and they work hard to make sure the students have accomplished certain tasks at particular times throughout the school year. This focus on assessment helps the teachers see where a child is struggling and needs more support. It is also helpful when thinking about the needs of children throughout their school career. Since I am in a kindergarten classroom, many of the students have not been diagnosed with special needs. Some of these students are being labeled and others are being worked with to make a decision about what their needs are to succeed to the fullest extent.
For students who have special needs we typically work on-on-one with them when there is enough support in the classroom. Each child has different needs and being able to work with them one-on-one allows for greater support in the areas which they need to further develop. In the article, “Learning-Disabled Students Make Sense of Mathematics by Jean L. Behrend she states, “ Encouraging Evan, who generally guessed the answer, to think about the problem changed his perception of mathematics….He realized that he could solve the problems.” Every students has their own needs as an individual and working with them through these problems whether they deal with self-confidence, academics, or anything else, is important for ALL children’s growth and development .

Corduroy