12/8/06

This week, my classes worked on problem 1.3 in Stretching and Shrinking. The problem asks students to compare the side lengths, angles, perimeter, and area of three similar figures. Right now I am teaching two math classes back-to-back. My first class is average, overall. There are a few high-achieving students and a few low-achieving students. The second class I teach is a slightly lower-level class, which (ironically) has fewer special education students in it.

My main goals with problem 1.3 were for students to recognize that the side lengths and perimeters of similar figures are changed by the scale factor, and the areas of similar figures are changed by the scale factor squared. This was pretty easy for my first class to conclude. However, I have one student, Michael, who just does not seem to understand it. He is a resource special education student. He can do math if he focuses and doesn't let other things distract him. He truly does not believe in himself and constantly says he is "dumb" or "stupid." When he is having a great day, he will sit in class and pay attention, and sometimes write some things down. When he isn't having a great day, he draws for most of the class period, only answers questions if you really pull it out of him, and refuses to write down anything or put forth any effort unless an adult is sitting with him and prompting him with questions or answers. On those days, I have no idea what to do. Today Michael really seemed not to understand -- but then again, he wasn't paying much attention to the lesson. I sat with him for a while once students were given a few minutes to add to their vocabulary journals. He was willing to answer most of the questions I asked about what we did in class, but he was incorrect most of the time. I really think he could do the math if he had more confidence in himself. I just don't know how to handle the situation.

In my second math class, students struggled with the material a bit more than the first class had. We created a chart as a class, before they began investigating the problem. They were told that they needed to do their measurements on lab sheet 1.3, but put the comparisons or patterns they found into the table.

All students were able to find the side lengths, angles, perimeter, and angles, but there was a surprising amount of measurement error. The problems started when students compared the measurements for the different figures. The angle comparisons were pretty easy for them, since they were all the same. Students had problems finding how much larger or smaller the copies were than the original. We stopped and talked about it, and the kids found that if they divided the measurement of the copy(image) by the measurement of the original, they would find the number of times bigger or smaller the copy is. With a lot of prompting, these kids found that the side lengths and perimeter changed by the scale factor.

There was one higher-level student, Jared, who figured out that the area changed by the scale factor squared. I had high hopes that all students would reach this level on the first day of comparing multiple objects. Should students leave this investigation with a full understanding of this fact? I don't think so. When should this be mastered? Is it important that all students, even my lowest-level student, master the fact that the original area * scale factor squared = image area? Click here to learn more about the mathematics founds in this unit.