1/19/07

The Stretching and Shrinking lessons are coming to an end, and I am sitting here trying to figure out whether my students have learned what I wanted them to learn. Yesterday, my teammate Yvette and I gave a quiz as a checkup on investigations 1, 2, 3, and 4. The grades from this quiz are all over the board. I have three A's, four B's, three C's, one D, and one F. Yvette has similar results. The question now is: Did the students learn all of the essential concepts? I know that the ones who received A's and B's do understand the essential concepts. However, I don't think that the students in the C range understand the essential concepts.

Our quiz covered these skills:

1. Characteristics of similar figures
2. Using scale factor to find the perimeter and area of a
   new figure
3. Using ratios to evaluate whether figures are similar
4. Equivalent ratios
5. Finding scale factor from a larger to a smaller figure,
   and vice versa
6. Finding missing side lengths
7. Using rules to create similar figures on coordinate grids

The students who struggled the most on this quiz had the most trouble with these two questions:

1. How do you use scale factor to determine whether a figure
   stretches or shrinks?
   
   1. Stretches: _______________________________
   2. Shrinks: _________________________________
2. Which of the following rectangles is similar to a 10 by 15 rectangle?

Obviously, these were not the only questions that these students did not understand/answer correctly.

I am asking myself: Did the questions not make sense? Do these students not understand the general idea of scale factor, or do they not understand how to apply it? The second question above only asked students to decide which of the rectangles is similar to the first; it didn't tell them which method -- scale factor or ratios -- to use. I struggle at this point in most books -- where do I go from here?

How can I effectively use data from quizzes, checkups, exit slips, and tests? My resource students did exceptionally well on this checkup. I wonder whether most of their knowledge came from my class or from their resource time. From the looks of it, the majority of their resource time is spent on reading skills. Therefore, I am assuming (and hoping) that what I am doing in class is actually working with these kids.

One student, Michael, whom I've written about before, did pretty well on this quiz. He has been rocking with this book! His hand is always raised and he really does know what is going on! I feel as though we are making such progress with him. And, as luck would have it, I have ended up being the teacher that he will work for. I don't know whether that is due to math class or the fact that we have built his trust this year. He could not do either of the above problems on the quiz. For the first problem, he answered: "It a bigger scale factor" for "a"; for "b" he answered: "It a smaller scale factor." He has the idea behind the problem, but I really wanted a more specific answer. We have spent a lot of time finding that a figure will stretch when the scale factor is greater than 1, and that the figure will shrink when the scale factor is less than 1. Isn't this something that I should really be looking for? I mean, he tried! He actually finished his whole checkup! He has the basic idea that if the scale factor is large, the figure will be larger, and that if the scale factor is small, then the figure will get smaller.

What do I do with the information gained? Well, so far I have pulled in the few students whom I felt could have done better if they had been given the opportunity to explain the concepts or steps verbally. This really helped one of them. I discovered that the other one really didn't understand scale factor. That was my fault. I guess that also shows that you can't tell how much a student has learned just by looking at the results of entrance and exit slips, along with the work that is done in class.

I have decided that I will focus on the toughest problems from the quiz during our test review. There were some problems that every single one of my students answered correctly, and I will just review those quickly. I need to spend more time focusing on the concepts that students don't understand and need more practice with.

Now I'm all excited to get started on a plan to make this work! (I know, I know -- I'm kind of a math geek!)