Simple Math Problem Essay

When presented with what seems to be a simple math “problem,” teachers from both the United States and China had different ways of approaching how to solve this “problem.” This could be attributed to the amount of education both groups of teachers have. Chinese teachers have on average eleven to twelve years of schooling while United States teachers have sixteen to eighteen. Keeping their educational backgrounds in mind, Ma presents both Chinese and United States elementary school teachers with this problem, “Imagine that one of your students comes to class very excited. She tells you that she has figured out a theory that you never told the class. She explains that she has discovered that as the perimeter of a closed figure increases, the …show more content…
After investigating the problem mathematically, sixteen Chinese teachers said that the student’s claim was correct. Twelve of these teachers justified the claim by discussing why it had to be correct, the other four addressed how the claim was correct. These teachers built their arguments on the correspondence of the length, width, and area of the rectangle with two numbers and their product. This response was grounded correctly, but mathematically incorrect. Fifty of the seventy-two teachers gave correct solutions, but their approaches showed various levels of understanding. The first level of understanding was disproving the claim. To disprove the claim, the teachers provided different kinds of counterexamples. For example, one teacher presented an example that consisted of figures with longer perimeter but smaller area. The second level of understanding the problem is identifying the possibilities. Eight teachers explored the relationships between area and perimeter. They gave different examples that supported, as well as opposed the claim. This showed the student that while their claim may be correct in some cases, it is not correct in all …show more content…
I feel that in today’s society, teachers are being told what to teach and when they are presented with something outside of the given subject, they would not know how to answer their students. I would also say that teachers in private schools would be willing to investigate the claims further because they are not always put under the standards of the common core. I feel that with today’s common core, many teachers are focusing more on what they have to teach and not taking the time to explore their students’ claims. But, in contrast, teachers from schools like Grove City are being taught how to solve problems. Teachers should never just accept a claim. Using mathematical formulas and definitions, they should work with the student to find an example that disproves the claim, if any can be found. In this example, many of the SMPs can be found. SMP 1: Make sense of problems and persevere in solving them is seen many times. Both Chinese and United States teachers try to understand the problem being presented. They analyze how the claim can be correct, and how the claim could be incorrect. Not all teachers are using this strategy correctly. Two of the United States teachers simply accepted the claim being presented by the student. These teachers did not try to make sense of the problem, or try to solve the