Before reading this article, I thought of math history being used in education mostly as a way of giving context to what we are doing in math classes and why we are doing those things. I thought it might be a useful tool to show that there is more than one way of doing things in math. Also, I thought it could be helpful to show students how much history and study went into creating the concepts that they learn in class. I thought that showing that what they are learning in class is the results of hundreds of years of work and study could be used to validate the feelings of students who are finding math to be difficult.
While reading one thing that stuck out to me what when different types of historical problems were being discussed. The discussion of problems with clever or alternative solutions stuck out to me. Before starting the reading, when I thought about history as a tool to show that there is more than one way to do things in math, I thought of showing how different cultures developed mathematical ideas in different ways and of using this to abstractly convey the message that its ok to be experimental and try different methods in math. However, when problems with alternative or clever solutions were brought up, I realized that there is a more concretely useful way in which math history can help kids: by showing that there is more than one way to do things. I think that showing alternative solutions to problems could be hugely beneficial in a classroom particularly for students who may struggle with doing a question in the first way that you teach. I feel that showing that problems can be solved in ways we wouldn’t necessarily think of can impower students to use tools from different areas of math to solve their problems (ex. Solving a problem that may seem more algebraic in a geometric way). This would be good because it can allow students to potentially apply concepts in math that they had an easy time grasping to concepts they might be more challenging. It is also good because I think it would encourage students to view math as a series of interconnected topics and ideas instead of as isolated topics.
Another thing that stuck out to me was when it was stated that a way to include math history in math education was to discuss mistakes that had been made by mathematicians throughout history. When I thought of using history to validate the feelings of students who are finding math to be a challenging subject I thought of using it to say “Look how long it took to develop these ideas. It is completely reasonable that they are hard to learn.” I didn’t think of using it to say “Look even these mathematicians who’s names we still remember today made mistakes. Making mistakes is ok and doesn’t mean your bad at math.” I like the idea of having students look at historical mistakes and having them try and show why they are wrong. It would teach them mistakes happen and are normal while also having them develop their mathematical skills.
I really liked your example of solving something that looks algebraic in a geometric way. It made me think about the article’s point about alternative historical solutions—sometimes seeing another approach can help students see connections between different parts of math, not just learn another way to get the answer.
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