In my classroom, I would use math history as a way to vary my teaching, making it more interesting. Stories and understanding origins make things stick. It can frame mathematics as a useful tool that was used to discover the things we know today. It also makes math less abstract or impossible to really understand as students analyze the development and sophistication of math language from its origins.
I agree that the history of math is relevant to the teaching and learning process of both the teacher and the student. For the teacher, it can deepen passion and understanding thus helping teachers develop more interesting lesson plans and activities. I wonder about one objection to integrating math history because of the lack of assessment. Is it necessary to be assessed? I believe if the history is done in manageable chunks, it may be more easily digestible than math equations learned through instrumental or relational understanding. History can be used as a tool to bridge language students are familiar with (probably English) and mathematical language which is largely foreign to students. Students learn through stories and imagery, which most people have experience with growing up.
Some students are more art-geared (art, history, English), so looking at math through history may help motivate these students who are not very interested in math. Math is often taught through instrumental understanding, so if teachers develop plans including history, maybe math could be better taught and learned. I believe this can be done efficiently through some history of the origins of math and easier to integrate multiple media into lessons (videos, experiments (how math problems were solved back then, models, etc).
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