Watching the Dancing Euclidean Proofs video gave me new perspectives on mathematical learning. I paused and rewatched the part where Carolina served as an anchor point while Samuel ran around her in a perfect circle. This is a beautiful way in which a circle is illustrated, through an equal radius in 360 degrees. In fact, words like 'radius' and 'degree' aren't even necessary when watching the video. The simplicity of a circle is enough for understanding. Another part which I paused on was when Samuels explained the choreography required a lot of thinking, which is a little unexpected. In my opinion, the choreography is an extension to the existing understanding of the Euclidean Proof which tests the person on his/her true understanding of the concept. This is how I approach mathematical learning as well, a true relational understanding should allow student to extend the topics further than just classroom exercises. People have a stereotypical view of the tedium and...
This has been a wonderful journey to learn about a rich side of Math which I thought really little about. While Susan has structured the course in the chronological order of past civilizations, it was eye-opening to see how capable ancient people were in using mathematics to aid their lives. Learning the intricacies of the base 60 system in Babylonian math and its relationship to time was fun. I still remember that the 24-hour system was introduced as early as around 147 BC Hipparchus. As someone who grew up only knowing base 10 and base 2 systems, I never thought about how base 10 is just a construct instead of an empirical truth. Another aspect of the class I enjoyed was also the recognition that math history and contributions have been largely euro-centric. The progression of the course focusing on other non-European history was helpful and insightful for someone who came from a Chinese background. Math problems have also been a challenge as an ELL student in the past. Seeing ho...
The chapter about Babylonian word problem from the book A Man Left Albuquerque Heading East (written by our lovely Susan) showed a fascinating history about this genre of math problems. In contrast with the recent math curriculum, they share the trait of the problems being somewhat absurd and unrealistic. In both eras, the word problems seems to be a tool for student's instrumental understanding. Questions related a multiple-storey tall stack of grain pile or value difference and multiples in father/son age are for apprentices/students to solve just because they can. My guess on the unrealistic nature of these questions are two pronged. Authors of the questions realized any real-world application requires tangible context. However, society advances and context changes, it's futile to change the question every time society moves forward. Hence, a choice of surreal context has been made for Babylonian and 21st century Math students alike. The other point is that the emphasis w...
Comments
Post a Comment