May 442 Blog

For your homework blog writing, please read the article linked here and comment on three things that stopped you in your reading or that struck you about the relationship of mathematics and Euclidean geometry to body, Land and movement. Your writing is due on your blog on Tuesday November 17 at 9 PM. One thing that struck me was the concept of being the proof oneself.  "we somehow enter the page. We imagine ourselves to be like the two dimensional characters in Abbott’s Flatland [1]. While dancing the proofs adds a temporal dimension to Euclid’s original representation, the positionality of the dancers and audience (in the same plane) involves some loss of the third spatial dimension." I think this is quite interesting because when one embodies the proof, one should never forget it. If we let our students do the proof using this method, they would hardly forget it.  As said, " The process of choreographing the dance proofs — making decisions, practicing, memorizing — bot...

 *NEW* Read through all your own posts from the course, and reflect on what you've learned from the course, how your ideas have developed, and suggestions for ways to improve the course for next year. This is my first course on the history of math. This course gives me some new perspectives on how to teach math. Using the knowledge of math history and learning about the perspectives of ancient mathematicians gives me some new insights on the mathematical world. For example, some theorems are not developed totally by Europeans. I always thought that most of the theorems or concepts came from Europe. Moreover, the assignments gives me some idea of using the history of math in my own teaching practices. The first assignment is about solving puzzles using the ancient method. If we use this in our own classroom, it could still be valid, as long as we keep the puzzle easier.  It would allow the students to search for information themselves and then come up with some solution themsel...

 *NEW* Personal reflection on what you learned and take away from Assignment 3 after you present  I learned the history and wisdom of a traditional game Tangram and we found it fascinating. It's so useful in the mathematical realm and it's quite easy to use in the mathematical classroom. Almost all grades could figure it out. For example the grade 8 's will be learning areas and volumes of different shapes. We could give the tangram shapes to them and let them figure the areas out using their existing knowledge about the areas of certain shapes. The parallelogram example in the video is an example. Also, even for surface areas we could let them use tangram to build things and figure out how many 2-d shapes we have in a 3-d shape. (how we add those areas of the 2-d shapes to get the total surface area of the 3-d shape) In a thinking classroom. the kids could totally get this themselves.  They could even figure out areas of strange shapes such as trapezoids and many other p...

 Final Art Presentation Google Drive Link https://docs.google.com/presentation/d/1_dVG3csojlbZqqCm7hGdqxALpLiw4IEm29FPVQ9jCRw/edit?usp=sharing Video: https://drive.google.com/file/d/1DxnumrK28pBO3lP703NO6FFz5uCCi6z0/view?usp=sharing

One thing that stopped me is that: " The other is his suggestion that the idea of number needed to be enlarged to include a new kind of number, namely ratios of magnitudes. For example, in ‛Umar’s view, the ratio of the diagonal of a square to the side, or the ratio of the circumference of a circle to its diameter (π), should be considered as new kinds of numbers." Also, "parallel postulate follows from the other Euclidean postulates" I never realized that it is the Muslim people who introduced the idea of positive real numbers. I always thought that our current math system probably came mostly from Europe, especially the algebra notations and definitions. and it's also very cool to challenge the Euclid's Element and say that the postulate actually follows from the other Euclidean postulates. It shows the spirit of the mathematician. another thing is that:  However, a culture’s acquisition of intellectual material from an alien culture is a complex process a...

  1. Our final project will be working the art of tangrams and trace back its history to ancient China 2. References                                                     Read, R. C. (1965).  Tangrams: 330 puzzles . Courier Corporation. URL: https://books.google.ca/books?id=80yRBQAAQBAJ&lpg=PP1&ots=EzOW0rhuWt&dq=history%20of%20tangrams&lr&pg=PP1#v=onepage&q=history%20of%20tangrams&f=false   Russell, D., & Bologna, E. (1982). Teaching Geometry with Tangrams.  The Arithmetic Teacher,   30 (2), 34-38. Retrieved December 6, 2020, from http://www.jstor.org/stable/41192134   Siew, N. M., Chong, C. L., & Abdullah, M. R. (2013). FACILITATING STUDENTS'GEOMETRIC THINKING THROUGH VAN HIELE'S PHASE-BASED LEARNING USING TANGRAM.  Journal of Social Sciences ,  9 (3), 101.   T...