Personal reflection for EDCP 442 and the future

EDCP 442 was one of the most interesting courses I have taken at UBC. I think one of the most overlooked aspects in learning mathematics within secondary and post-secondary education is learning about the history of mathematics and origins for different ideas. Knowledge about early civilizations and contributors to the field of mathematics is very beneficial to developing a stronger sense of understanding of how these ideas became theorems and rise of conjectures and proofs.

Moving beyond well-known mathematicians such as Euler, Euclid, Archimedes, Gauss, Fermat, Fourier, (to name a few), and learning about ancient civilizations such as the Babylonians and non-European roots of mathematics was refreshing. It was very thought provoking to learn about how “different” solving mathematical problems in the past were as there were no variables or algebra used how we use them today. Babylonian multiplication, classical Mayan mathematics, Alcuin’s recreational word problems, and problems from medieval Islam have changed the way I see how math problems could be presented. For example, using head/mask variants or different strokes to represent different counts of numbers, or using base 60 to count differently have changed the way I see different representations for numbers. This course has helped me consider different avenues to explore and incorporate in my teaching so that students can get a “bigger picture” of mathematical history beyond well-known mathematicians.  

A suggestion for the course in the future, could be to include more mathematics from an Indigenous perspective. I would be interested in learning how Indigenous cultures use numbers to record different aspects of their lives and how mathematics is rooted in their artwork and designs.

I'd like to thank Amanda and Susan again for all their hard work, feedback, and instruction during this course. I learned a lot and had so much fun attending class! 

Ada Lovelace Project Reflection and Take-aways

This was a really fun project and I enjoyed presenting the information researched in the format of a video. It seems almost “full-circle” in the sense that we researched about a person who contributed to the creation of the first “programmable computer” and created a video on the history using a computer. Due to time constraints and other factors, we were unable to record voice-overs for the video. Nonetheless, we as a group were satisfied with the outcome of our project.

Interestingly, this project has overlaps with other groups such as the short story on Alan Turing and history of coding and computer algorithms. The thought process in deciding on the topic surrounding Ada Lovelace for this group was because we wanted to uncover histories of a mathematician that was not very well known for their contributions to mathematics. Ada Lovelace was a mathematician I had not heard about in any years of my learning, and yet computers and technologies alike were taken completely for granted during my studies and entertainment. I hope that as a teacher, I can give voice to many more not-so-well-known mathematicians, especially female mathematicians, to help inspire more women to enter the fields of STEM and STEAM.

Ada Lovelace “draw-my-life” video

Ada Lovelace “draw-my-life” video: https://drive.google.com/file/d/11r9fq8ZYN3fp1VBWtcU23RsmgoG1JArr/view

Assignment 3 Topic

Zoe, Ivan and I will be researching the history and life-story of a not-so-well-known mathematician: Ada Lovelace and present the topic in the form of a “draw-my-life” video.

Bibliography:

Famous Scientists The Art of Genius, n.d. Ada Lovelace. Website. Retrieved from https://www.famousscientists.org/ada-lovelace/#:~:text=Lived%201815%20%E2%80%93%201852.,much%20more%20than%20just%20calculations.

Wolfram, S. 2015. Untangling the Tale of Ada Lovelace. Wired. Retrieved https://www.wired.com/2015/12/untangling-the-tale-of-ada-lovelace/

San Diego Supercomputer Center, n.d. Ada Byron, Countess of Lovelace. Retrieved https://www.sdsc.edu/ScienceWomen/lovelace.html

Fuegi, J., Francis, J. 2003. Lovelace & Babbage and the Creation of the 1843 ‘Notes’. IEEE Annals of the History of Computing. Pp. 16-26. Retrieved from https://pdfs.semanticscholar.org/81bb/f32d2642a7a8c6b0a867379a4e9e99d872bc.pdf

Hollings, C., Martin, U., Rice, A. 2017. The early mathematical education of Ada Lovelace, BSHM Bulletin: Journal of the British Society for the History of Mathematics, 32:3, 221-234. Retrieved from https://www.tandfonline.com/doi/pdf/10.1080/17498430.2017.1325297

An introduction to the mathematics of the Golden Age of medieval Islam

This reading introduced several Islamic scientists and mathematicians including: al-Khwarizmi, al-Biruni, Umar al-Khayyami, and al-Kashi. Content from this week’s reading would be useful to use as a background to provide students when introducing topics on algebra or other related math topics.

It was interesting to learn more in-depth about al-Khwarizmi, as his name appeared in my individual math history research on exponents and powers. Al-Khwarizmi contributed to four areas of science: arithmetic, algebra, geography, and astronomy. From this reading, I noticed that many early mathematicians were astronomers. I also learned that algebra comes from the Arabic word al-jabr. As a math teacher, I think it would be interesting to teach a math lesson bridging with astronomy like how early mathematicians studied the stars. One idea I have could be for students to learn and trace out planetary orbit movements; we can tie an apple to a string and tape a marker to the apple and swing it over a piece of paper to map out it’s path of movement. From this activity, we can see interesting patterns form on the paper.

I learned that Umar al-Khayyami found that the ratio of the diagonal of a square to side (sqrt 2) and ratio of circumference of a circle to its diameter (π) and wanted to consider these as new kinds of numbers. These became known as irrational numbers. This history could be interesting to mention to students when teaching the number system. An idea I had was to design a “just for fun” assignment that get students to create their own way to classify and group numbers into a system like the number system. For example, students could great a classification for just prime numbers and another classification for numbers that at first glance look like prime numbers, when are in fact, composite numbers (eg. 2431).

Al-Khwarizmi and al-Kashi both correctly estimated the value of 2π to the first 16 decimal places. Al-Kashi solved a cubic equation to correctly obtain the value of sin(1^o) = 0.017452406… Al-Kashi developed a calculator method that can repeat a procedure each time using the previous result to obtain numbers near the true value of the root of an equation. This reminds me of Euler’s method, which a technique used to analyze a differential equation using the idea of linear approximation by calculating the result using the previous result.

 

Reading:

Berggren, J.L. (2016). Episodes in the Mathematics of Medieval Islam. Springer. 2nd Edition. 1-23.