My Plan for Assignment 3 (with Nanxi)

 For this assignment, I had origianly planned to explore the work of Bhaskar II - specifically his book called Lilavati. This book contains a number of interesting, poetic problems, which give a flavour of ancient Indian school problems. Lilavati  is the first volume  of his main work Siddhanta Shiromani (”Crown of treatises”) alongside Bijaganita, Grahaganita and Goladhyaya. It is the most celebrated work of the traditionsl of mathematics in India. 

One hurdle that I encountered with this was that this work is in Sanskrit and though there are translations available, they are extremely hard to find unless I buy a book that contains them. So, instead I decided to partner up with Nanxi and explore the work of the Italian female Mathematician Maria Gaetana Agnesi. She was the first woman to publish a mathematics textbook and is best known for her work on the "Witch of Agnesi," a curve that holds significant value in the history of mathematics.

We have chosen to create a collage on the Witch of Agnesi.

Assignment 2 Reflections

 For the second assignment of this course, I chose to research history of the origins of Trigonometry. In my presentation, I highlighted the Greek astronomer Hipparchus of Rhodes who tabulated the ratio of the chords of a curcle to the radius of 3438 associating it with the central angle. I was not able to provide a reason as to why he worked with the radius of 3438 at the time of my presentation so I will write th reason in my blog - it was because the circumference of this circle (21600) is the same as 360x60 - this means that every degree of this circle would represent one minute of the hour.

Next, I highlighted the Indians who realized the efficiency of working with half chords and double the central angle. Indians started tabulating half chords instead. There was also a little pice about where we get the name of the sine ratio from, which was very interesting for me. Being able to connect it to Sanskrit and Hindi, I'm able to reaffirm my understanding of sine. Lastly, I talked about Al-Battani, who introduced tangent and cotangent in a right triangle. Researching about him was eye opening for me as I realized that my education in India was full of inplicit bias against the middle eastern and Islamic contributions to math. I was very happy to finally learn greater details about Islamic Golden age not just in my presentation, but from my peers as well.

Nov 13 - Dancing Proofs

 Reflecting on "Dancing Euclidean Proofs," two aspects stood out and made me pause. First, I was struck by how the authors highlighted a shift in learning perspective—from passive observation of a proof on paper to active, physical participation in creating it through dance. This dynamic approach to proofs made me rethink how much learning geometry could benefit from physical engagement, helping students visualize and internalize mathematical concepts. It was eye-opening to see movement transforming abstract geometry into something deeply tangible.

Second, the authors' integration of natural elements, like sand and shells on a beach, showed how environments can become active participants in learning. This reminded me of the many conversations I've had in my classes about integrating land and nature into our learning. I can see how this kind of activity can make geometry—and even math history—more accessible to high school students. By embodying ancient methods, students might better appreciate the historical and cultural contexts of mathematical discoveries.

In a high school setting, this approach could engage students who struggle with traditional methods, allowing them to learn by “doing” instead of just memorizing steps. However, there could be obstacles. Space limitations or students' self-consciousness about performing might restrict the activity’s effectiveness. During my practicum, i have noticed the unwillingness of students to raise their hand and participate. Still, overcoming these constraints, perhaps by using small groups or allowing students to express ideas through minimal movement, could offer a powerful way to connect with math’s logic, creativity, and historical evolution.

Nov 6 - Was Pythagoras Chinese?

 I have always felt really strongly that acknowledging non-European sources of anything, not just mathematics, is highly important. In today's time, we are aware of Europe's past of attempting to erase cultural and historical identities of a lot of countries, I feel we should make an active effort to acknowledge where certain ideas and concepts originate from. This is also making me think of the ELL students in our classrooms. Surely, they feel more accepted, welcome and important if the history of their native country was brought up in their new classroom in Canada. Moreover, we would be encouraging our students to think critically when we take a moment to mention non-European sources of mathematics. When we pose questions like "why is Pythagorean theorem called the Pythagorean Theorem?" we encourage them to truly think about the history and discuss with their peers what if the names of theorems they learn are appropriate. 

In regards to the naming of the Pythagorean Theorem, I do believe that knowing all that we do now, thanks to researchers and historians, we willfully participate in ignoring the contributions of the people that deserve credit for it. I understand that we, as a society, have agreed on this name when we refer to the right triangle theorem and changing it now would be a hassle (much like changing the whole curriculum). It would be meaningful though, when we refer to this theorem, to sandwich it like so: "The right triangle Theorem - the Pythagorean Theorem - The right triangle theorem." This will get the students to make connections between the two names without losing the meaning of it. This is a strategy I learned in LLED 360 for introducing new words to ELL students. I determined to try this out in my classroom!

Nov 4 - Euclid and Beauty

 Euclid and Euclidean geometry are still studied to this day because his contributions laid the foundational framework of mathematics. His postulates are set the ground work for more logical deductions to come later on. Euclid starts his work with basic definitions and every concept to come next is built on the previous one, making it rich in simplicity. In my opinion, any work rich in logical reasoning and simplicity will always endure through the centuries.

Euclidean geometry is not only simple, but also rich in beauty. I remember introducing my student to Euclidean geometry and her enthusiasm to come to class everyday was tenfold. My student appreciated the universality of Euclidean postulates and found it very inspiring that these concepts were intuitive rather than complex. When I myself was introduced to Euclid in grade 8, I thought his proofs were logically harmonious, almost like a poem. The use of logicals reasoning to prove geometric concepts is the reason why his work is considered beautiful. One cannot forget that it was this beauty that inspired great minds like Newton and Descartes among many others. Euclidean geometry also embodies visual symmetry and structure using circles, triangles, and polygons.

Euclid's Elements and the appreciation of its beauty come from its ability to combine logical rigor with simple, universal truths that resonate both intellectually and aesthetically. It has provided a basis for how to think, argue, and deduce that has shaped mathematical thought for centuries.

October 16 - The Dishes Puzzle

 My solution (and the process) to the dishes puzzle without using modern algebra is this - when I first read this problem, I want to define x as the number of guests and build an equation to solve and I am so used to thinking in algebra that I had to pause and think of what mathematical concepts and ideas I am employing when I use algebra and I realized it's all about the LCM. So with smart guessing and checking, I began thinking of a number that would be divisible by 2, 3, and 4 since we're given that every 2, 3, and 4 guests share dishes of rice, broth, and meat respectively. The solution beautifully turns out to be 60. In the following image, I use algebra to verify my answer.

By relying on my past experience as a math educator, I can confidently say that offering rich histories and background to a problem does in fact make a difference to our students. Story telling and adding context is one of those things that lets people connect real life with mathematics and we should absolutely continue to incorporate history from all the cultures into math. Moreover, doing so will make the ELLs in the classroom feel included if teachers incorporate history of mathematics from their culture into the classroom. For the same reason, puzzle story and imagery matter as well. They create excitement in a topic that would otherwise be boring and frustrating. As well, keeping the First Peoples' Principles of Learning in mind, embedding histories, story-telling, imagery and other context into learning is important.

Assignment #1 Write up + Reflection

 

For this assignment, my group (JJ, Nanxi and myself) presented the problem 1.2.4 that deals with a 3x4 rectangle and its diagonal. We presented the modern solution, the ancient Egyptian solution and extended it to the Binomial Theorem.

For the modern solution, we decided to solve the problem using Pythagorean theorem as today it is arguably the easiest way to solve a problem like this.  I showed ancient Egyptian solution on the slide as a translation of the original text and was explained using modern algebra. I offered a few limitations of the Ancient Egyptian 'formula' as well. Nanxi also offered a beautiful geometric solution what combined 4 of the congruent rectangles to the original one and using a bit of algebra and the area of a rectangle, we were able to arrive at the correct length of the diagonal. Then JJ extended this to apply to the Binomial theorem and explained some benefits of visualizing binomial expansions geometrically.

Here are the slides that we used.

My Reflection:

I thought I did well overall. A couple of areas to improve would be use my media smartly. I found myself turning my back to the audience in order to look at the slides and point things out. I should perhaps find a way to set up my computer in a way that its easier for me to look at the slides while giving attention to the audience as well. Moreover, due to momentary nervousness, I wrote a wrong math statement on the whiteboard but I think I was able to correct it and managed to not confuse the audience. This goes with my EDCP 342A reflection as well that I believe for my initial lessons that I deliver in the classroom(just until I build enough confidence) I would like to explore writing a script for myself so that I have something to fall back on in moments of nervousness.