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!