Final Reflection

This has been my favorite course out of the nine I’m taking this term, largely because of the inspiring classroom community and the wealth of ideas I’ve gained from our discussions and activities.

In my university "History of Mathematics" course, I explored many Western mathematical developments, including geometric constructions and contributions from Greek mathematicians. However, this course offered a much broader and more inclusive perspective on math history. It emphasized that cultures around the world have made incredible and innovative discoveries, often reflecting their unique beliefs and values. I found it fascinating to consider how much of the mathematical knowledge we take for granted today is the result of countless contributions from diverse people across time and space. This collaborative nature of mathematical advancement was a recurring theme in my reflections, including in Assignment 2, where I explored the history of the normal distribution. Math history provided me with a fresh and engaging way to approach topics I had previously struggled with or overlooked.

My inquiry project with the question "What are the impacts of storytelling on improving students' math identity in the classroom?" was directly inspired by this course. I was captivated by the stories we learned, such as those about Mayan mathematics and Chinese story puzzles, as well as the narratives shared during classmates’ presentations. Stories have a universal appeal—they’re fascinating, inspiring, and relevant—and I believe math historical stories can play a key role in helping students connect with and engage in math class.

This course also helped me improve my own math identity. Even when I encountered unfamiliar topics, the process of researching them sparked my interest, and the feedback I received from teachers and classmates validated my efforts. Through the stories we explored, I saw different representations of mathematicians and their work, which helped me realize that I, too, can belong in the math community.

Assignment 3 Reflection

This presentation was an absolute delight for me. Jacob and I thoroughly enjoyed collaborating and exploring the fascinating world of Chinese and Japanese abaci—ancient mathematical tools with rich histories and diverse applications. While counting devices like these have appeared in cultures worldwide, the suan-pan and soroban uniquely reflect the cultural lenses of their origins, enriching mathematics with their distinctive insights and making this knowledge both accessible and thought-provoking.

The abacus itself offers a multi-sensory approach to mathematics, engaging sight, touch, and sound. Watching the movement of the beads, feeling their shifts, and hearing their clicks provide a holistic, embodied experience of number sense. As we highlighted in our presentation, sustained training with an abacus significantly enhances mental math skills, improving fluency and making advanced mathematical concepts more approachable. Interestingly, this reminds me of a moment from years ago when I watched an international "Super Brain" competition. A Japanese contestant became famous for her extraordinary mental math skills. In one clip (from 0:36-0:44, though unfortunately without English subtitles), she recalculates a lengthy multiplication problem using what I now recognize as a mental abacus. Her quick, fluid hand motions left a lasting impression on me, and understanding the method behind her "trick" was a revelation.

The abacus’s history also reflects different cultures' approaches to representing numbers, the significance assigned to specific values (such as fractions), and the accessibility of mathematical knowledge in its time. More than just a tool for mathematicians, abaci were essential for everyday life, empowering users to tackle complex calculations and focus on broader, conceptual ideas. It’s fascinating to consider how this humble tool laid the foundation for modern calculators, demonstrating the lasting importance of accessible mathematical instruments.

During my research, I became particularly intrigued by different numerical representations, both visual and auditory. Diverse visual systems, such as Braille or Morse code, grant people unique access to numbers in various contexts. Our art piece, "The Abacus Enigma," builds on this idea. It reimagines number representation through a binary lens: on/off, black/white. The puzzle follows abacus rules, where the four "earth" beads must be used sequentially and from top to bottom. This simple yet elegant design offers a fascinating and beautiful way to represent numbers.

Auditory representations also resonated with me deeply. Tools like Desmos’s "hear graph" feature transform graphs into sound, helping to internalize concepts like rate of change, highs and lows, and frequency. Similarly, the film shown in class, "New Math Teachers Riff on Kandinsky in Binary", creatively paired concentric circles with accompanying sounds. These representations were not only intriguing but also inspiring in their accessibility and inclusivity.

Overall, this project was an incredibly enriching experience. I learned so much and left feeling deeply inspired.

Assignment 3 Presentation - Jacob and Jasmine

 This is the link to our presentation on Chinese/ Japanese abaci and its accompanying artsy puzzle.