Oct 16: Dish puzzle

To solve the dish problem, I reduced it to a smaller problem. To avoid using algebra, I utilized a number line to understand the pattern behind the distribution and total number of dishes. In the end, I concluded that the distribution of dishes would be the sum of all (number of guests)/(handout pattern). This would equal the total number of dishes being handed out. Since dishes are integer values, we also must consider the floor of the ratio. Applying this strategy to the larger problem, I got n/2+n/3+n/4=65 with n being the number of guests. After computing, we get n=60. Therefore, there are 60 guests. 

I believe introducing examples and puzzles from ancient history can be exciting and engaging for high school students because these concepts may be unfamiliar. Often, students disengage from problems when they are too difficult for their current skill level, rather than due to the context or story of the problem. Thus, the novelty of ancient problems may actually enhance their engagement. I also think students may find many ancient puzzles simpler than modern ones. This is because they involve tangible scenarios and originate using non-modern methods. Consequently, students may start puzzles with confidence due to their reliance on modern strategies and learn valuable lessons about their preconceived notions when they encounter challenges.

The narrative or context of a word problem is crucial for engagement. If the story does not capture the audience’s interest, they are less likely to invest time in it. Furthermore, during an age where entertainment is constantly accessible, it is important to ensure that problems are relatable, fresh, creative, and clear to maintain engagement. Lastly, from the FPPL, we know that learning is embedded in histories and stories. Thus, having story and imagery in word problems or puzzle is crutial.

Assignment 1 Reflection

My group initially chose this ancient question because of the familiar feelings that arise when a mathematician encounters "Pythagoras." I believe the extensive education around his theorem and the application of right triangles in nearly every high school classroom provides a sense of comfort. However, this familiarity created a bias that made it challenging to approach the ancient Babylonian methods with fresh perspectives. It took me some time to grasp their normalization techniques (such as normalizing an adjacent side versus the radius) and their concept of reciprocals (where their reciprocals multiply to 60 instead of 1). I think that if we had been introduced to the history of mathematics and various ancient methods at a younger age, it would have been easier to appreciate multiple approaches to problem-solving.

This project also highlighted the Eurocentric biases that persist in our historical narratives. I knew that many contributions from ancient Chinese and Indian mathematicians have gone unrecognized, but it was eye-opening to realize this issue extends beyond those civilizations. As a result, it is disappointing to see the lack of progress made in renaming mathematical discoveries to credit their rightful origins in textbooks and materials. As a teacher, I can play a role in this renaming process by educating my students about the rightful attribution of these discoveries. This approach may contribute to a more inclusive understanding of mathematics.

Lastly, I reflect on the evolving nature of mathematics. Before exploring extensions, I did not realize there were very modern solutions, like the use of complex numbers and planes, for addressing Pythagorean problems. This experience reminds me that mathematical methods are not fixed; they are constantly evolving. It was also satisfying to see how our problem, and many others, was solved using graphs, models, and diagrams instead of algebra. I find this shift away from algebra may help students build and trust their intuition more often.

Slides: https://docs.google.com/presentation/d/1Zh3KI2XFcd55FQTPpcuDYn1CV4C7EKXrHwDTp-TZSes/edit?usp=sharing