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.
Great work and reflection, Manveen! I find it interesting that you approached the “solving without algebra” challenge by still think in algebra first. After getting used to relying on algebra for most of our math education, sometimes it can be a challenge to solve problems completely without algebra, eh? Perhaps one way to approach the challenge is to imagine how grade 6 students would solve this problem. What would they do? Draw pictures? Use tables? This is actually a helpful exercise when teaching Math 8 and 9.
ReplyDeleteI like how you made connections to supporting ELL students and incorporating First Peoples' Principles of Learning!