The Dishes Puzzle

Pictured: My work for this problem

To address the first question, I believe that I used very minimal algebra already (if any). Instead of creating a formula or some kind of algebraic notation monsterpiece which I feel like would be harder, I decided to go for a more direct, brutish approach. After getting through the initial interpretation phase -- for some reason I had trouble deciphering "every 2 used a dish..." -- it was just a matter of writing down which guests would be receiving which things, filtering out guests that wouldn't receive anything, and tallying up the number of dishes as I went up the guest numbers. I think that this problem could be solved without algebra if we just did the brute force process the entire way if we really despised any semblance of algebra. However, as you can see, I noticed that the pattern of 1 + 1 + 2 + 2 + 2 + 1 + 1 + 3 = 13 repeated every 12 numbers. From there, I extrapolated the number of repetitions needed, and multiplied it with 12 in order to get the answer: 60. My definition of algebra is still a bit hazy, but since there was basically no algebraic notation or "let letter be meaning", and all the math could be converted to words (e.g. "65 / 13 = 5" could be stated as "there will be 5 groups of guests, and each group will identically take 13 dishes").

As for the second point, I would say yes! The first thing that came to mind when I read "examples, puzzles, and histories of mathematics from diverse cultures (or from 'their' cultures)" is that it sounds an awful lot like the advice being given in my LLED 360 textbook, which is all about how to make ELL students feel welcome in the classroom. This exact idea was suggested as a strategy in that textbook as a means to incorporate and celebrate the cultures of the students in the classroom. This doesn't necessarily need to be an ELL thing either, as a classroom will inherently have students of diverse backgrounds. In addition to this benefit, I would also like to admit as a partially Chinese person that when I saw the word "China" in the problem description, my subconscious made me say out loud, "WOO China mentioned!!" This also happened in my number theory course when the mere mention of "Chinese Remainder Theorem" had my eyebrows raised. If even a basic name drop could evoke such reactions, imagine what incorporating various cultures could do to make students feel welcome, connected, and celebrated.

For the final question: I think in this case, the word problem had a frustrating component (at least for me) because of the vague and confusing wording. "every 2 used..." made me confused. "Every 2 what? Every 2 guests? I guess?" Not only that, but "every 4 used a dish of meat between them" felt like a red herring was at play here. "Between them? Them, as in the rice and broth? But that wouldn't make sense, why would we put meat between rice and broth? The rice and meat would just sink together!!! Ok, this is silly. I'm going to just assume that the meat between them is just another item, this time associated with every 4th guest." Other than that, the word problem itself is fine once the premises are understood. It's not particularly flashy outside of the historical background, as it has a simple scenario with a mundane setting. The numbers are also relatively grounded, so it's not as funny as the Ahmes' loaf problem, or the other example I provided in a previous blog post about a Wal-Mart customer pushing a shopping cart of 100 Twinkies boxes, which I imagine would have fantastic imagery to go along with it. As a word problem, it does carry the benefit of being a humanizing medium to pose mathematical scenarios. To that I'll give it credit.

On the note of imagery, I think it absolutely helps and am surprised that it doesn't happen more with problems. Remember my mural from my Assignment 1 for this course? Think back to every word problem that you've done in math class where a picture is provided. Yes, all 5 of them. In my experience at least, the images are a complementary form of art that enhances the flavour profile of the problem. It's also great for accessibility purposes; going back to the ELL students, they benefit greatly from having visual aids to help them learn our language, which is particularly important for an intermediate language-involved subject like mathematics. Depending on the execution, humour, and a bit of artistic talent, these story problems can be enjoyable. It can feel like we're trying to solve a problem that someone had ages ago, someone whose struggles aren't so different from our own.