How could you solve this puzzle without algebra (or at least, without the algebra we are used to)?
Upon reading this reflection question, I just tried to solve it without algebra. What I did was just list out the first 12 people, as 12 is first common multiple of 2, 3, and 4 and found that there would need to be 13 dishes for every 12 people. After this it became easy to see that since there were 65 dishes there must be 60 people. Here is my work:
I think so! Although I also think it is important that this is done carefully so not to offend anyone and to avoid any stereotyping or problems. I think puzzles like these that are historical are particularly interesting to everyone, and even more so when they are from diverse cultures. I think it really speaks to the ability that math is mediator that can help us share, appreciate, and find common ground.
Actually one possible problem I see with it, especially if a culturally relevant question was given on a test is that I believe in some old psychology study it was found that if you ask a student to report their ethnicity before taking the test, it may negatively affect their performance, especially if they are marginalized groups. Although it is also possible that these culturally relevant questions may also combat this finding. I don't really know.
Do the word problem or puzzle story and imagery matter? Do they make a difference to our enjoyment in solving it?
I would argue yes, imagery/story matters to an extent. I think that stories can be beneficial especially when puzzles are presented in games. I remember playing Nancy Drew or Professor Layton games and the story of the puzzle was sometime quite important to me. On the other hand, in common math problems, I do find excessive wording to sometimes be unnecessary or cumbersome. However in this dishes problem, I did enjoy imaging a big party with good food. It made it more enjoyable for me to solve, rather than given just some number to process.
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