The Dishes Problem

 • How could you solve this puzzle without algebra (or at least, without the algebra we are used to)?

Similarly, how do you do probability and combinatorics without the formulas? It is all about pattern recognition, logic, and deduction. Pictorial diagrams, words, and things like fractions might work. For instance, another approach would be to represent n as the number of guests. Thus, we have n/2+n/3+n/4=65, and we can find a common denominator and solve for n using fractions. Fractions were used by the ancient Babylonians and does not involve much if any algebra.

• Does it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)

Yes, but it depends on the level of mathematics. For lower mathematics, there is more flexibility and time to explore topics of interest from various cultures, and thus, students of diverse cultures can feel included and represented. However, I believe that in senior mathematics, the curriculum is quite fixed and thus it is hard take time off the curriculum's content to look into topics of interest.


• Do the word problem or puzzle story and imagery matter? Do they make a difference to our enjoyment in solving it?

Yes, the word puzzle and imagery matters. So many textbooks and teachers provide word problems that have no real life context or make no sense, and it does affect the enjoyment in solving it. Especially for students who struggle to find the importance of mathematics, it doesn't help to provide "application" word problems of topics that make no sense.