Why Do This Particular Math Task? Because It’s Interesting
Last year, I watched a group of grade 7 kids working on Pascal’s Triangle. Some were in deep “flow”, in the sense that they were entranced by generating the next row of numbers by adding with their calculators. One kid, as will happen, wanted to know: “why do I need to know this?”
We’ve all faced that question down. Good on kids for asking this question. It is good to be practical, and it is good to search for a “why” about anything that is to be learned.
The stock answer in this case might be something about seeing patterns as necessary to further work in algebra, where we need to recognize more and more patterns, to get better at seeing relationships between “things”.
This question, in a sense, is the bane of a mathematics teacher’ existence. How do you answer? Because you will need it later? Or, “I can’t be sure that you will need it, but you need to do it.”
Other possible course of action:
- dodge the question
- give a vague non-answer
- go on a long lecture about how math builds on itself, and you need to learn some things so you can learn other things later on.
Or, could you just say this:
We are doing this, because it’s interesting, because mathematics is interesting. We are doing this because we are here to think, and this is something that is worth thinking about.
We are doing this, because it’s interesting.
You could argue with the subjectivity of “interesting”, and it is subjective. Necessarily so. But you can build a classroom culture where you are curious, and, well…interested. It is accepted that some people find celebrities’ love lives interesting. It is accepted that some people, many people, find sports interesting. Why is it not accepted that, as a culture, we can find mathematics interesting?
Here is a non-scientific, entirely subjective, and very personal principle:
Mathematics tasks are worth doing if they are: interesting, useful, or beautiful.
Hold up any question or task to these three describing words. I guarantee you can make any task or question meet at least ONE of these criteria.
Don’t tell me that 8 x 7 isn’t interesting- it is. It’s between two squares, it’s close to other primes, and so on. You could make 8 x 7 interesting, if you wanted. It’s a trivial example, and you wouldn’t always take the time to make 8 x 7 interesting, but you could.
What if, as a matter of pedagogical principle, we made judgments about what tasks to give by deciding if they are interesting, useful, or beautiful, or some combination, thereof?
“Utility” or “usefulness” is probably the most overrated of these three descriptors (kind of the Sergeant Pepper’s Lonely Hearts Club Band of this list), or at least, immediate utility is, as it’s not often apparent.
Here is where this theory gets knocked: “interesting” is highly subjective. Sure. But chances are if you find a concept or result interesting yourself, you can convey that interesting-ness to kids.
Beauty is even more elusive, being in the eye of the beholder and all that. It may not often apply as an every day criteria, although I would argue that readily accessible geometric proofs for things like the Pythagorean Relationship, for example, do rise to the level of beauty. Relationships between numbers as well, have their aesthetic value, which was can hopefully show to kids.
Find me at: @MatthewOldridge on Twitter, and www.matthewoldridge.com.
