Imagine the kindergartner asking “Where will I ever use the vowels?” One could answer that they are part of a cute ABC song or the ABC’s lead to words which leads to phrases which leads to sentences which leads to paragraphs which leads to pages which leads to articles which leads to books… But what if the youngster does not understand words yet? How does this young student conceptualize pages of words? Truthfully, trust in a qualified/competent teacher or parent is required. At some point reading and writing is part of everyday living just like different levels of math is part of “everyday chemistry” or “everyday economics” or “everyday nuclear physics”. How high should I go in math? Maybe the better question is where do you want to stop and limit your career choices or limit your ability to function? At what level do you want to limit yourself? What are your transitional goals? Do you WANT TO BE READY FOR THE NEXT LEVEL? Practicing the ABC’s and words leads to a flow and understanding of reading and writing just like proper algebra understanding leads to a flow and understanding of higher level math, science, business, engineering, etc. I contend that the biggest puzzle to solve is will I as a student be ready for the next level?

When the questioning student looking for a way out of working asks, “Where will I ever use this math?” I often kindly reply that maybe they don’t need the math at all, but others need it to be ready for this or that or the next level…

So the question that comes to mind for me now is what puzzles students?

Great question! For the second time in a day, I’m going to punt. Believe me we’ll pick this back up, but for now I’d encourage you to look at puzzles you enjoy and ask “why?” For a starter, here’s Ben Orlin talking about Tic Tac Toe. That’s a puzzle that’s fake from skin to bone, but which doesn’t struggle to engage the public.

My guess is that it is engaging because it is very obviously about figuring out how something works, it seems like it is possible to figure it out, and there is immediate and clear feedback.

With so much math, real or fake world, the problem or dilemma involved isn’t presented very clearly (or isn’t even there) and it is cumbersome to get feedback on your answer.

But this conversation is making me wonder what it even means for something to be relevant to our lives. I know what I think is relevant to students. I realize though, that what students want for themselves, is maybe a better measurement of relevancy. It may not be what I want for them, but if it is of interest to them, then it is relevant.

Dan, you say, “The point of math class is to build a student’s capacity to puzzle and unpuzzle herself — no matter what form those puzzles take. Find those puzzles in the real world, the fake world, the job world, or any other world — it doesn’t matter.” So the question that comes to mind for me now is what puzzles students? I don’t think that just any puzzle will puzzle students. But maybe if something seems important enough, absurd enough, or fascinating enough, it may puzzle a student. And it may be more motivating if it is a puzzle that seems worth solving.

I feel that it does matter what types of problems we give them to consider. You mention that teachers can “Find those puzzles in the real world, the fake world, the job world, or any other world — it doesn’t matter.” If it doesn’t matter what types of puzzles we give them, how would you propose motivating students to engage if they do find the work terribly disconnected to their lives?

Hi Anna, thanks for the comment. Just to clarify: I think the type of puzzle we give students matters very much. There are satisfying puzzles and frustrating puzzles. My point is that it’s possible to form those puzzles from numbers, variables, cats, kittens, fake and real-world objects alike.

I realize this really begs the question: “how do you create the satisfying kind?”

I’ll articulate some thoughts about that at some point in this series. In the meantime, I’d encourage you to read Megan Schmidt’s recent post on a math task that is utterly fake — nothing real about it — that her students seemed to enjoy quite a bit. Not honors kids either. Kids who struggle with math. Any thoughts on what made it so engaging in spite of its fakeness? I have a couple but I’d rather hear yours.