Using The Psychology of Optimal Experience In The Math Classroom
A few years back, I came across the book Flow: The Psychology of Optimal Experience. It was a dense read, especially given the fact that Mihaly Csikszentmihalyi did a wonderfully condensed TED Talk in 2004 of his own book.
However, it was only when I was writing my own book, Pi of Life: The Hidden Happiness of Mathematics, did the immersive power of “Flow” leave evidence of that almost ineffably happy state of the mind. The chief reason I know that I had this optimal experience is, ironically, I have little memory of writing my book. Yes, those are my words. But, I don’t recall how/why those words appeared. Being lost for hours — losing track of time — I experienced being outside of myself. That some divine force was intervening. That my writing muse was not in the domain of things where it was easily retrievable.
I am sure that is not the only time that I have been in Flow. I know that because I love mathematics. And the problems that have put me clearly in the top right-hand corner of the matrix have been ones that are at the nexus of high challenge and high skills.
The matrix below has more detail as to the what Flow feels like. Now think about the the whole range of math problems that you and your students have dove into. I am sure, like myself, they have been in every triangle and trapezoidal section of the Flow Model.
I would think that students would have no problem recounting the hundreds of Anxiety and Boredom problems they have encountered in their decade-plus math career.
While it may be wholly unrealistic to have every single math question that is a Flow math question, I don’t think it is unrealistic to curate a curriculum of learning mathematics that can cover Arousal and Control — always being tangential to mathematical thinking that resonates with Flow.
Unfortunately, this probably does not exist in the culture of speed, correctness, testing, and political accountability. Well, to be frank, it just cannot. The Flow Model is predicated on happiness and freedom. The general response of the exiting public from school mathematics — since forever — has been mired in worry, apathy, and boredom.
The simple upshot is that we need to give a steady diet of problems that are more flowesque.
I haven’t even given you the question, but I am guessing there is some automatic intrigue/interest/challenge that your brain has picked up — even though it is riddled with unknowns. Unless you are friends with Peter Harrison(the author of this 30 year-old question), then this question is also new for you — and that is a cool thing!
ABCD represents fields of cows — yes, actual cows! So we are only using Natural numbers for ABCD. Can’t have zero cows, negative cows, or eeeesh, fractional cows(we are not making hamburgers). And, wxyz are bridges that represent, in this case, the sum of adjacent fields. I said “in this case”, because Peter Harrison’s Cows is a thematic tour of mathematics from elementary school to high school and beyond — it even goes to eigen vectors!
So, the challenge is to put single digit numbers 1 to 9(no repetition) so this particular set of fields and bridges with the sum rule works. What’s interesting to me is that this question has Flow characteristic regardless of the age. Young kids can try trial and error, with some insights like the bridges cannot be numbers less than 3. Older kids might have some ideas about odd/even numbers, and then the restrictions on the bridges. High school students might be intrigued by trying for an algebraic solution. It just seems that the abilities to tackle this problem will always be high and the visual layout/construct/uniqueness will elevate the challenge to high as well.
This is what a Flow mathematical problem looks like. Beyond being delightfully challenging and in synch with her abilities, math problems which are emblematic of Flow are authentic, intrinsically motivating, and generally have doors that are entry points into other Flow concepts. In this case, as in the whole Cows set of problems(there are well over a hundred), the thematic narrative of algebra and the natural, coherent bridge that brings students to this delightful abstraction is literally overflowing…
There is a common misconception we are happiest when we are relaxed — ie. on vacation. No doubt we are. Having maybe that third Mohito before noon on a tropical beach is a pretty sweet state. But, it is not Flow. And, as humans we are capable of having experiences that are richer, fuller, and deeper, based on our own unique skill set.
The Flow of Mathematics is not an exclusive club for those that love mathematics. Rather, it is a philosophical design of questions/curriculum that leads to that love.
In 2002, Queens of The Stone Age, released one of the greatest songs/videos called “Go With The Flow”. While the song title has nothing to do with the philosophy of Flow, there is a lyric from that song that speaks to the best of what mathematics can be:
I want something good to die for
To make it beautiful to live.
The best math problems drip with the poetry of the words above. Again, while reality may not allow us to live up to the ideas of Flow all the time, we should, at least, be consumed by trying to. There is magic in the attempt.
Let’s share better math problems — our happiness literally depends on it.