The Holy Trinity of Theories — Number, Game, and Graph — Are Not Visible in the K to 12 Math Spectrum
Odd and even numbers. Hide and Seek. Euler Characteristic. Which one doesn’t belong? Is that the question I could be asking? Actually, it’s not. Each, is related to number, game, and graph theory, respectively. And, they are all accessible as early Kindergarten.
Odd and even numbers are definitely done. Kids might play hide and seek at recess. And, Euler Characteristic is done much too late.
The problem is that none of these ideas are rarely mentioned to the branch of mathematics they are housed in. The main reason is that we don’t really have any of these theories anchoring K to 12 math education. Three important branches of mathematics that are responsible from anything from encrypting credit card security to salary negotiations to scheduling problems. Not only are the applications rich, but they are actual branches of mathematics — very important branches of mathematics.
When we teach science, we don’t just casually omit something like astronomy. We try and teach all the branches of science. Outside of the sciences, say something like history, subjectivity and bias starts to creep in, and we tend to favor things that are familiar and/or traditional. Unfortunately, mathematics is plagued by some of these issues, and calcification to some rather outdated ideas have set in.
Teachers and parents often moan about kids not having strong number sense or math facts recall. Well, all of that could be remedied if we formalized number theory into K to 12 education.
Is 6 x 7 equals 42 an important math fact? I dunno. Maybe? What’s far more important is knowing 2 x 3 x 7 equals 42. Pick any number. 2? Now multiply the other two numbers 3 x 7. You have now created your own math fact for 42, namely that 2 x 21 equals 42. Knowing the prime factors for 42 allows you to create your own “family” of things that multiply to 42.
And so the journey begins…
As far as game theory, one of the best resources, drills down the essence of game theory to a historic idea — that is definitely needed now — trust.
As far as graph theory, Mathigon has a wonderful resource for graphs and networks.
As well, the popular game, Ticket to Ride, is all about networks and graph theory — such an enjoyable game for kids/adults to play!
Number, game, and graph theory are part of the thematic development of mathematics. Not only are they rich in applications — our students should be learning mathematics that is contemporary and filled with analysis/decision-making — but each is a fascinating portal for awe, wonder, and curiosity.
Below is one of the greatest moments in the British game show, Golden Balls. Game theory at its finest! I showed this episode many times with my classes years ago.
Bottom line. Students need to be playing more games inside of the classroom, and seeing how some of these games create a social crossover to some pretty nifty mathematics.
Ummm…with a third viewing of The Queen’s Gambit under my belt, don’t even get me started about having Chess be part of the K to 12 math curriculum. For starters, kids could learn about the thinking required for the Cartesian plane with the chess board. I think I will save that article for later:)