If you have little kids and you’ve been privy to an episode of Team Umizoomi, then perhaps the title of this post evoked a little jingle in your head. You’re welcome; I’m here all day.
My daughter, although she doesn’t choose Umizoomi over Mickey Mouse as often as I’d like, picked up on patterns relatively quickly after watching this show a couple of times. She’s 3 years old, and she finds patterns all over the place. Mostly color and shape patterns, but a string of alternating letters can usually get her attention as well. These observations of hers made me realize that pattern seeking is something that is innate and our built-in desire for order seeks it out.
High school students search patterns out as well. For example, I put the numbers 4, 4, 5, 5, 5, 6, 4 so that the custodian knew how many desks should be in each row after it was swept. It drove students absolutely CRAZY trying to figure out what these numbers meant. I almost didn’t want to tell them what it really was as I knew they’d be disappointed that it lacked any real mathematical structure.
I’m not as familiar with the elementary and middle school math standards as perhaps I should be, but I’m confident that patterns are almost completely absent from most high school curriculum. Why are most high school math classes completely devoid of something that is so natural for us?
Dan Meyer tossed out some quotes from David Pimm’s Speaking Mathematically for us to ponder. This one in particular sheds light on this absence of pattern working in high school mathematics:
Premature symbolization is a common feature of mathematics in schools, and has as much to do with questions of status as with those of need or advantage. (pg. 128)
In other words, we jump to an abstract version of mathematical ideas and see patterns as lacking the “sophistication” that higher-level math is known for. To be completely honest, this mathematical snobbery is one of the reasons I discounted Visual Patterns at first. Maybe it was Fawn Nguyen’s charisma that drew me back there, but those patterns have allowed for some pretty powerful interactions in my classroom. I’ve used them in every class I teach, from remedial mathematics up to college algebra because they are so easy to differentiate.
I think high school kids can gain a more conceptual understanding of algebraic functions with the use of patterns. For example, this Nrich task asks students to maximize the area of a pen with a given perimeter. The students were able to use their pattern-seeking skills to generalize the area of the pen much more easily than if they had jumped right from the problem context to the abstract formula.
I also notice that the great high school math textbooks include patterns as a foundation for their algebra curriculum. For example, Discovering Advanced Algebra begins with recursively defined sequences. IMP also starts with a unit titled Patterns. I think these programs highlight what a lot of traditional math curriculums too quickly dismiss: patterns need to be not only elementary noticings of young math learners but also valued as an integral part of a rich high school classroom.