This started as a comment on Fawn’s post on Euclid’s Algorithm, but was getting obscenely long, so I’m making a new post. Go read Fawn’s post, because it’s really cool, and Fawn shares a ton of what her students are thinking, which is fantastic. Kids brains are so amazing.
I’m really curious about what we choose (or are told) to teach students. I absolutely get the need for standards and I’m not suggesting we shouldn’t have them. We should, but it makes me crazy that the standards are seen as the boundary of knowledge for a given grade. I know we can have really interesting conversations about nearly every topic in math, because I have had to eat crow every time I’ve said something stupid like “_____ is boring.” MTBoS corrects me every time. (Nicole Bridge, I’m looking at you.)
But I do think we do a huge disservice when we relegate some of the really good stuff: graph theory, abstract algebra, infinite series etc. to college. Fawn did something awesome here in that she brought a topic totally relevant to her 6th grade classroom out from the college curriculum and shared it with kids WHO WERE TOTALLY ABLE TO PLAY WITH THE IDEAS AND LEARN FROM THEM. Who cares if they didn’t actually write out Euclid’s algorithm and prove it? Fawn told us what she planned to do the next day, but it’s not clear to me that this whole thing will get wrapped up with a bow on it. And if it doesn’t, I bet her kids will still have some done phenomenal problem solving and pattern seeking. They’ll have explored relationships, written and revised conjectures. That’s the good stuff, folks.
I am a bonafide math nerd who regularly does math in my free time – I have more time than many other teachers who have kids and/or coach sports & clubs – so I’m able to find and bring a lot of math into my classroom that is not necessarily called for in the standards. Here are some examples of what I’m talking about:
Now, sometimes, “bringing this into my classroom” only means that I tell students about it. Sometimes, we actually play with the ideas. What I can say, is that almost EVERY TIME: kids are absolutely rapt. Students love learning about brand new ideas. They’re totally into it and are willing to do more math because of it.
I’ve heard the fear that if you start encroaching on the material for future grades, you’re not doing the future teachers of your students any favors. I think that’s a valid thing to think about and consider when we choose what to teach if/when we go “outside” the standards. But I’m pretty sure there aren’t many subjects in the above table that are covered in HS. And if by introducing students to it, they’re more likely to take math classes in college, then EXCELLENT, I say. Disagree in the comments (please!) if you have objections. I’m curious what others think.
I don’t want to run for office, but it has occurred to me that a good goal for my career would be to somehow get on a council that decides on standards. I wonder why synthetic division is a thing we have to teach but platonic solids aren’t.