[This whole thing is a ramble, but it’s an oddly accurate representation of what my brain does as I try and assimilate new information and ideas into the current structure. You’ve been warned.]
I mentioned a few posts back (and yes, I’m still thinking about elevator questions–trying to finish a book first that’s helping me thinking about them) that I’m reading The Art of Explanation by Lee Lefever. Throughout the book so far he’s been making use of the following diagram as a way to plan explanations:
One analogy he uses that I like is that if someone needs to change a tire, they probably already have the big idea down and are over on the right side of the chart needed an explanation of how. On the other end of the spectrum I think about the students I’ve had in my class. How many times did I start with “how” before establishing why? And I’m good at “how”! I can lay out steps like a pro with three examples and then practice time but if that kids is still over at the start of the alphabet, then I suspect that “how” is just going to cause them to tune out or teach them how to mimic.
The “why” bit means a lot of things to me that I’m still poking at. Why this method? Why this problem? Why should I care? How do I, as a teacher, present problems in such a way that those “whys” are answered? Off the cuff, I think different tasks are going to do this in different ways. Some will, to borrow Dan‘s phrase, perplex the kids. Others will be topics with human interest (“real world” applications). Whatever we choose, we need to get an answer to “why” that a student will follow down the alphabet into the weeds of “how” and that’s where all sorts of mathematical fun can be had.
So I’m still processing, but I’m liking the image as a way to think about where students will start before designing lessons around specific problems. Yes I’m recognizing that it’s like a fancy way to say the kids need to buy into what you are doing, but I like thinking about ‘givens’ from new frame works and the why/how understanding spectrum depicted in the picture is new for me.
Lastly, I’ve worked with a lot of struggling kids who had a hard time getting to “how to be an active, engaged math student” because they were stuck on why they would want to be one and why they would want to worry about doing well in a math class when there were other things going on in their lives. I can’t address every why my kids come in the door with, but hopefully I can not add to their list and give them a place where more understanding can happen and give them something to be proud of.