Ha-Ka-Se and the [LoA]

Dan Meyer just made an excellent post and I thought my first entry to this blogging thingie was something that really stood out to me in the video. Towards the end the instructor asks his students if the table fits their Ha-Ka-Se (or loosely Fast-Easy-Accurate) model. I am beginning to see the connection between the Ladder of Abstraction and this idea of math being Fast-Easy-Accurate.

I always want my students to be accurate, they need to get it correct even if it requires slowly counting fingers, moving Algebra tiles, or walking through a graph; in other words being very concrete and tangible.

Next I want them to make it easier. This becomes less concrete, but it is a lot easier to draw a table of values and graph than to draw what the 100th pattern will look like in a recursive sequence. We start to climb the ladder a bit.

Finally I want them to be fast. “If only we had an equation to represent any spot in the pattern.” This is much more abstract, but much faster to work with. We have reached the top rung.

In the end, it is still necessary to climb back down the ladder to make sure your tool or method was easy enough and ultimately accurate enough. Thanks for reading through my first posting, all of you #TMC12 folks were right, this was very helpful.

T-minus 25 days until the first day of school!

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