This recursion thing has been a great example of when a person does *not* have to understand a procedure before practicing it and drilling in it.

Dear person defending your approach to teaching: if you tell me that students can’t really learn by memorizing first, then you’ve just flushed your credibility down the drain. Not only is it possible, it’s a *good* way to learn complicated things.

I went to a cute website that had the Tower of Hanoi as a game yesterday. I started out clueless…but the Java text gave the moves for the tower of 3. I worked through it, then did it without the directions, and then then practiced it until I could do it from memory.

Because I *knew* that combination by heart, I could then identify what parts of the sequence were doing what. I messed around and got to level four and five, and figured out some tricks to get me to the next step… that didn’t hold up when I didn’t have a bare pole to go to as often. However, I had enough memorized to be able to analyze and change how I was defining things so that by lesson six, I had enough understanding to do levels seven and eight based on those definitions.

I didn’t fall into the common trap of using unrelated visual pattersn ’cause I just don’t think that way, and I know to focus on meaning. I know that lots of people, given the option to memorize, just want to get through… and so they *do* memorize and never understand — but why not memorize and then analyze?

And now my task is to apply what I understnad about the tower of Hanoi to Recursion in General and the Sierpinski triangle. However, even a highly confident learner as myself really likes nailing down something as *known* … and memorizing should be included in that category. I do know there are learners who need understanding for things to stick, but … memorizing has been given a bad name.

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Rachel Baron

April 16, 2014

Memorizing is a powerful tool in part because it makes things familiar. If I have already memorized the formula for the area of a circle, then it is easier to understand how the formula for the surface area of a cylinder works (and how to adjust it if you don’t need all the parts). What looks at first like a complicated, nasty formula turns much more manageable. At the same time, whether the understanding happens early or late, it must happen in order for the memorized information to remain accurate over time. After a period of neglect, the difference between “pi r squared” and “two pi r” can get pretty fuzzy–unless the connection between areas and square units is understood (and, of course, the difference between squaring and doubling…). I am the sort of person who finds memorization without meaning to be very difficult, but the repeated use or close observation of a formula that is required in order to make sense of it will help me cement it in my head. I don’t need complete understanding, but I need to be able to fit new information into a scema if it’s going to stay with me. Not everyone thinks the way I do, though…teaching requires me to be flexible about the order in which people go about the tasks of understanding, using, memorizing, and manipulating formulas–and ideally, each of these actions supports the other three.

xiousgeonz

April 21, 2014

Thanks! I think a much more important part of teaching is getting a student to keep digging once s/he has a formula.

I love your point about the simply memorized formulae getting modified and/or confused. That’s why I (probably utterly bore the students when I) walk through showing “r squared” as a length and width of a circle, and shading that square, noting that it’s not *quite* a fourth of the area… it’s a little more than 3/4…