remembering and forgetting

from a comment left by Le Galoisien:

But really. If they for example, require you to know logarithms, the general attitude is like, "You probably forgot how to do these. Here's a refresher." and you learn the concept over again ... because it is true even the top students in the school forget them because the syllabus is structured in such a way that it is hard to exercise them all year.

I remember the seniors would cry, "awww, you mean we had to remember those?" when there was a rare AP problem that required us to know a trig identity we had learned a year before. And the teachers would respond, "of course. You didn't learn them for nothing," implying it was our fault (but begrudgingly teaching them to us again). But somehow, even though it was partially our fault for not revising the concepts we had learned over the years (even when we had been assigned no work that dealt with them after we finished the unit) I often wonder if it is someone else's fault as well.

I mean, imagine all the time that has to be used reteaching concepts, and generally just in time for the examinations, before we put them in the closet again.

If we reinforced them all along, I wonder if students would save so much time with progress so much quicker that doing linear algebra in your senior year would be no big deal.

That's the story around here, only worse.

Learn percent, forget percent.

Learn percent again, forget percent again.

Repeat, repeat.

Meet with math chair; math chair says class had no business flunking latest test because "they saw that material last year."


inputs, not outputs

I'm realizing, again, how deadly the inputs model is. When school quality is defined by class size, per pupil spending, and number of Masters degrees held by teaching staff (pdf file), there isn't much incentive to design curriculum & instruction that ensures students will actually remember what they've "learned."

In my next life I plan to live on a planet where schools and curriculum designers focus on:

a) how to get content and conceptual understanding into students' long-term memory

b) how to keep it there


Here's Stanley Ocken addressing the National Mathematics Advisory Panel:

My second suggestion is that you investigate and make recommendations regarding common sense issues of pedagogy. It's important to think about the sequence of tasks and knowledge that lead to success in algebra, but it is critical and possibly easier to find out why so many entering college students seem to have forgotten the algebra they learned in school. You could begin by stripping away the obfuscating rhetoric of blind rote and drill and kill. Then you might examine the proposition that repetition and practice, properly implemented, are essential to success in mathematics, just as repetition and practice, properly implemented, are
essential to success in music, sports and the study of foreign languages. You could conclude by identifying prior indicators of successful college math students.

Before they got to college, did they experience rigorous and frequent in-class assessments? Were they required, for example, to master the multiplication facts by the end of third or fourth grade, or were their programs grounded in the principle that it doesn't matter if children master the material this year, since they are going to relearn and re-relearn the same elementary material in later grades? In other words, please investigate the role of basic interventions that clarify the scheduling and rigor of learning goals, these may be more effective and easier to implement than complex manipulations of curriculum and pedagogy.

Here’s my third and final suggestion. Enunciate the importance of a coherent K to 16 mathematics curriculum, one grounded in the principle that K to 12 math instruction must permit and encourage students to prepare for the rigors of calculus. To bring that principle to life, we'll need to see fundamental changes in the dynamics of K to 12 curriculum design.
source:
National Mathematics Advisory Panel (pdf file)
Thursday September 14, 2006

I'm fairly certain the only group of people who measure the success of their instruction by student achievement, which means, among other things, student remembering, are the behaviorists. I may be wrong about that, but I suspect not.