My traipsing through the tutoring lab today — extremely busy, so that I’m tag-teaming with the Faculty tutor — is making me realize the extreme handiness of having some skills & concepts to automaticity.
I’m thinking that should be a serious priority in finding an instructional delivery method that differentiates and incrementalizes and automaticitizes (to completely abuse the language) for those specific skills, with a firm conceptual framework.
I wouldn’t put fractions on that list right away, for the simple reason that so many people struggle with fractions that the instructional materials aren’t designed with the expectation of mastery.
So, the question is: What skills *should* be on that list?
I’m thinking that integer operations might actually be ahead of multiplication and division facts… that division might be ahead of multiplication (because more students don’t really understand what division is)… (and, by the way, I’ll find a way to tweet this, think of as many hash tags that people I follow use… and I’ll bet ten minutes on the trainer tonight that I get not. a. single. response. )
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Sue VanHattum
September 19, 2012
They say twitter questions get lots of responses, but I haven’t had great luck there, either.
I don’t have an answer for you. I wonder if you could show us what your first draft of your list looks like. Maybe it would be easier then to figure out what to add or move around.
Kate Nonesuch
September 19, 2012
Saving you from the trainer 😉
I agree with you about integer operations being ahead of facts. I’ve asked many students to show me what 3 x 5 means, using manipulatives of some kind, and the response is a student with three units in one hand and five units in the other, wondering what to do next. And nearly no one gets that 10 divided by 2 might mean two groups, or groups of two.
I did develop a program for adults learning basic operations (i.e., not reviewing them at a higher level class) that involved repetition of concepts over time, practice to automaticity, and work with manipulatives. It was a pleasure to teach, and students responded well, but it was time consuming and completely teacher led. I can see that at higher levels, the urge to cover content would make it an unpopular approach.
xiousgeonz
September 19, 2012
My thinking, though, is that this is exactly where we could use a computer for the “practice this element ’til mastery and then move up to the next level’ approach — but a computer with pictures and as close to manipulatives as we can get (and drag and drop comes close… and hey, can we get a touch screen that has tactile changes as well as visual? Bet we can…)
xiousgeonz
September 19, 2012
Oh, and that gives me another thought: that for some specific skills it might behoove us — *maybe,* I don’t say it lightly — to put “student-led” on a back burner, so long as the student has led the walk to the class to develop the given concept and skills. When I was learning math, my understanding of it would have led me to make choices that would have kept my understanding of it at a lower level. No, that Alg II-Trig teacher who made us think did me great favors.