Friday, June 12, 2009

Slide 4: f = formal instruction

Unless you’re teaching preschool or kindergarten, your students already have a history of formal instruction in math when they enter your classroom. Did the prior instruction build on the child’s innate mathematical capacities and informal experiences? DId it treat each state standard as a separate, isolated and atomized bit of content, divorced from the other objectives. Or did it provide a coherent and connected progression of instruction with new instruction explicitly building on what students already had learned? Did the prior teaching protect students from cognitive overload by constraining new learning demands and providing time for practice and mastery before moving forward? Did the students fall victim to the math wars with overemphasis on either mindless procedural mastery or unformalized invented algorithms and approaches?

I could ask more questions, but the point is that past instruction matters. Many of the struggles students have with math come from what and how they were taught. Confused ideas about equivalence and the equal sign (=), overgeneralization of whole number algorithms into fractions, the lack of a unified number system across integers and rational numbers, and so on are really instructional issues. Without a good understanding of the models and approaches students have accumulated in school, it’s tough to make the kind of connections that can move them forward sensibly.

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