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by Joshua A. Taton, Ph.D. | November 9, 2023 | 1 min read

A simple way to tell the difference between procedural- and conceptual-focused instruction in math...When students encounter a new idea for the first time, say, a problem involving a multiplication scenario...

• If you tell them how to do it, that’s procedural.

• If you ask them how they might try to solve it, that’s conceptual.

And if they get stuck with the latter, if you ask them to...

• • Act out the scenario, 

  • Draw something (anything!) that represents the scenario, 

  • Use tools (like blocks) to represent the scenario, 

  • Consider the units involved, 

  • Interpret the problem without numbers, 

  • Bounce ideas off each other,

...then that’s called scaffolding.

Taking an experience that is inherently conceptual, turning it into a “follow-the-procedure,” is—quite simply—NOT scaffolding. That's called reducing the level of rigor.

Scaffolding enables productive struggle, which is offered—just in time—in the absence of forward movement on a conceptual-focused question.

And conceptual-focused instruction—scaffolded or not—when maintained, has been shown to increase understanding AND improve fluency.

Procedure-based instruction, exclusively used OR used before concept-based instruction and conceptual understanding, undercuts learning outcomes.

References

Schwartz & Bransford (1998)

Stein, Silver, & Smith (1996)

Tarr et al. (2008)

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