In response to “Another Definitive Report ‘Proving’ That Discovery Learning Fails in Science/Math!,” Dave Marain of MathNotations calls for a mix of direct instruction and discovery in math teaching.
Researchers study extreme examples: “students are given a problem to work on with little or no prior instruction or explanation and the students are left entirely to their own devices for much of the classroom period to reinvent knowledge from the ground up.” It doesn’t work. But it’s not typical. Neither, he writes, do many teachers use direct instruction exclusively.
In another post, I described how an Algebra I teacher distributed a worksheet containing 20 or more numerical examples of exponential expressions which students had to evaluate on their calculator. They were then asked to group several examples and describe what they had in common and to formulate a generalization. This was not an honors class. Having set the stage for the general rules, this outstanding educator then DIRECTLY provided the rules both orally and on the chalkboard in the clearest of terms, then provided several guided exercises (worked-out examples) and then had students do a few Try These. She asked numerous questions and walked among the rows observing and guiding. How would you rate that lesson?
This mix of styles may account for the inability of “John Dewey” to find a constructivist classroom.