Is It Really Either/Or?

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Of course, not all valuable learning is constructivist. Other types of learning, such as rote memorization, have an important role, too - as, for example, in learning foreign language vocabulary words. The instructional challenge for a teacher is in knowing when to use which approach.  - Charlotte Danielson

In her excellent Enhancing Professional Practice, Charlotte Danielson identified one of the most problematic decision points for today's teacher. Essentially, it boils down to this: When do I tell and when do I ask? Recent Core Reading sessions have reminded me that, because of curricular expectations, Todd County teachers struggle with this question more so than teachers from other districts.

Hopefully, we will come to realize that you can do both! Distinguished teachers avoid throwing constructivist strategies up against the left wall, explicit instruction up against the right, and then stubbornly adhering to one or the other. Distinguished teachers make judicious use of both practices.

Now, having identified a need for both approaches, I don't want to imply that there is some sort of perfect PC balance between the two - at least not in mathematics.

Questioning is a far more difficult form of pedagogy for teachers than are coaching and telling, because it is the least predictable.  - Ted Sizer, Horace's Compromise

The new Common Core Standards identify 8 "Standards for Mathematical Practice" describing the variety of expertise that mathematics educators at all levels should seek to develop in their students. The strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: 

• adaptive reasoning, 
• strategic competence, 
• conceptual understanding (comprehension of mathematical concepts, operations and relations), 
• procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and
• productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)

Given this list of proficiencies, a math teacher would be most likely to use more explicit forms of teaching in helping students reach procedural fluency. Again, this isn't to say that the other proficiencies lend themselves exclusively to constructivism. But constructivist learning theories will certainly inform the majority of an accomplished math teacher's repertoire. Assuming, of course, that reasoning and sense-making are high on their list of objectives.