How does metacognition support the development of problem-solving strategies in children?

Van de Walle, Karp, & Bay-Williams (2010) define metacognition as, “Conscious monitoring (being aware of how and why you are doing something) and regulation (choosing to do something or deciding to make changes) of your own thought process” (p. 46). They continue, “Good problem solvers monitor their thinking regularly and automatically” (Van de Walle et al., 2010, p. 46). They say this because, “Students can learn to monitor and regulate their own problem solving behaviors and those who do so show improvement in problem solving” (Van de Walle et al., 2010, p. 46). And this is important to us as teachers because, “There is evidence that metacognitive behavior can be learned” (Van de Walle et al., 2010, p. 46). So, to recap, metacognition is a skill that can be learned (and therefore can be taught) which improves students’ critical problem solving abilities by aiding them in monitoring their own internal mental processes.

I particularly like George Polya’s four-step problem-solving process. Van de Walle et al. (2010) describe it this way:

1. Understanding the problem. Briefly, this means figuring out what the problem is about, identifying what question or problem is being posed.
2. Devising a plan. In this phase you are thinking about how to solve the problem. Will you want to write an equation? Will you want to model the problem with a manipulative? (See the next section, “Problem-Solving Strategies,” for more on this one.)
3. Carrying out the plan. This is the implementation of your plan.
4. Looking back. This phase, arguably the most important as well as most skipped by students, is the moment you determine if your answer from step 3 answers the problem as originally understood in step 1. Does your answer make sense? (p. 42).

I like this structure and plan to teach it to my students.

However, this question echoes with the ongoing conversation in my head about constructivism versus test prep teaching. There is not an ounce of metacognition required for drill and kill. I watch students dutifully trying to copy what they’ve been taught about regrouping. They move the “1” to the ones column and reduce the ten’s column but I wonder how many they truly understand the logic. I don’t know how just knowing the procedure of regrouping will help these children as they grow up. Soon, they’ll have calculators and won’t need to regroup in this way. But I think it’s good to be able to do simple math in one’s head and that comes from being fluent in “making 10’s,” which comes from being very clear on regrouping as borrowing 10 ones from the tens.

Metacognition would allow the students to realize that they don’t know WHY they’re doing something. This would allow them to ask, “Why?” However, if we teach children to be an informed consumer of their own education, all of our lessons need to be able to withstand the scrutiny.

I continue to feel the talons of constructivism grip me. It’s not something one can embrace partially, it would appear…