One of the core principles of vertical learning is that we learn by constructing and revising mental models. This comes straight out of Piaget’s constructivist learning theory. When I entered the teaching profession in 1995, constructivism was all the rage. Well over half the math teachers I met self-identified as constructivists. But then TERC Investigations and CMP happened, igniting the math wars. The public backlash was enormous, and constructivism was an early casualty.
The failures of TERC Investigations and CMP had nothing to do with constructivism itself. Constructivist learning theory is a theory for how we learn, not a theory for how we should teach. We construct our own understanding whether we are playing with blocks or sitting in a lecture. One learning experience is not inherently superior to the other.
So, what does constructivist learning theory tell us?
- We construct our own understanding by developing internal theories (mental models or schema) to explain our experiences.
- Two people having the same experience may not use or develop the same mental models to explain it. We explain our experiences differently.
- We force new experiences to fit into existing mental models using a process called assimilation.
- We experience cognitive dissonance when we notice discrepancies between our experiences and our mental models.
- If we experience cognitive dissonance, we attempt to revise our mental models to better fit our experiences using a process called accommodation.
Imagine that you have a friend who believes that Democrats always vote to increase the size and power of government. Now, imagine that this mental model is naive: your friend believes that there are no exceptions to his theory even though there are clear cases where his theory does not line up with reality. When your friend is confronted by a discrepancy, he can either deny the discrepancy (assimilation) or note the discrepancy and revise his theory (accommodation). If he is able to revise his mental model so that it fits better and explains more, then his mental model has become more sophisticated.
I believe that the primary role of a teacher is to encourage us to actively test our mental models as widely as possible, and to take note of discrepancies where they exist. If we experience cognitive dissonance, then we will feel compelled to revise and improve our own mental models. But do we need teachers in this equation at all? Can’t we test our models and find discrepancies on our own?
As we grow as learners, we get better at testing our models and detecting discrepancies. Where reluctant learners avoid cognitive dissonance, independent active learners seek out and embrace cognitive dissonance. But I don’t think we ever reach a point where we can see everything ourselves. We may not need a formal teacher, but we do need to interact with people who can point out our blind spots. For example, I thought I knew Piaget and Dewey well. It wasn’t until my friend Alec gave me a nudge that I questioned that belief and uncovered that I didn’t know Piaget and Dewey nearly as well as I thought. I don’t think I was being defensive and avoiding discrepancies; I just thought I was too busy to go back and double check every little thing. Now I’m glad that I did.