To be more successful with math instruction and math learning, I think we need to shift the way we conceive of students' brains. Thinking of students' brains as containers to be filled with skills, concepts, and tools makes us prone to accepting what has been called the "tyranny of curriculum." That is not to say that math curriculum is not important, but in and of itself for most people it simply is not memorable. Their math learning exists for a short time as a somewhat isolated and fragile network of neurons which are eventually pruned like so much dead wood on a tree.

Judy Breck's image below is about science rather than math curriculum but it illustrates very well the differences between conceptualizing kids brains as 'containers' vs. 'connections'.


(Click the pic to see the entire image full sized)

The standards approach neatly carves up knowledge into compartmentalized learning 'units'. The underlying assumption is that the students' minds are somehow blending the individual units into a comprehensive whole -- which we know is not always the case or even often the case in math class. In the words of Judy Breck (linked above):
  • 'We require students to learn subjects inside of little boxes, while students think about them in highly connected networks. The boxes in the Standards are separated from each other in all sorts of ways: living things are in different boxes than processes of the Earth. Different things about the same subject are spread out over five different grade levels. There seems little chance of having a thought that relates an early box in 'A' to a late box in 'E.' "

For most learners, acquiring new skills either adds new blocks or fills up a pre-existing block some more, but the blocks remain essentially self-contained. The experiences don't coalesce into a bigger integrative picture that gives meaning to the parts.

Changing the fundamental task of teaching to one of helping students create a framework for the development of a network of learned information puts the emphasis on the connections. For the learner memory resides in the network. More resilient neural architecture which embodies more durable learning comes with building connections in a way that is meaningful and memorable to the learner.
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