Hewitt’s differentiation between arbitrary and necessary
aspects of math education emphasizes the reliance on memory by some students
that in fact hinders their understanding. Teachers that solely impart
information cause students to perceive math as one massive set of rules and
situations they need to commit to memory and are then unable to discern the
concepts themselves.
The arbitrary outlines the tools that teachers need to
explain so that students become equipped with otherwise unknown knowledge.
Without being told standard conventions, and using ways such as math history to
establish these practices, students are unable to explore mathematics in a way
that can be understood by the general community. They will also encounter difficulty
in understanding higher level concepts as they will not be able to interpret
other information and explanations that heavily employ standard expressions. By
strengthening memory capacity surrounding arbitrary knowledge, teachers move to
building awareness and comprehension when necessary knowledge is later
introduced.
As the author states “… a teacher’s role is to work within
the realm of awareness rather than memory.” (p. 5) By first establishing a firm
foundation of arbitrary knowledge, students can move to uncovering knowledge
that they have acquired the ability to discover on their own.
Arbitrary and necessary knowledge divide methods of gaining mathematic
knowledge. It serves as a specific model of scaffolding to assist students in
having a firmer grasp of how to approach the subject of math and develop the
required skills at all academic levels.
You can’t build a house without knowing how to use a hammer…
(and without having a hammer in the first place!)
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