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High-Voltage Insight Outlets for Manipulatives
What
This project's goal is to produce a set of tools and activities which
produce insight when the manipulatives are "plugged in" to them.
Why
Manipulatives are a tremendous tool for building mathematical insight.
Most activities with manipulatives are "software" oriented--you attempt
to solve a problem, stated in writing or by the spoken word. We want
to supply "hardware" to express these problems (and, more importantly,
to facilitate their exploration) physically.
How
We are currently prototyping and testing these materials, with the
intention of seeking a manufacturer once the prototypes are finished.
For example...
A "puzzle back" with a space in it the size and shape of the hexagon in
a standard set of pattern blocks. An individual can use this to
easily and naturally explore the question "what fits in this space?",
with the template helping keep the pieces in place while they explore.
For children still developing fine motor skills, this helps separate
the question "what fits in this space?" from "what do I have the
patience and skill to hold together while I try to figure out
what fits in this space?". For the more manually dexterous,
it serves as a framework for the exploration of more sophisticated
questions like "how many distinct ways can pattern blocks be used
to fill this space?".
Having a framework like this helps suggest deeper mathematical
thinking, since the abstract concept of "what will fit" is
made physically intuititve. The beginnings of the concept
of a formal proof often stems from intuition gained through
experience.