Make a Memory... Build a Model

Saying it doesn’t always mean understanding it. You can probably say “nuclear fusion”, and you may be able to use it in the right context, even though you may have only the slightest understanding of it. Building models of mathematical ideas and investigating what happens to them as new variables are considered, helps students (all of us) dig deep into concepts to uncover meaning.

Investigating models allows room to continually adjust our thinking as new information is gathered and provides a wealth of opportunities to evaluate our own understanding.

Where investigating ideas through models is a regular occurrence, students quite quickly develop a rich bank of understandings. They can then draw from that bank, pulling partial knowledge together to build complete ideas and to establish connections between those ideas.

But deeper understanding isn’t the only advantage for students. As they investigate physical materials, a snapshot of the accompanying understanding is captured and stored in the brain for future reference. When faced with a new situation involving a similar idea students can then refer to the stored images to bring understanding to the new situation or make predictions. Students who have frequent interactions with the materials actually develop an ability to move the models around in the mind (a process called visualization) to accommodate the new situation.

Consider the all-too-common rule given to students to ‘help’ them multiply by 10. In most cases, students are simply told to “add zero”.

The following exercerpt from the series “I Get It!” Math is an example of how constructing models and investigating the idea of multiplying by powers of 10 can lead students (all of us) to discover the reasoning behind the rule and even construct their own rule from their observations.