Understanding math can be difficult. Explaining math can feel even more difficult. This week in math we tried to break down our counting system. The above description is one given by the Wolfram Alpha website. I think ours are a bit easier to understand.
The instructions were to explain, using diagrams, pictures, and words what 1241 means. Explain its value. Explain it's set representation.
In many of the answers we saw some really good explanations of how base systems work. Differentiating that numbers are symbols called integers was a big step in understanding how number systems work.
Also, understanding the difference between a numbers innate value and it's symbolic representation can be critical for long term math understanding.
So often in math we focus on rote memorization.
But what happens when we get our students to really understand math?