Numbers can be represented in different ways. The kind of representation we choose can highlight or de-emphasise the properties of the numbers. Studies about understanding mathematics discuss about two kinds
The house of quadrilaterals
In Investigating an Ordering of Quadrilaterals published in ZDM, Gunter Graumann shared a good activity for developing students mathematical thinking. The activity is about ordering quadrilaterals based on its characteristics. He gave the following
The nature of math vs the nature of school math
The mathematics experienced by students is so much different from the real nature of math. What a tragedy! What is the nature of mathematics? Mathematics is human. It is part of
What are fractions and what does it mean to understand them?
Negative numbers, the irrationals, and imaginary numbers are not that easy to make sense of for many students. But this is something understandable. One only needs to check-out the histories