Tag Archives: understanding mathematics

What can the representations of numbers tell us?

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 of representations of a mathematical idea: (1) transparent representations and (2) opaque representations. A transparent representation has no more and no less meaning than the represented idea(s)… Read More »

Teaching the derivative function without really trying

New mathematical ideas are usually built on another mathematical idea or ideas. Because of this, the teaching of mathematics if it is to make sense to students, should reflect this ‘building on’ process. Students should be able to see how the new idea is connected to what they already know. Good teaching of mathematics also demand… Read More »

Bedrock principles of math and what it means to understand math

In one of my LinkedIn group, someone started a discussion with this question What is the bedrock principle of mathematics? May I share some of the answers. 1. “The bedrock principle of mathematics is the axiomatic system. The realization that there are propositions that must be taken for granted in order to have something to… Read More »

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