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 is reasoning? How can we teach it?

The  world does not give us complete information that’s why call on our power of reasoning to complete this information the best we can and produce new knowledge.  Mathematics is

Explore, Firm Up, Deepen, Transfer

When we were just being trained to be teachers of mathematics it was emphasized to us that in planning our lesson we should think of manipulative activities whose results will

Why math education is failing

A backlink to my post What kind of mathematical knowledge should teachers have?   brought me to the essay by Matthew Brenner titled The Four Pillars Upon Which the Failure of Math Education Rests