In his paper The Transition to Formal Thinking in Mathematics, David Tall presents W.P. Thurston’s seven different ways to think of the derivative: Infinitesimal: the ratio of the infinitesimal change in the value
Category: Algebra
What are the Three Worlds of Mathematics?
There are three worlds of mathematics according to David Tall: the world of conceptual embodiment, the world of symbolic calculation and manipulation, and the world of axiomatic formalism. This classification is
Develop your ‘Variable Sense’
Number sense refers to a person’s general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop
How to derive the quadratic formula
As I wrote in my earlier post about solving quadratic equations, introducing the quadratic formula in solving for the roots of a quadratic equation is not advisable because it does not