Knocking down the building blocks of learning: Constructivism and the ventures program

Many people believe they are incapable of learning anything beyond the most trivial of mathematical ideas. Constructivism has two quite separate contributions to make in the struggle against this mistaken belief. The first is to indicate that incompetence is a dangerous mental construction, dangerous because it creates experiences that provide for its own confirmation. To overcome the limitations of mathematical incompetence, one must recognize it as a construction and leap to the counter-construction all people can leam. A second obstacle to the learning of mathematics is the naive notion that the ttuth of mathematical propositions is absolute, the mathematical is the naive notion that the truth of mathematical propositions is absolute, that mathematical validity is defined by an omniscient mathematical authority. Understanding the manner in which mathematical ideas are constructed by humans can help to free learners from being constrained under the terror of a mathematical thought police.