1 - A Framework for the Analysis of Mathematical Behavior

Abstract

This chapter presents a framework for the analysis of mathematical behavior. It introduces four categories of knowledge and behavior. Resources are the body of knowledge that an individual is capable of bringing to bear in a particular mathematical situation. They are the factual, procedural, and propositional knowledge possessed by the individual. Heuristics are the rules of thumb for effective problem solving. They are fairly broad strategies for making progress on unfamiliar or difficult problems. Control deals with the question of resource management and allocation during problem-solving attempts. In this context, it is reserved for major decisions regarding planning, monitoring, and assessing solutions online. With good control, problem solvers can make the most of their resources and solve rather difficult problems with some efficiency. Lacking it, they can squander their resources and fail to solve problems easily within their grasp. Belief systems are one's mathematical world view, the perspective with which one approaches mathematics and mathematical tasks. Beliefs establish the context within which resources, heuristics, and control operate.