A common complaint of mathematics students is that mathematics is highly abstract. Students often find it difficult to attach meaning to the mathematical concepts they are expected to master. In addition to coming to grips with the abstract nature of the subject, mathematical proficiency requires engagement at a more concrete level. Students must be able to perform step by step algorithmic procedures, detailed algebraic manipulations and master new symbol systems. Mathematical competence often requires thinking at high and low levels of abstraction almost simultaneously and this creates a tension which lies at the core of mathematics education. This tension has been addressed in the literature on procedural versus conceptual approaches to mathematics education and in the literature on cognitive and metacognitive mathematical demands. Construal level theory, and to a lesser extent dual process theory, are theories in cognitive and social psychology which provide a lens through which the difficulties of reasoning at multiple levels of abstraction can be viewed. Construal level theory posits that thinking about psychologically distant objects influences the extent to which we view possibly unrelated objects abstractly or concretely. Psychological distance and abstract thought are cognitively linked together and make up Far Mode thinking. Psychological proximity and concrete thinking are intrinsically linked together to form Near Mode thinking. It is argued that construal level theory forms a useful framework for interpreting much mathematics education research as well as helping to explain the difficulties students experience in implementing problem solving heuristic strategies. Evidence is presented suggesting that priming mathematics students to adopt either a Near or Far mental mode has an impact on their performance in solving conceptually challenging mathematical problems.

Includes bibliographical references.