Procept

In mathematics education, a procept, a term coined by the researchers Eddie Gray and David Tall, is an amalgam of three components: a mathematical process, such as addition or a limit operation, the concept produced by carrying out that process, and a single symbol that can stand ambiguously for either the process or the resulting concept. The expression three plus four, for example, can be read as an instruction to carry out the process of adding three and four, or it can be read as simply naming the number seven, the object that process produces; the symbolism itself does not force a choice between the two readings, and Gray and Tall argued that this built-in ambiguity is a genuine cognitive strength of mathematical notation rather than a flaw, because it lets a learner move flexibly between doing a calculation and having a number or object to reason about further. Gray and Tall proposed that the ability to think proceptually, shifting fluidly between process and concept as a single compressed symbol, is a key marker separating more successful mathematics learners from those who remain tied to carrying out each procedure step by step, and the concept has since been used to analyze why some students struggle to move from arithmetic procedures to more abstract algebraic reasoning.