Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic

@article{citeulike:378464, abstract = {In this paper we consider the duality between process and concept in mathematics, in particular, using the same symbolism to represent both a process (such as the addition of two numbers 3+2) and the product of that process (the sum 3+2). The ambiguity of notation allows the successful thinker the flexibility in thought to move between the process to carry out a mathematical task and the concept to be mentally manipulated as part of a wider mental schema. Symbolism that inherently represents the amalgam of process/concept ambiguity we call a "procept." We hypothesize that the successful mathematical thinker uses a mental structure that is manifest in the ability to think proceptually. We give empirical evidence from simple arithmetic to support the hypothesis that there is a qualitatively different kind of mathematical thought displayed by the more able thinker compared to that of the less able one. The less able are doing a more difficult form of mathematics, which eventually causes a divergence in performance between them and their more successful peers.}, author = {Gray, Eddie M. and Tall, David O. }, citeulike-article-id = {378464}, journal = {Journal for Research in Mathematics Education}, keywords = {arithmetic, ch2, concept, learning, mathematics, object, proccess, procepts, symbol}, number = {2}, pages = {116--140}, posted-at = {2005-11-03 01:46:03}, priority = {0}, title = {Duality, Ambiguity, and Flexibility: A \"Proceptual\" View of Simple Arithmetic}, url = {http://www.jstor.org/stable/749505}, volume = {25}, year = {1994} }

TY - JOUR ID - citeulike:378464 L3 - citeulike-article-id:378464 TI - Duality, Ambiguity, and Flexibility: A "Proceptual" View of Simple Arithmetic JF - Journal for Research in Mathematics Education VL - 25 IS - 2 SP - 116 EP - 140 N2 - In this paper we consider the duality between process and concept in mathematics, in particular, using the same symbolism to represent both a process (such as the addition of two numbers 3+2) and the product of that process (the sum 3+2). The ambiguity of notation allows the successful thinker the flexibility in thought to move between the process to carry out a mathematical task and the concept to be mentally manipulated as part of a wider mental schema. Symbolism that inherently represents the amalgam of process/concept ambiguity we call a "procept." We hypothesize that the successful mathematical thinker uses a mental structure that is manifest in the ability to think proceptually. We give empirical evidence from simple arithmetic to support the hypothesis that there is a qualitatively different kind of mathematical thought displayed by the more able thinker compared to that of the less able one. The less able are doing a more difficult form of mathematics, which eventually causes a divergence in performance between them and their more successful peers. KW - arithmetic KW - ch2 KW - concept KW - learning KW - mathematics KW - object KW - proccess KW - procepts KW - symbol AU - Gray, Eddie AU - Tall, David PY - 1994/// UR - http://www.jstor.org/stable/749505 ER -