@article {MATHEDUC.06448890,
author = {Haavol, Per {\O}ystein},
title = {Mathematical competence -- what is it and what ought it be?},
year = {2011},
journal = {Philosophy of Mathematics Education Journal [electronic only]},
volume = {26},
issn = {1465-2978},
pages = {11 p., electronic only},
publisher = {Professor Paul Ernest, University of Exeter, Graduate School of Education, Exeter},
abstract = {From the introduction: In this essay the author will take a closer look at the terms achievement and competence in the context of school mathematics. Previous research indicates that in some cases even high achieving students make use of superficial reasoning, lack a deep conceptual understanding and struggle with non-routine problems. Here the author uses the terms reasoning and understanding loosely, knowing well that they are aspects of internal, cognitive processes that are impossible to observe directly. Nevertheless, this creates an apparent paradox as the terms competence and achievement are obviously interrelated and it raises the question: aren't high achieving students also mathematically competent students? On the surface these might seem like a trivial question. Surely those students who do well in school are also competent students. High achievements mean that the students are mathematically competent. However, this inference rests on the premise that the socially defined label of high achievements corresponds with the concept of mathematical competence. Examining what the terms achievement and competence mean in a school mathematics context can shed some light on this question. To investigate more closely the underlying premise, the author intends to differentiate mathematical competence into a descriptive point of view and a normative point of view using Hume's famous is-ought dichotomy. The focus of this essay is on the difference between descriptive and normative statements in more general, rather than being limited to issues of ethics and morality.},
msc2010 = {D20xx (D30xx C30xx)},
identifier = {2015d.00277},
}