
06448890
j
2015d.00277
Haavol, Per {\O}ystein
Mathematical competence  what is it and what ought it be?
Philos. Math. Educ. J. 26, 11 p., electronic only (2011).
2011
Professor Paul Ernest, University of Exeter, Graduate School of Education, Exeter
EN
D20
D30
C30
mathematics and philosophy
competence
mathematical ability
cognitive ability
epistemology of mathematics
learning
educational diagnosis
sociocultural aspects
cognitive processes
mathematical thinking
problem posing
problem solving
mathematical model building
mathematical reasoning
representation of mathematical objects
mathematical language
communication
making use of aids and tools
imitative reasoning
teaching
situated competence
competence dilemma
http://people.exeter.ac.uk/PErnest/pome26/Haavold%20%20Mathematical%20Competence%20%20What%20is%20it%20and%20what%20ought%20it%20be.pdf
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 nonroutine 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 isought 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.