# Key word "mental mathematics"

Proulx J. (2013) Mental mathematics emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics 84(3): 309–328. https://cepa.info/6850

Proulx J.
(

2013)

Mental mathematics emergence of strategies, and the enactivist theory of cognition.
Educational Studies in Mathematics 84(3): 309–328.
Fulltext at https://cepa.info/6850
In this article, I present and build on the ideas of John Threlfall [(Educational Studies in Mathematics 50:29–47, 2002)] about strategy development in mental mathe- matics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition, particularly in issues of problem posing, for discussing the nature of the solving pro- cesses at play when solving mental mathematics problems. I complement this analysis and conceptualization by offering two examples about issues of emergence of strategies and of problem posing, in order to offer illustrations thereof, as well as to highlight the fruitfulness of this orientation for better understanding the processes at play in mental mathematics contexts.

Proulx J. (2013) Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics 84(3): 309–328.

Proulx J.
(

2013)

Mental mathematics, emergence of strategies, and the enactivist theory of cognition.
Educational Studies in Mathematics 84(3): 309–328.
In this article, I present and build on the ideas of John Threlfall [(Educational Studies in Mathematics 50:29–47, 2002)] about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition, particularly in issues of problem posing, for discussing the nature of the solving processes at play when solving mental mathematics problems. I complement this analysis and conceptualization by offering two examples about issues of emergence of strategies and of problem posing, in order to offer illustrations thereof, as well as to highlight the fruitfulness of this orientation for better understanding the processes at play in mental mathematics contexts.

Proulx J. & Maheux J.-F. (2017) From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research. Constructivist Foundations 13(1): 160–167. https://cepa.info/4425

Proulx J. & Maheux J.-F.
(

2017)

From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research.
Constructivist Foundations 13(1): 160–167.
Fulltext at https://cepa.info/4425
Context: There has always been a tremendous and varied amount of work on problem-solving in mathematics education research. However, despite its variety, most if not all work in problem-solving shares similar epistemological assumptions about the fact that there is a problem to be solved and that solvers make an explicit selection of a strategy and apply it to solve the problem. Problem: Varela’s ideas about problem-posing provide a means of going beyond these assumptions about problem-solving processes. We propose to explain and illustrate the way we found inspiration from these ideas in our work through a discussion grounded in data excerpts collected in our research studies on mental mathematics. Method: Concrete data and observations are referred to for discussing issues related to problem-solving processes and activity in mathematics. Results: Engaging with Varela’s work led us to revisit and reformulate many common notions in relation to mathematical problem-solving, namely concerning the meaning of a problem and of a strategy, as well as the relationship between the posing and solving of a problem. Through this, these notions are conceived as dynamic in nature and co-constitutive of one another. This leads us to engage in what we call the dialectical relationship between posing and solving. Implications: We illustrate the sort of educational insights that might be drawn from such conceptualizations, mostly in terms of affecting the way we look at students’ productions and engagements in mathematics not as pre-fixed or pre-definable entities, but as activities that emerge in the midst of doing mathematics.

Export result page as:
·
·
·
·
·
·
·
·