
06546573
j
2016b.00401
Falk de Losada, Mar\'{\i}a
Further remarks on a research agenda for WFNMC: research into the nature and characterization of geometric thinking based on students' solutions of competition problems.
Math. Compet. 28, No. 1, 4256 (2015).
2015
AMT Publishing, Australian Mathematics Trust, University of Canberra, Canberra
EN
D50
E20
D20
B60
mathematical thinking
research
understanding
problemsolving strategies
mathematical competitions
student competitions
geometric thinking
geometry
concept of area
Greek mathematics
Euclid
proofs
Pythagorean theorem
curriculum links
measurement
abstraction from actions
abstraction from objects
constructing
decomposing
recomposing
comparing
actions of the subject
transformation of the figure
analysis of the results
From the text: Recently I found myself reading an article written by Guershon Harel in which he stresses the fact that mathematics education should focus on the development of the mathematical reasoning of the student, reasoning which in turn he breaks up into two components: ways of understanding and ways of thinking an analysis that has both piqued my interest and stimulated much thought. Both understanding and thinking contribute to the construction of meaning for mathematical concepts, leading to strategic knowledge, strategic in that it is in turn used to foster further understanding and to empower new ways of thinking. Furthermore, Harel maintains that the field of mathematics education has focused almost exclusively on the component of mathematical understanding. I have been working somewhat sporadically on a project aimed at characterizing geometric thinking, and have found that the literature contains some advances on the theoretical level and others on the pedagogicaldidactic level, altogether falling short when it comes to describing the nature and characterization of geometric thinking. The first year of the project was aimed at gleaning clues to mathematical thinking in historical contexts, not only from writings but also from artifacts, remnants of architecture, tools and ornaments that reveal the geometric knowledge, ideas and fancy of their makers.