Mathematical reasoning and its various obstacles - the case of over-using proportional methods

Abstract

Looking back at a bit more than a decade of involvement in mathematics education research, I noticed one clear Leitmotiv: Nearly always I ended up investigating students of various ages blatantly making mistakes to problems for which they – in principle – possess all required domain specific knowledge to come to a correct answer.

In this keynote lecture, I will use research that we conducted at the CIP&T on various domains (including: overuse of proportional methods, unrealistic answers to word problems, natural number bias, misinterpretations of statistical graphs) as examples to show how specific research techniques need to be used to unravel the underlying obstacles. In search for a full understanding of these obstacles, it will become clear that one needs to recur to a variety of theoretical and methodological approaches. Obstacles in mathematical reasoning can only be partly understood by recurring to cognitive-psychological theories. These unavoidably need to be complemented by a taking sociocultural perspective on the setting in which the mistake took place, and by thoroughly considering the mathematical concepts that are involved in students’ reasoning.

About Wim

Wim Van Dooren works at the Centre for Instructional Psychology and Technology of the Catholic University of Leuven in Belgium. His main teaching is in the domains of educational psychology, mathematics education, and statistics. In his research, he tries to build bridges between the domains of educational psychology and mathematics education. His main research interests are mathematical problem solving, word problem solving, statistical reasoning, the use of representations, the role of intuitions and biases in mathematical reasoning, and conceptual change in science and mathematics. Until 2016, Wim was vice-president of the International Group for the Psychology of Mathematics Education, and he currently is associate editor of Educational Studies in Mathematics.