Mathematical reasoning and its various obstacles

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 seminar, I will use the over-use of proportionality as a case. Based on a variety of research that we conducted at the Centre for Instructional Psychology and Technology on various domains (including word problems, geometry, probability, physics) I will illustrate how specific research techniques need to be used and various theoretical frameworks complement each other in unravelling and understanding the underlying obstacles. 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, by looking at children’s development, and by thoroughly considering the mathematical concepts (and their historical evolution) that are involved in students’ reasoning.
 
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