This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering a different view on mathematical thinking and learning and, in particular, on the source of mathematical errors and on ways of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They may differentially account for the behavior of different students on the same task, the same student in different stages of development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research literature) and one from abstract algebra (based on our own research).
- How nice! Actually, I thought it might be you when I heard your name, Raymond (@MathEdnet)! We should talk tomorrow :-) 2 months ago
- Enjoyed rehearsing rehearsals at #Novemberkonferansen with @ekazemi today! Choral counting has a lot to it! 6 months ago
- J. Skott: «Generic example of generic proofs is Gauss: 1+2+3...+100=?» #Novemberkonferansen #playonwords 6 months ago
- Next up at #Novemberkonferansen is Jeppe Skott, who talks about Goldilocks, mathematical reasoning and proof. Nice combination :-) 6 months ago
- Listening to a very nice lecture on the importance of maths by Chris Budd ( people.bath.ac.uk/mascjb/) at #Novemberkonferansen 6 months ago