Torquetum

 

Interesting: I am starting to see some themes running through these papers. There was the bit on empirical validation I mentioned in the paper just before this. Here I am seeing, again, the emphasis on how students don’t know what a proof is or what it is supposed to do. This is really important. It’s rearranging the deckchairs on the Titanic for us to quibble over misuse of symbols, for instance, in an algebraic proof, when the students don’t even know what constitutes a proof or why we bother to place value on them. Anyway, back to the paper.

 

The students involved in this study are pre-service mathematics teachers. If they don’t, as university students, have a good conception of proof, then they’re not going to be able to teach proof well to the learners in their classrooms. (Interesting segue into grading concept maps – something I’ve never thought about.) There was a correlation between the complexity of the proof concept map and the student’s passing grade on the course, however the author argues that neither passing grade nor complexity of map relates to being a better teacher. The author makes a good point that many of the studies on student’s conceptions of proof are based on small studies – not that he’s disagreeing with them. The author closes with a call to break the “vicious circle” of training maths teachers without attention to proof who then fail to pass on understanding of proof to their classes.