I attended an interesting research seminar today given by Dr. Chris Sangwin of the University of Birmingham. This was on a software package called Geogebra which is a tool for dynamic geometry.
The interesting part, beyond the actual demonstration of the tool, was the way Chris had used Geogebra. He had been teaching a course on mathematical reasoning using the tool and teaching this using Moore method teaching. This is a method developed by Robert Moore in which the teacher does not show the students how to do the mathematics but rather gives problems and the students solve these using their own reasoning. Students then present their solutions to the class. In this case, the group got through 31 problems in a 10 week course, which Chris regarded as slow going in terms of content but he felt very strongly that the course had helped his students develop their mathematical reasoning skills.
The problems were geometry problems. An example is the following: "A ladder leaning against a wall slides to the ground. What path does a cat sitting halfway down the ladder make at it falls?" The students were not given the solution, nor any clues.
Chris reported the use of Geogebra as a reasoning/visualisation tool and as a presentation tool by some students (some preferred pen and paper). He said some students would go down lines of reasoning that were not getting anywhere, and not all students solved all problems before seeing a solution from another student. But he felt that this exploratory reasoning procedure has made them better mathematicians.
The point here is that when I wrote about small group teaching I felt that having a small group discuss the material rather than be shown it by the teacher would not work for my course. What interests me here is that this is exactly the sort of thing Chris is doing with the Moore method. However, it should be pointed out that he is teaching mathematicians to reason, whereas I am teaching scientists and business students a tool they can apply. I do not believe this method is appropriate for building a mathematical toolkit, though it would be interesting to give it a go with some students who are interested in learning mathematics for its own sake.
Because I am showing the students how to do problems then having them follow me, they are not necessarily developing an understanding of the deeper complexity that might help them see how the mathematics should be applied, or help them remember the lessons better. But am I just thinking this because I am a mathematician?
