So. I'm going to be teaching 'Geometry and Measurement for Elementary School Teachers' during the summer session - 75 minutes a day, Monday-Thursday, for 8 weeks. I've been wanting to get involved with teaching potential teachers for a while, so I'm pretty excited. The course is designed to introduce students from the education department to the elementary school geometry syllabus. It covers learning to measure, geometric figures, finding unknown angles, unknown angle proofs, congruence and similarity, pythagoras, area and volume.
My aim going into the course, unsurprisingly, is to not only make sure that the students understand the material, but also that they feel confident teaching it. For a while now I've felt that a didactic style is not a great way to teach mathematics, so I'm looking at this course as a chance to try out some of my ideas. One of my main issues with lectures is that students see a 'grown up' write down a maths problem on the black board, and straight away solve it correctly. But maths doesn't work that way - or at least not all the time. My suspicion is that students go home, try a homework problem, get stuck, make mistakes, and conclude 'Well, I guess I suck at maths, otherwise I would be able to do this perfectly first time'. Which is not necessarily true at all. Whether my suspicion is true or not, immediately perfect solutions do lead to the other issue I see frequently: students don't learn how to confidently deal with things when they go wrong - which for me is a pretty essential part of mathematics (not to mention life).
While I was in Cape Town I was chatting about teaching with CF, who Knows Stuff about action learning, and later she forwarded me this link, which has made me think quite a lot about how to go about 'teaching' this course. I'm pretty sure that what I need to be is a catalyst, more than a traditional teacher - but how to do this? Given that I have been (and will continue to be) scathing about the 'education diploma' I did at my former cherished institution, which emphasized action learning, I do find it funny that I'm coming round to the idea, albeit somewhat differently from the 'let's spoonfeed the little darlings and make sure they're never, ever uncomfortable' view of the diploma teacher.
Given that I fully believe that the second best way to learn something is to teach it*, it seems to me that putting the students in the role of teacher as much as possible is a good way to go - especially since they're training to be teachers! CF also sent me this link, which includes as a principle of action learning 'not giving advice'. I've been pondering this; I think it might be quite profound.
*The best way is to invent it in the first place.
So. What do I hope my students will be able to do at the end of the course?
- Understand geometric definitions, how to build them intuitive notions, why they're important, and why a definition is formulated the way it is. Use examples to show what weird things can happen when bits of a definition are left out.
- Understand geometric 'facts', and how to use simple teaching tools to give an inductive or deductive 'proof'.
- Be able to confidently solve geometric problems, preferably in several different ways.
- Be able to pass on all of the above to the next generation in a way that will not cause the next generation to want to slit its throat, or refuse to do maths ever again.