I worry about the teaching of mathematics. Lack of student confidence in the application of mathematics is one of the biggest problems we have in Engineering: it hampers the development of our courses, limits how far we can go, and is a primary source of lecturer concern when we have to deal with the consequences at examination boards. Yet the attitude is too often “the quality of the students is at fault”. As if raising the A-level score in our entry requirements by 10 points is all that is required to solve the problem.
Well I’m sure that the problem is a bit more fundamental than that and our approach to dealing with it seriously flawed. I’m also sure that there is much more that we as a School and University could do to address the issue but because I don’t teach it, as e-learning champion in my School, all I can do is highlight best practice when I see it. Here is one inspirational piece of advice from Dan Meyer, a US high school mathematics teacher who has to deal with remedial students. He takes the problems that typically appear in text books, removes all the step-by-step hints and gets his students to solve the real problem.
Take the filling the tank problem. In a text book there’d be a picture of the tank (essentially a prism), and step by step directions to the answer: calculate the area, use the area and the height to find the volume, work out the flow, use the flow and the volume to calculate the time.
Dan’s approach is simply to photograph the tank, make a video of it being filled up (including a clock), and then get the students to validate the actual time taken by solving the problem themselves from first principles. They don’t apply Euclid and Newton, they have to become Euclid and Newton!
Which is the most inspirational way to teach? Which lesson style achieves the learning outcomes? Watch the video from TED talk Math Class Makeover
and then you decide! Real engineering is about using mathematics so reason about and solve real problems. You don’t know the steps in advance and you might not have a formula.
If you have any more suggestions about how to really improve the teaching of Mathematics, leave them in the comments.