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.
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I am grateful to my friend and former Swansea colleague Dr Farzin Deravi of University of Kent at Canterbury who read my blog post on Euler’s identity (“The Most Beautiful Equation in the World”) via Facebook and told me about this video proof of the equation:
It’s well put together, but for me crucially omits the vital step that substitutes cos ? = -1 and sin ? = 0 to reduce ei? = cos ? – i sin ? to ei? = –1 + 0 which of course can be rearranged to give ei? + 1 = 0.
This was not the only “Euler Video” available on YouTube, looking further, I found this nice example, also a proof of Euler’s identity, that shows what you can do with a tablet and screen recording software.
Two very inspirational demonstrations of the power of video in the teaching of mathematical concepts.
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In today’s Guardian and Media Guardian there where three articles about how Web technologies are having disruptive effects on traditional media and even (in one case) on one Web 2.0 poster-child technology itself. Here’s a quick summary with links to Guardian On-Line:
- In the Financial Pages Katie Allen discusses the potential effects on sales based on downloading might have on the DVD. In short, it might go the way of the VHS in as little as 10 years!
- In the Media Guardian, Gareth McLean discusses how the BBC iPlayer is transforming television.
- Also in the Media Guardian Jeff Jarvis comments on the Google FriendConnect service and it’s possible impact on Facebook (who controversially refused Google access to Facebook friend lists). Again in summary: by refusing to be open, Facebook may end up being a dead-end.
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In another experiment in Web 2.0 for learning technologies I recorded a soundtrack for a presentation that I make annually to my first, second and final year students, and put it up on Slideshare. This wonderful site is a social sharing site for PowerPoint files. It allows the usual social networking features. So you can upload a PowerPoint presentation, tag it, share it, and comment on others. You can also link it to an MP3 track, and there’s an easy to use tool for synchronizing the audio track to the slides.
Because I tend to use slides that, because of copyright, may not be publishable in this way and my recorded lectures are recorded and published as podcasts which have to be listened to with a copy of the downloads slides. However, Slideshare has real potential as an alternative presentation medium. It certainly compares favourably with to the expensive desktop tools that do the same sort of thing. It’s also really easy, which desktop tools often aren’t!
Here’s the presentation. Leave your comments here or on the Slideshare site.
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