How should mathematics be taught to non-mathematicians? (2012)
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How should mathematics be taught to non-mathematicians? (2012)
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Re: How should mathematics be taught to non-mathematicians? (2012)
#2Mathematics is just the extreme end of the two most fundamental concepts Abstraction and Generalisation. Start the intro to these concepts including showing how these concepts are useful and used by everyone in their day to day life in using natural language.
Re: How should mathematics be taught to non-mathematicians? (2012)
#3Gower suggests story problems. Many, many story problems.[1]
Re: How should mathematics be taught to non-mathematicians? (2012)
#4Gower suggests story problems. Many, many story problems.[1] [1] https://pbs.twimg.com/media/BTwHsS5CAAAzBBu.jpg
Yes, in the loose sense they involve words, but he points out the problem with standard word problems in an earlier post https://gowers.wordpress.com/2009/07/11/help-im-stuck-in-my-...
Re: How should mathematics be taught to non-mathematicians? (2012)
#5Gower suggests story problems. Many, many story problems.[1] [1] https://pbs.twimg.com/media/BTwHsS5CAAAzBBu.jpg
The problem with story problems is, as the article states, that they are never really presented in the open ended way they claim to be. You almost always teach a class a fixed operation, multiplication for example, and then give them a bunch of word problems where multiplication is thinly disguised.
A much better exercise is to give an absurdly open ended exercise. "I'm at the supermarket, which checkout should I go to?" is one I have used in classes before. You can get a discussion going and generate a lot of interesting ideas, and almost every time I do it in a class someone says something I've not thought of. Once students have given you some good ideas you can massage it into a model and do some more 'proper maths' work. Of course, this takes a good teacher that can engage and steer the class.
Re: How should mathematics be taught to non-mathematicians? (2012)
#6Great article. Did anything come of the Gove-era math education policy changes he's referring to?
Re: How should mathematics be taught to non-mathematicians? (2012)
#7> Objection 5. You’d never find enough teachers who were capable of teaching a course like this. To do it well, you need to have a very sophisticated understanding of probability, statistics, game theory, physics, multivariable calculus, algorithms, etc.
Objection 6: If it's hard to find teachers to teach it, maybe it's a little challenging for students (even though a good math expert might find it interesting).
Just because a math expert thinks something is interesting doesn't mean low performing students will find it interesting.
For a more HN friendly example - what bunch of high school students wouldn't want an IT class that taught compiler design, instead of stuffy old Excel? Even Python is more fun that spreadsheets, right?
Certainly there are large swaths of high school math that can be cut, and replaced with more relevant stuff. But some care needs to be taken that it's actually teachable.
The article does partly cover this though:
> Thoroughly road test questions before letting them loose on the nation’s schoolchildren. In fact, that applies to the entire course: make sure one has something that definitely can work before encouraging too many schools to teach it.
Re: How should mathematics be taught to non-mathematicians? (2012)
#8Capturing the interest must always be first.
So to capture the interest, one must use math applications like game or physic simulations that allready captured the audience, allow beginners to modify the laws and abstractions within and create a "im at home with this"-intuition to delete the "im just not cut out for math" bias.
Questions would not come from the teacher, questions will come from the students on how to modify the application.
Re: How should mathematics be taught to non-mathematicians? (2012)
#9Applied math around areas of interest.
Re: How should mathematics be taught to non-mathematicians? (2012)
#10When you consider how mathematics, an understanding of probability, and so on enhances your ability to see through bullshit in advertising, government, and to some extent religions (not faith, just religions); it's not hard to understand why so many people are not thrilled at the notion.