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Gower 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.

So much this. Through a series of unexpected events, I ended up studying math in undergrad with no clue why or what I was going to do with it. My senior year I took a class called "Applied Modelling". The first project was a simple, one sentence question: "What would happen if the Greenland ice cap melted?".

It reminded me a lot of Randal Munroe's "What If" blog on the XKCD site [1]. Easy to understand, open ended questions that encourage readers to learn a little about topics _outside_ of math to answer the question. The class gave me an appreciation for math that was lost during all those years of study before that, and it's basically my career now.

[1]: http://what-if.xkcd.com/

My university's Engineering Science department runs a competition each year for high school students along the same lines -- mathematical modelling of an open-ended question.

I also found it very valuable; it was one of the factors that pushed me over the line into studying STEM at university (I was a better English and economics student in school).

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-...

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