Some Old Favourites

How many triangles are there in this diagram?

I once ran a session in a school that I was working in where I presented a few classic maths problems to a group of teachers from a variety of subjects. The one above and also an old favourite of mine Frogs.

I titled the session Thinking In The Classroom. Which I thought was an uncontroversial title. I was wrong. I ended up on a deep discussion with a history teacher who didn't believe that students needed to think in the classroom. It was the first time I really understood that other people might have a completely different educational philosophy to me. This led to some reflection of my own beliefs.

Why was I setting my students 'interesting problems'? Of course it is because they excite and interest me and I want to excite and enthuse them in turn. But also I was trying to develop their ability to work mathematically. In the example above they might need to work systematically and develop ways to represent their thinking. In Frogs you need to think strategically and it helps if you notice the structure of the problem. Aren't these important mathematical skills that we should be encouraging in the classroom?

On a practical note I like to run Frogs as a whole class activity with chairs as lily pads and students holding printed pictures of frogs but there is also a lovely interactive version on NRICH.