think again!

It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps him young. - Konrad Lorenz

We have come to trust that, given appropriate starting points, students will come up with all the mathematical questions we would want from a context. We have also realised, as we get more experienced in working with these tasks, that we are able to notice and hear more and so students seem to get further and into more complex issues each year. We find working in this way students become enthused and motivated by studying mathematics, and learn to view it as a subject which makes sense and over which they have control.

To find out how they are working to achieve these uncommon results, click here.

Rotate square sections of the grid to arrange the squares into numerical order starting from the top left.

In the basic game, you rotate a 2×2 square section. Left-click in the centre of that section (i.e. on a corner point between four squares) to rotate the whole section anticlockwise. Right-click to rotate the section clockwise. - Play the game here.

The game is part of an impressive game collection by Simon Tatham that you may play offline or online.

I wrote this collection because I thought there should be more small desktop toys available: little games you can pop up in a window and play for two or three minutes while you take a break from whatever else you were doing. And I was also annoyed that every time I found a good game on (say) Unix, it wasn’t available the next time I was sitting at a Windows machine, or vice versa; so I arranged that everything in my personal puzzle collection will happily run on both those platforms and more.

- I don’t get this?
- What don’t you get?
- John and Paul are both on the committee and they sat next to each other!
- Please explain!
- A committee of three was selected at our last meeting. There were 20 people sitting around the round table and three people were selected randomly.
- And your point is?
- Isn’t it incredible that two of the three elected sat next to each other?
- Do you expect the election was rigged?
- I don’t know. I just want to know what the chances are that at least two of the three committee members sat next to each other.

Problem source: Fortnight problem, Department of Computer Science, San Diego State University.

Mathematics must be written into the mind, not read into it. “No head for mathematics” nearly always means “Will not use a pencil.” - Arthur Latham Baker

Problem source: Strategies for solving problems in the BAMO contest (the Bay Area Mathematical Olympiad) by Tom Davis.

Most people are other people. Their thoughts are someone else’s opinions, their lives a mimicry, their passions a quotation. - Oscar Wilde

A big circle is painted in the corner of a room. It touches the two walls. If you were to paint a small circle that touches the big circle and the two walls, how big would it be?

Problem source: dansmath.

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. - John von Neumann

Read more here and here. If you have a math blog of some sort, please include these links.

Kindly informed by Nick Brown.