"Find the number of the last page of a book. Consider the first digit of that number. What is the probability it is a one? What is the probability it is a nine? Investigate."

Transum,
Tuesday, May 05, 2009

"Investigate the strategies you might use when playing a game of noughts and crosses (tic tac toe)."

Transum,
Saturday, May 30, 2009

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Younger students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.