Traditional problems, innovative solutions
Many students have too few opportunities to make and test conjectures, and to generalise and try to prove their generalisations. Instead they are often occupied answering questions that provide little mathematical insight. But Paul Andrews has created, for the Association of Teachers of Mathematics, a collection of starting points for problem solving that does lead to real maths.
Although all 15 explorations are presented on a computer screen, learners use pencil and paper, returning regularly to the computer to enter findings and receive further stimuli. The displays never look like spreadsheet files. Apart from the method of entering responses, you are not aware of using a spreadsheet. But, by following instructions in the book, which accompanies the Excel files on a CD, you can change wording or add new questions. The rest of the book consists of comprehensive guidance for teachers.
The way into each exploration is explained, with illustrations showing what appears on the computer screen. The author describes the maths that learners are likely to do, giving examples of possible generalisations and ways of reasoning about them. To get started you only need to be able to apply simple operations to small numbers. However, there is often the potential to express generalisations, and reasoning, algebraically.
Although students might be any age, this material will be particularly valuable in key stages 3 and 4, and I would recommend every maths teacher to explore it.
Free samples are available to download from the ATM website.