1. Researching How to Make the Most of Technology Dave Pratt (Institute of Education) Janet Ainley (University of Leicester)

2. Overview An illustrative task Discussion of what might happen in a classroom What did happen and the issues raised about the role of technology If there is time… –Applying those ideas to a second task

3. A familiar task with a twist Maxbox… How can we make a box to hold as much as possible?

4. Maxbox… through Active Graphing Start with a problem to explore and find a solution

5. Getting started A group of 4 worked on the task. Three of the children made their boxes, and then measured the width and length. The box with height 1 cm was hard to make, but it was easy to work out what the width and height would be.

6. Discussion Many of you will have observed, read about or used for yourself Maxbox in the classroom… …But perhaps without using Active Graphing. Discuss what might happen in a classroom using this approach. –What sort of issues might be raised about the use of scatter graphs? –What role might the technology be playing in that process?

7. The next steps The children have worked out the values for the new points. It looks as though the maximum is when the height is around 4cm, but they want to fill in more points to check.

8. Using the spreadsheet Using the spreadsheet generates new points easily, but it looks as though something has gone wrong!

9. Using the spreadsheet They realise that some of the measured data was inaccurate, and generate all the data with the spreadsheet. Now they have a smooth graph, but need to look more closely at the points around 4. Height 3 Volume 1057.5 3.51102.5 41118 4.51107 51072.5

10. Using the spreadsheet Graphing points for heights between 3 and 4.8 in steps of 0.1 cm lets them see that the maximum volume is at height 4cm.

11. Opportunities arising from using technology Using (scatter) graphs before knowing how to draw them (the ‘power principle’) Learning from feedback Making and testing conjectures Building on intuitive knowledge Teaching the computer

12. Designing opportunities Purpose: a meaningful outcome for pupils within the classroom in terms of an actual or virtual product, or the solution of an engaging problem. Utility: why and how mathematical ideas are useful. Pupils can appreciate this utility through purposeful tasks.

13. Opportunities for understanding utility Graphing – using the graph as a tool for problem solving Generalising a method of calculation Creating a formula to generate data

14. Opportunities arising from using technology Using before knowing (the ‘power principle’) Learning from feedback Making and testing conjectures Building on intuitive knowledge Teaching the computer Understanding utility

15. Halfway house Build a house that your partner can use to design their own