The report has been widely publicised, mainly for what it has to say about calculator use. Although Key Stages Two and Three are outside my area of expertise I think there are useful reflections that can be made with reference to the use of technology, including calculators as well as other tools, in GCSE and A level Maths.
Calculator use has a positive effect on students’ calculation skillsThe conclusion in calculator use states: "When calculators are used as an integral part of testing and teaching, their use appears to have a positive effect on students’ calculation skills. ... When integrated into the teaching of mental and other calculation approaches, calculators can be very effective for developing non-calculator computation skills; students become better at arithmetic in general and are likely to self-regulate their use of calculators, consequently making less (but better) use of them."
This emphasises the importance of calculator use being integrated into the teaching and learning (and assessment). As with any technology simply adding in a technology without changing the teaching or activities is unlikely to have positive impact on students' understanding. However, if they are used purposefully, with appropriately designed tasks, this is suggesting that students' calculation skills will improve. The challenge is to design appropriate tasks that take advantage of this opportunity. This point is further highlighted by a suggestion that such tasks can enhance students' problem solving skills.
I think much of this will apply at GCSE and A level too. Some classroom activities that can be tried are:
- attempting the same problem with and without a calculator and comparing;
- using a calculator to investigate a function numerically, such as sin(x) or ln(x).
Technology: technological tools and computer-assisted instructionA separate section of the report discusses technology tools other than calculators. These are split into two categories: technological tools and computer-assisted instruction. I am pleased that this split has been made. I think technology tools for learning mathematics have a much greater potential than computer-assisted instruction.
The analysis looked at three types of tools: dynamic geometry software, exploratory computer environments and educational games. Here the report suggests that dynamic geometry software has huge potential but stresses the importance of how these tools are used if they are to have a positive impact and that there is a need for professional development for teachers to keep pace with this change.
I think there are parallels with the use of technology in GCSE and A level Maths; however, the technology tool that is most widely used (apart from calculators) is graphing software. This is probably due to the nature of the GCSE/A level content: there is a much greater emphasis on the behaviour of functions and understanding them through a combination of graphical and algebraic techniques. For graphing tools it is still essential to use them carefully, and in a structured way, if they are going to have the most impact. This is similar to the use of calculators in that care should be taken to design and use tasks that take advantage of the technology and not just replicate what is done with pen and paper in the software. Detailed consideration is required about how the features of the software, such as sliders, can be used to illuminate mathematical concepts and this then needs to expressed through appropriate tasks (and professional development for teachers).
I would be interested to see a similar analysis of graphing software at GCSE and A level. I have definitely found it more difficult to design classroom tasks for dynamic geometry software than I have for graphing software, though this possibly warrants a different blog post.