Sue Johnston-Wilder and Tony Hirst investigate how robotics can enhance and motivate maths learning right across the curriculum
Motivating Mathematics through Robotics - Proceedings of a Day Conference http:cme.open.ac.ukcon f04 RoboCupJunior http:rcj.open.ac.uk
Planet ScienceScience of Robotics project http:robofesta.open.ac.ukplanetscience RoboFesta UK http:robots.open.ac.uk
First Lego League International www.firstlegoleague.org
For a digitised version of the original film of the Senster, a robot created by Edward Ihnatowicz, go to www.senster.com
Many students do better at maths if they understand how it is put to use in the world around them. As highlighted by the recent Smith report, the maths curriculum is failing to excite interest in and provide appropriate motivation for maths in many pupils, who are not sufficiently aware of the importance of mathematical skills for future career options and advancement.
Smith calls for, among other things, new approaches to pedagogy and for the use of ICT to be adopted to ensure that all students acquire an appreciation of the power and applicability of maths. The government response has agreed that teachers need to use ICT to teach applications of maths and to harness ICT and maths skills in motivating the study of maths.
Those of us involved in work with young people using robotics have seen that robotics is an area of particular motivation for many of them. At The Hills Lower School in Bedford, for example, 50 per cent of the Year 4 pupils volunteered to take part in the first robot after-school club and all of these completed the six-week course.
Computers first came into the maths classroom in the 1980s as a tool for teaching programming, and were soon followed by programmable robots. In the primary sector today, robots are still a regular feature of maths lessons, most notably in the form of the Logo turtle or its derivatives. However, programming has dropped out of the maths classroom, and you would now expect to find secondary schools using robots to teach control in Design and Technology or ICT, if at all.
However, much maths lies behind further study of robotics. Many youngsters interested in robotics (or ICT) are going into this field with insufficient tools in their mathematical toolbox. The solution lies in: * bringing attention to the simpler mathematical skills and thinking involved in school-level robotics; * demonstrating harder maths such as trigonometry through robotics; * describing the engineering maths that is used in robotics further up the chain.
One of the current challenges facing the robotics community is to create robots that will beat humans at football by 2050, as the computers have succeeded in beating humans at chess. Out of this challenge has arisen RoboCup Junior (RCJ), a staged series of challenges for school children - Robot Dance, Robot Rescue and Robot Football - scenarios in which robots must be programmed to behave in a variety of ways and which give rise to specific use of school level maths.
In Robot Dance, pupils are invited to "mathematise" a piece of music and to build and program a robot to dance to that music for two minutes.
In Robot Rescue, pupils develop a line-following robot that can also identify "casualties" lying across the line. Data from a light sensor mounted on the robot may be graphed by the computer and then used to develop data interpretation skills, as well as control the robot.
In Robot Football, robots may use a variety of sensors, including light sensors, touch sensors and electronic compasses to play football with an infra-red ball on a greyscale pitch. Pupils must produce and read calibration charts of the sensor readings and then interpret this information for use within their control programs.
An ongoing Science of Robotics project, originally funded as a pilot outreach project by Planet Science, is working towards providing a set of structured maths and physics investigations to support the RCJ challenges.
Robotics can be used to teach trigonometry, for example, by considering the position of a robot hand when rotation and length of the arm is known or working on a robot location and navigation problem.
It is widely accepted that conundrums faced by engineering researchers in areas such as control and robotics create challenges that push the boundaries of maths research. One example of the use of maths is the programming of a robot to estimate visual orientation using the symmetries of a cube.
In the 1960s, the sculptor Edward Ihnatowicz developed a series of sculptures that moved to sound. It was important to Ihnatowicz to make a sculpture that moved smoothly - indeed, jerky movements made audiences frightened of his larger sculptures. By learning about mathematical models of the movement of jointed structures that move smoothly, such as human arms, he was able to control his own sculptures so that they showed similar fluidity of movement.
There is a related problem in two dimensions, which is to make a "smooth" bend capable of joining two parallel bits of road. The method commonly used is to fit a cubic curve, something which is accessible to many young people learning maths with ICT.
While experience shows that robot challenges can undoubtedly engage pupils emotionally in a targeted inquiry or investigation, this is not to say that robots will necessarily remain highly motivating to the students of the future. As Dr Mike Reddy, of Glamorgan University has pointed out, if robots are to maintain their motivational appeal, they should be used as tools for learning, not as the objects of learning in their own right.
Whether or not we seek to embed robotics in the curricula of the future, the same sentiment is potentially true of the skills that we teach in maths education more generally.
Sue Johnston-Wilder is a senior lecturer in maths education and Tony Hirst is lecturer in artificial intelligence at the Open Univeristy Thanks to Dr Alex Zivanovic, Mechatronics in Medicine Lab, Imperial College London and Professor John Mason, Centre for Mathematics Education
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