# LINKING MATHEMATICS CURRICULUM AND CONCEPTS TO ROBOTICS ACTIVITIES

We regularly receive at the university students from high school as part of our STEM educational activities. The students have very different backgrounds because they can be as young as year 6, or already in year 12. They also may have chosen a profile for Engineering and Technology (and thus they are studying or completing different mathematics curricula), or because they are not even in high school (Year 6), they have an initiation to mathematical concepts and programming.

Thus, we face the challenge of designing learning activities that teach robotics concepts within two hours, and that can be adapted to the diversity of the group in turn. We want to make explicit to the visitors the links between STEM (Science, Technology, Engineering and Mathematics). We want to excite the students about the changing technological world and leave them with opportunities for further investigation and exploration.

We have designed a stream of activities accompanied by a book of problem-solving exercises that jointly offer a series of challenges. The activities involve programming LEGO-Mindstorms. The problem-solving exercises introduce many concepts and provide a rapid learning curve, from simple problems to even open issues within the research community. The aim is that students would be motivated to study further the exercise book, suggest problems to their teachers back at school and gain an appreciation by the motivation the problems provide for several mathematical ideas.

We have used the design activities and the book of problem-solving exercises in 4 sessions with students. We have also described the activities to 3 groups of high-school teachers as part of two professional-development conferences to teachers. Feedback from teachers and student participants has been very positive regarding the motivation implied by the challenges and open problems.

For example, our first activity may be rather simple. It requests to build a program so the robot moves its arm in a specific position. The configuration of the robot is such that there is only one fine motor and the program is tiny. It only uses one block. By using the vast amount of resources about LEGO-Mindstorms or the gudance of the instructor, we have seen every Year 6 child or older complete this task. Thus, every child succeeds with the first problem.

However, from here one can communicate the next challenge to the pupils that is conceptually quite advanced. But this is the virtue of our problems, they are understood across the diversity of the students. We immediately suggest creating (coding) behaviour, so the robot can engage, or compete against other similar robots in a tournament of the game, scissors, paper. We introduce concepts such as Nash equilibrium and mixed strategies.

Children change of perspective when we think of machines as instruments that deterministically repeat a task, such as ordinary microwaves. It is another matter to think of machines which would execute a random choice. That is, under exactly the same settings and circumstances, they may act differently. Even more fundamental, whether machines could think.

Later challenges introduce frame of references, similar triangles, trigonometric functions, vectors, limits, differential calculus, control theory, and connections to ethics, science, and the theories of the mind. All of these enable children to at least understand the problem and what is a suitable solution (even if such solution is hard to obtain).