# LEARNING AND PLAYING MATHEMATICS

P. MorandoUniversita' degli Studi di Milano (ITALY)

One of the main problems in teaching Mathematics in the initial years of any kind of scientific curriculum is the considerable difficulty in keeping the attention of the students at a sufficiently high level.

Another important problem is that students coming from different high schools have very different level of knowledge, and often students with a lower mathematical background can feel absolutely inadequate to attend the courses. For these reasons is important, on one hand to encourage collaboration between students, and on the other hand to propose didactical situations where all students are stimulated to participate in an active way.

With this aim, during my course of mathematics for the students of first years of the Agricultural Sciences Faculty, I proposed some games, and the experience was very satisfactory, both in terms of participation and in terms of results during the final examinations. I want to report here about two of these experiences.

•The first game I proposed was “Guess who”.

The idea is the following: I give to the students copies of a sheet containing 24 graphics of functions identified by numbers from 1 to 24, and I select between these one function. The object of the game is to be the first to determine which function I selected. This is done by asking various yes or no questions to eliminate functions. I declare what kind of questions are allowed (for example question about limits, or question about domains, or question about the sign of the function, and so on). In turn they ask questions and, depending on my answer, eliminate functions which do not fit the criterion. If there are many participants, they can work in groups, and in this case any group have to choose a “leader student” that is the only one in the group allowed to ask questions. In my experience it was very interesting to see how colleagues try to convince the leader about the best question to ask, and how these discussions help students to understand what kind of information can be deduced from the graphic of a function.

•The second game I proposed was “Function’s Bingo”.

For this game I give to each student a score-card with 6 conditions on functions (for example the value of the limit of the function for x approaching infinity, or the existence of asymptotes, or the minimum of the function, etc). Then I start to extract functions and the student have to check if the extracted function satisfy one of the properties on his score-card. Any function can be used only once, and the winner is the first one that complete (correctly) his score-card. If a student presents a score-card wrongly completed, he has to pay with a candy, and the winner get all candies given from colleagues that were wrong in the course of the game (usually a big amount!). To give further motivation, I also offered as prize for the Function’s Bingo two points in the grade of final examination, but none of the winner really used it, because they passed the examination with the highest grade!

In my experience students react in a very positive way to this strange didactical experience: the participation was really high in numbers and students looked enthusiastic about the experience.