In 1999, the first four mathematical toys were produced by Samuel Bengmark and others in what was then called “Resurscentrum MD” (Resource centre MD). The idea was to form something that could serve as a base when school children visit the department. Besides the toys, the study tour also included computer simulations and meeting researchers. As opportunities arose, the toys came to use in other contexts, such as the Science Festival and the Faculty of Science Day.
For the last few years, Laura Fainsilber has been the keeper of the toys. She runs “Mötesplats matematik” (Meeting place mathematics), where the department gets into contact with schools and the general public, together with Åse Fahlander. Over the years, more mathematical toys have been developed, but the base has stabilized around a few that they know work well. The Science Festival has become the big occasion with up to 40 visiting classes between grades 4 and 9 during two weeks in the spring.
– It is never difficult to get the pupils going, they tend to be eager to try on their own. Sometimes, it can be difficult to focus on the follow-up discussion. The commitment of the accompanying teachers is important; if they are not involved it is harder to motivate the pupils. But some teachers are a bit too committed also, and are keen to explain before the pupils have tried to figure things out themselves!
Laura’s favourite amongst the toys is the “Leaning tower of Gothenburg”. The instructions are simple – build a tower where the plates lean out as much as possible without falling down – but the construction has elements of surprise and brings up fairly deep mathematics. This toy usually works best with secondary and upper-secondary school pupils. In the game “The car and the goats” (the Monty Hall game), you try to find the prize in one of three sealed boxes. Many pupils find it exciting even if it now appears in some mathematical textbooks. Many pupils also want to play “First to 20”, where you take turns moving a piece one or two steps and win if you reach 20 exactly, but it is sometimes harder to make them think about the strategy behind. They also usually play with the “Scale of the wholesaler”, “Towers of Hanoi” and “Function boxes”.
Besides the Science Festival, the toys are used when schools are visiting the department, often because they have pupils who are especially interested and want to encourage them in mathematics. This happens a few times each term. Groups from a school for children with special needs have sometimes tried the toys and it has worked well. The toys are used in a popular introduction to a course for student teachers, breaking the standard image of a math class Trying things out and thinking about problems motivates students and helps them develop a deeper understanding and is better remembered than reading about it or being shown. The toys are also a part of the Faculty of Science’s “Windows to Science”, and of the department’s in-service teacher training, with the idea that the teachers can pass on the toys to their schools.
– The physical parts of the toys are not high-tech in any way, but made by us in simple materials. The idea is that you should be able to go home to your school and easily make something similar yourself. We would like to promote the mathematical toys so that others try them elsewhere, we have for example talked about them with the Intize mentors, who meet high school students. Sometimes we have pupils as interns during the period of the Science Festival, and we have suggested that they can bring the ideas home to their classes, but we do not know if they have followed it up. During the conference “Mathematics Biennial” we had a lecture “learn to lead a session with mathematical toys” but people were mostly eager to try all the toys themselves! Maybe it is easy to feel insecure, I watched how Samuel did it a few times before I lead a session myself. Here at the department we always have a few colleagues that can step in, and it feels good that we have that backup when we invite so many classes during two intensive weeks.
The Science Festival also has an “Experiment Workshop” with lots of activities. There we offer a different set-up: “Draw in circles”. Special interlocking wheels are required to draw good-looking hypotrochoids, and those used by “Mötesplats matematik” are custom made with selected relationships between the circles’ radii, so that the underlying mathematics can be figured out. The advantage is that it is something you cannot do at school, but Laura and Åse are still working to find the right setup where you get an insight and discover something in just ten minutes. The mathematics is not immediately apparent so it is necessary to find the right questions and formulations. The important thing here is the experience of creating a beautiful figure with a mathematical pattern, it is a good complement to school mathematics.
Text: Setta Aspström
Photos: Åse Fahlander, Laura Fainsilber and the leaning tower, Setta Aspström
At the school programme of the Science Festival, Setta Aspström
Hypotrochoids, Laura Fainsilber