The first floor of the MaD Building in Mattilanniemi currently features, among other things, an ellipse-shaped pool table. It is a part of the Signs of Mathematics exhibition of the Department of Mathematics and Statistics, which seeks to open a channel to the world of mathematics by means of tangible devices.

Mathematics raises strong emotions. It is understood, hated, doubted, feared, loved, and criticised. Nobody, however, can deny its necessity. Mathematics is present everywhere and in everything – it’s just a matter of noticing it. The Signs of Mathematics exhibition in the Department of Mathematics and Statistics offers practical examples of such settings. In addition, the exhibition provides hints and concrete approaches for the functional teaching of mathematics, which develops students’ mathematical thinking and understanding of basic concepts through concrete and diverse experiences. In addition, the exhibition aims at improving ordinary people’s conceptions of modern mathematical research while also building bridges between university, schools and society by promoting broader understanding of mathematics.

“It can be difficult to find anything concrete in mathematics,” says University Teacher Tuomo Äkkinen, one of the four persons in charge of this project. “The idea of the exhibition is to offer something tangible that will inspire young people to engage with mathematics.”

Concepts familiar from school

The exhibition encompasses several areas of mathematics, including geometry, analysis (limits), and statistics. The themes relate to issues that are easy to integrate into school mathematics at the lower and upper secondary level. For example, playing billiards on the ellipse-shaped table is much more difficult, as balls bounce from the arching walls quite differently from ordinary pool tables.

“In addition to the joy of playing, we can use the table to demonstrate various geometric problems, like what kind of figures a ball draws on the table or how a ball is reflected from the ellipse-shaped wall and how billiard would be easiest to play on this table,” Äkkinen explains.

Normal distribution is a concept familiar to everyone from school, and it is demonstrated in the exhibition by means of a Galton board. At the same time, other concepts familiar from school, such as Pascal’s triangle and binomial distribution, will be explored.

“The idea is similar to the one in the TV-programme The Wall,” Äkkinen explains. “On the Galton board, a large number of balls are dropped through equally distanced pin rows into compartments below, after which we can notice that the balls are distributed across the boxes nearly according to normal distribution.”

The exhibition includes altogether six big items, but there are more under construction. A 3D printer makes it possible to produce different demonstration objects for mathematics, which can be studied in the exhibition.

Experiential learning

Studying mathematics may sometimes feel boring, but integrating the topic with everyday activities makes it more interesting and also increases understanding of mathematics. The Signs of Mathematics exhibition responds to this challenge and gives a new perspective on mathematics teacher education as well. The exhibition project offers possibilities for thesis work at the Department of Mathematics and Statistics. One master’s thesis has already been completed, but there are more to come.

“In our daily work, we have to continuously consider and develop different ways of learning,” Äkkinen explains. “These include teaching methods that promote student motivation, patience and understanding.”

Open for everyone!

If normal daily life returns after next summer, schools will be invited for a visit and some cooperation. The purpose is to make the exhibition open for all so that people can come to see it anytime. The exhibition will be open for various public events such as Applicants’ Day and Researchers’ Night.

“If the exceptional conditions continue, we will organise virtual visits,” Äkkinen says, “but it would take away part of the fun, as then the students cannot get their hands on and test the devices.”

The exhibition has been created mainly by researchers Augusto Gerolin, Tuomo Äkkinen, and Ville Kivioja from the Department of Mathematics and Statistics, together with Markus Hähkiöniemi from the Department of Teacher Education. The exhibition is funded by a grant from the Finnish Cultural Foundation.

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