Mathematics as beautiful reality.

Teaches the beauty of mathematics

Text: Eva Lundgren Photo: Johan Wingborg

– Numbers and symbols are the language we use to describe what mathematics stands for. But mathematics is really something else: an elegant way of describing aspects of the world, says Lena Pareto.

She was recently appointed Professor of Pedagogy with the task of strengthening the University of Gothenburg’s collaboration with Universeum.

Universeum’s warm, humid rainforest is a stark contrast to the cold rainy weather we hurried in from, getting more or less soaking wet. The air is full of chattering, chirping and croaking sounds, and the waterfall roars. Even though the rainforest is not really something Lena Pareto usually works with, she still wants to point out that the jungle can also inspire mathematical thinking: For example, how can you calculate how much water is in the piranhas’ aquarium?

But really, Lena Pareto’s professorship is about being part of developing Universeum’s latest initiatives: a new visualization lab where visitors can examine research data, as well as Sweden’s largest visualization dome. It should provide opportunities for new 3D experiences of things that are too big, too small, too fast, too slow or too complicated for humans to study. In addition, a “miniverseum” is underway for younger visitors. – Universeum already collaborates with the University of Gothenburg and Chalmers, as well as with other universities, Lena Pareto points out. – But now the collaboration will be more systematic with even more focus on various research projects. Among other things, I hope that students will be able to have courses or do project work here and that the collaboration with the school can increase even more. For example, I hope to have the opportunity to start a research project on how Universeum could develop its online activities for schools that do not have the opportunity to physically bring a class here.

Digital technology is special, Lena Pareto points out. – All physical material, such as wood, steel or textiles, have inherent properties that must be taken into account when using them. Digital technology, on the other hand, is like a material without any properties at all. Since everything is just an illusion, you can test anything and see what happens. Therefore, Universeum’s new environments will provide incredible opportunities for data visualization in a variety of ways. All this freedom to design an illusion of something makes it at the same timedifficult because we understand things differently.

In 1995, Lena Pareto defended her thesis in computer science with a theoretical thesis on how to assess the accuracy of computer programmes. The following year, she continued her theoretical research at the INRIA Sophia Antipolis-Méditerranée Research Centre in France.

But since then, she has devoted herself to technology that is much closer to people’s everyday lives, for example a project to create better sound environments in office landscapes.

It was a question from a friend, who was studying to be a preschool teacher, that made Lena Pareto start thinking about the practical applications of her research. – Given my knowledge of digital technology, she wondered if I might be able to do something to promote the teaching of mathematics in schools. I have always wanted to try to understand how we learn different things, so I began to think. Since there is a general idea that everything to do with numbers and symbols is difficult, I started to wonder whether you could learn mathematics in a different way.

It resulted in the graphic computer game Rutiga familjen (Checkered Family), where children can learn the four rules of arithmetic, positive and negative numbers and the decimal system, without any numbers.

– The players pack and unpack boxes with different coloured squares, which represent positive or negative numbers. What you are able to do with the squares is controlled, so that it is always mathematically correct. Addition, for example, is about adding, regardless of whether you add positive or negative squares. Eventually, however, children discover that deleting a positive number has the same effect as adding the same negative number.

The game can be used by children from about 4 years and throughout primary school. – Older children can play very strategically: If I do this then maybe my teammate or opponent will do that, and then I will have to do this…

Mathematics that just involves providing the correct is boring, says Lena Pareto. – Therefore, Rutiga familjen does not ask questions such as: What is 5 plus 5? but instead: Which numbers can be added together to make 10? And then you discover that it is possible to find as many solutions as you like.

In collaboration with various schools, the game has gradually developed. Together with primary school teachers, special educators and students in the training school, Lena Pareto has developed the game primarily for students with mathematics difficulties. And together with researchers from Stanford University, she has recently added another dimension: students are commissioned to teach how to play the game. – The program has been provided with a digital agent that the children are given the task of learning mathematics. The agent asks questions based on what the child is doing in the game, which means that the children must explain and motivate their play behavior to the agent. The mathematics studies become more fun but also facilitate conversations with the students; it is the agent who may have difficulty with certain aspects, not the student himself. In the latest project around the game, I investigate, together with colleagues, what happens when we use a physical robot, which moves and talks, instead of a digital agent. How do the children perceive it?

Lena Pareto is driven by a desire to make the world better with the help of technology. But to do that, you have to be curious, she says. – My role model is Astrid Lindgren’s “Rumpnissar” (Rumphobs) who constantly ask “Vaffor då då?” (Why’s that then?). But I also want to convey the beauty of mathematics. Those who think maths is boring should talk to some mathematicians. Their fascination is not about counting very complex numbers, but about

mathematics being the logic we use, bit by bit, to build the world. Yet the very basis of all mathematics is a number of axioms that we can only accept; if a single one of them falls, the whole of mathematics falls as we understand it and have understood it for a long time.

Two small bright red ibises with long, curved beaks have come very close and are looking at us. This makes Lena Pareto talk about her second great interest, after mathematics: nature.

– You have to have a different pace in your life, it’s not possible to hurry and rush around constantly . I live with my partner on a farm on Orust and have acquired a Dutch Warmblood, among other things. I love riding, skiing and diving but also to just be out in nature and swim in forest lakes. Due to hip problems I previously had difficulty doing everything I wanted to do, but now I have had two hip replacements and most things are possible again.

Lena Pareto previously also enjoyed travelling, but that desire has waned. – The best thing about traveling is to come home and realize that the place where you live is actually the nicest in the whole world. Being on Orust when it is really windy and at the same time raining a little is the best way to empty your head – but the island is its most beautiful at sunset in the summer.

Digital technology, on the other hand, is like a material without any properties at all.

LENA PARETO

Lena Pareto

Currently: New Professor of Pedagogy who will collaborate with the Universeum initiative on data visualization. Family: Partner and daughter. Lives: On Orust. Most recently read book: Lucinda Riley: The Shadow sister. Most recently watched film: Hunger Games 4. Other hobbies: Horses, riding, hiking and biking in nature and mountains, skiing, kayaking.