# Searching the past for future answers

Mathematics researcher Johanna Pejlare wants to understand why Swedish school pupils’ test result curves in algebra are trending downwards. To assist her, she has 300-year-old textbooks, among other things.

Three large paper tomes lay on a table in Johanna Pejlare’s office. Both the front page and the contents are printed in an ornate German typeface, and one of the books is written in Latin.

‘I’m a bit extreme’, she says, smiling. ‘They are transcriptions of books that are based on the lectures of the 18th century mathematician Duhre and a transcription of Euclid’s the third century BC Elements from a 17th century edition by mathematician Gestrinius.

The heavy volumes, in more ways than one, will be used by Pejlare in the research project that she helped launch in the spring 2016, which is funded by the Swedish Research Council. Along with some of her colleagues from her days as a doctoral student, she will spend four years studying historical and educational perspectives on algebra education in school.

‘We want to contribute to the dialogue about the problems involved in implementing algebra in school mathematics’, Pejlare says. ‘International studies indicate that Swedish students’ knowledge of algebra is not good, and we want to find out why that is the case and what can be done about it.’

Since the spring of 2015, she has been employed at the Department of Mathematical Sciences. The journey there has not been straightforward. Initially, Pejlare studied archaeology, but via some elective courses in mathematics, she decided on that subject instead.

‘When I finished my master’s degree, I saw that the Swedish Foundation for Humanities and Social Sciences was going to start a doctoral school in mathematics that focused on education. I applied for a doctoral studentship and got it. It wasn’t according to a plan, you see’, she says, laughing. ‘But I’ve always tried to do what seems to me to be exciting and challenging.’

Within the framework of the doctoral school, she took a course in mathematics history, felt that it was the subject she wanted to work with, and since then her research field has been mathematics, with a focus on the history of mathematics and education.

‘It’s a very exciting area. It combines so many different themes that interest me, such as history, mathematics and the philosophy of mathematics. How has mathematics evolved into what it is today? Why do we have the mathematical concepts we do, and how have they evolved into the way they look today?’

She received her PhD in 2008 at Uppsala University with a dissertation that, among other things, deals with the visualisations of mathematics throughout history. After a few years at the University of Borås, a position in Gothenburg was announced that fit her perfectly. She applied and got it, and almost two years ago she moved into her office at Campus Johanneberg.

Johanna Pejlare is critical of the simplistic way in which the history of mathematics often is applied didactically, where the starting point is an assumption that the mathematical concepts we use today have been developed by and for us in a specific, orderly fashion. She maintains that there are many examples of how different cultural contexts have influenced the historical development of mathematical concepts, causing them go in different directions.

‘Take negative numbers, for example. In the West, development of a full understanding of negative numbers was a long and complicated process, but in China people understood what they are and how they work very early. So it becomes difficult to draw parallels between the historical development and students’ conceptual development. Which narrative should we choose in that case?’

Pejlare spends part of her time on the Pedagogen Campus where she teaches basic mathematics to future teachers. That includes not only teaching them the subject, but also preparing them for the challenges that teachers are going to face in school.

‘Sometimes I wish that I had had even more time for research. But the students, and above all their prospective pupils, are what is most important. I always put them first.’

#### Johanna Pejlare

Profession: Researcher in mathematics history and didactics

Age: 40 years

Family: Husband Michael, also a mathematician, and children Alexander and Isolde

Lives in: Gothenburg

Leisure time: ’Devote a lot of time to the family, like to go on outings — the sculpture park at Pilane on Tjörn and the Louisiana Museum of Modern Art in Humlebæk, Denmark, are two favourites.’