# She wants to remove obstacles to teaching algebra

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Why is algebra perceived as so difficult? Anna Holmlund, a doctoral student in mathematics, believes teachers need to see it the way students do to understand how to better teach equations. Her dissertation will provide help to do this.

Teaching equations is not easy. Anna Holmlund knows. As a teacher at NTI Gymnasiet upper-secondary school, she noticed that many students found it difficult to understand the logic of the mathematical field of algebra.

“As a teacher, you think you can explain it, and you can easily show students ‘what to do’. But how do you get someone to see what you see? We teachers need to understand how students think and what experiences they bring to the table. Otherwise, we can’t influence the teaching so that students really understand,” says Anna Holmlund, doctoral student at the Department of Mathematical Sciences and the Centre for Educational Science and Teacher Research (CUL).

## A different approach is needed

Algebra can be described as a branch of mathematics in which one or more variables in an equation or expression are unknown and to which one adds letters, like x or y, in addition to figures and characters. This means that algebra requires a different way of thinking compared with calculating percentages or fractions.

“Numbers have a different role in algebra, and it’s the relationship between the different elements of an equation that is important. This is often perceived as a challenge, since students have experiences from other methods of calculation that make it hard to see these structures,” she says.

Some research on components and concepts in algebra that can be perceived as difficult, such as the equals sign and the role of variables. But there is not much research on the actual numbers in equations and what significance they have for student comprehension. This is Anna Holmlund’s focus. She has seen that negative numbers and numbers between zero and one – in decimal format – can lead to students having trouble solving equations they were able to solve in whole numbers, even if they have calculators.

## Context and models needed

To handle this issue, Holmlund believes in experimenting with various approaches to teaching. In one of her projects, students will get to work with models for solving equations in which both negative numbers and decimals can be illustrated. For example, a simulation of an electrical circuit will be used to illustrate equations for upper-secondary students attending a vocational electrician programme.

“I believe in working with contexts and models that are approachable for students, where they can experiment with different kinds of numbers. This can improve understanding and address the intuitive misunderstandings and experiences students bring with them.”

## Observing students

Anna Holmlund has always been fascinated by scientific perspectives on teaching. She is driven by the opportunity to find new ways of viewing teaching and would gladly contribute to research.

“The most fun I’ve had as a doctoral student has been getting to interview students. They’ve really shared their thoughts, and I’ve learned a lot about how they perceive things. After my time as a doctoral student, it would be fun to be able to combine research with continuing to teach.”

## Important sharing in the graduate school

CUL is a graduate school in educational sciences, and the doctoral students are spread out at several departments. Anna Holmlund is currently the only doctoral student in mathematical sciences with a focus on educational sciences. She feels it is particularly valuable when the University creates opportunities for CUL doctoral students to share experiences.

“For example, we have the chance to meet at a writing week at Kristineberg Center to read each other’s texts. Being able to get away like this, to get that informal feedback and to really have time to focus on writing – it’s wonderful.”

Text: Ulrika Ernström

Anna Holmlund

Is a: Doctoral student in mathematics with a focus on educational sciences and part of the CUL graduate school at the University of Gothenburg.

Grew up in: Borås

Age: 35

Fun fact: She used to dislike coffee, but as a new doctoral student, she started drinking a cup a day. Now she loves it.