Anne Tossavainen recently defended her doctoral thesis in Mathematics Education.

# New framework can help teaching fractions

Fractions are a difficult content area in elementary school mathematics, for both students and teachers. A new doctoral thesis at Luleå University of Technology has examined prospective elementary teachers' knowledge for teaching fractions and suggests implications for teacher education.

“Fractions are difficult but also very important. You need to understand fractions for further development in mathematics,” says Anne Tossavainen, who recently defended her doctoral thesis in Mathematics Education.

In her thesis, Tossavainen investigated future elementary school teachers’ knowledge for teaching fractions. The first study in the thesis shows that there are deficiencies and limitations in how prospective teachers solve mathematical tasks involving fractions. The results are in line with the findings of previous international research.

## Need understanding on deeper level

Anne Tossavainen has also analysed prospective elementary teachers’ conceptual knowledge of fractions.

“It is most common to interpret fractions as parts of the whole, but there are also other interpretations that you need to be aware of to understand fractions on a deeper level. For example, as a division, as a number or as an operator,” she says.

The results showed substantial differences between the participants in their conceptual and procedural knowledge of fractions. Some prospective teachers demonstrated comprehensive fraction knowledge in some knowledge categories, but had severe deficiencies in other categories. A prospective teacher who had a well-functioning way of solving fraction tasks could at the same time have difficulties understanding other solution methods or the concept of fractions.

“As a teacher, you need to have knowledge of different aspects of fractions to be able to adapt your teaching to different pupils,” says Anne Tossavainen.

In the interviews, the final-year prospective teachers who already had a positive attitude toward mathematics during their own years at school expressed a positive mathematical identity and positive attitudes toward mathematics teaching. Those who had difficulties with mathematics at school still had a negative view of the subject. However, all the interviewees expressed that they would have needed more knowledge about how to teach mathematics to different kinds of pupils.

## Framework to use in teacher education

In her doctoral thesis, Anne Tossavainen has devised a framework that connects different aspects of fractions. The framework is based on core aspects of fractions in four categories: interpretations, representations, procedures and notions. She hopes to see that the framework is used in teacher education to develop future elementary school teachers’ mathematical knowledge.

“I know that some teacher educators have already tested the framework in their teaching with promising results. The framework is an important contribution of my doctoral thesis and I hope that it can be developed further in teacher education and used for future research on fractions. I think we need to focus more on fractions in teacher education since fractions are so fundamental to other areas of mathematics as well," she says.

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