# Profiles

## Universitetslektor

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 Works at Telephone 08-120 766 18 Email kerstin.larsson@mnd.su.se Visiting address Svante Arrheniusväg 20 A, E-huset, Arrheniuslab Room E 377 Postal address Institutionen för matematikämnets och naturvetenskapsämnenas didaktik 106 91 Stockholm

Kerstin has a PhD in Mathematics Education and works in the teacher education. Her research interests are mainly foucussed on students’ learning and understanding of arithmetic, including explanations and justifications for arithmetical properties.

## Teaching

Kerstin teaches mathematics education to teacher students and master students. She also work with supervision on all levels.

## Research

My research focusses elementary students’ understanding and learning of foundational mathematics, such as arithmetic and proportional reasoning. I am interested of their reasoning, for example, what arguments they use to explain and validate calculation strategies and how that reasoning can be transferred to general expressions; early algebra.

## Publications

A selection from Stockholm University publication database

Multiplicative understanding is essential for mathematics learning and is supported by models for multiplication, such as equal groups and rectangular area, different calculations and arithmetical properties, such as distributivity. We investigated two students’ multiplicative understanding through their connections between models for multiplication, calculations and arithmetical properties and how their connections changed during the school years when multiplication is extended to multi-digits and decimal numbers. The case studies were conducted by individual interviews over five semesters. The students did not connect calculations to models for multiplication, but showed a robust conceptualisation of multiplication as repeated addition or equal groups. This supported their utilisation of distributivity to multi-digits, but constrained their utilisation of commutativity and for one student to make sense of decimal multiplication.

• 2016. Kerstin Larsson (et al.).

Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. Hence there is consensus on the importance of acquiring multiplicative reasoning. Multiplication is typically introduced as repeated addition, but when it is extended to include multi-digits and decimals a more general view of multiplication is required.

There are conflicting reports in previous research concerning students’ understandings of multiplication. For example, repeated addition has been suggested both to support students’ understanding of calculations and as a hindrance to students’ conceptualisation of the two-dimensionality of multiplication. The relative difficulty of commutativity and distributivity is also debated, and there is a possible conflict in how multiplicative reasoning is described and assessed. These inconsistencies are addressed in a study with the aim of understanding more about students’ understandings of multiplication when it is expanded to comprise multi-digits and decimals.

Understanding is perceived as connections between representations of different types of knowledge, linked together by reasoning. Especially connections between three components of multiplication were investigated; models for multiplication, calculations and arithmetical properties. Explicit reasoning made the connections observable and externalised mental representations.

Twenty-two students were recurrently interviewed during five semesters in grades five to seven to find answers to the overarching research question: What do students’ responses to different forms of multiplicative tasks in the domain of multi-digits and decimals reveal about their understandings of multiplication? The students were invited to solve different forms of tasks during clinical interviews, both individually and in pairs. The tasks involved story telling to given multiplications, explicit explanations of multiplication, calculation problems including explanations and justifications for the calculations and evaluation of suggested calculation strategies. Additionally the students were given written word problems to solve.

The students’ understandings of multiplication were robustly rooted in repeated addition or equally sized groups. This was beneficial for their understandings of calculations and distributivity, but hindered them from fluent use of commutativity and to conceptualise decimal multiplication. The robustness of their views might be explained by the introduction to multiplication, which typically is by repeated addition and modelled by equally sized groups. The robustness is discussed in relation to previous research and the dilemma that more general models for multiplication, such as rectangular area, are harder to conceptualise than models that are only susceptible to natural numbers.

The study indicated that to evaluate and explain others’ calculation strategies elicited more reasoning and deeper mathematical thinking compared to evaluating and explaining calculations conducted by the students themselves. Furthermore, the different forms of tasks revealed various lines of reasoning and to get a richly composed picture of students’ multiplicative reasoning and understandings of multiplication, a wide variety of forms of tasks is suggested.

• 2016. Kerstin Larsson. Nordisk matematikkdidaktikk 21 (2), 69-88

This article presents a study in which grade 5 students' responses to multiplicative comparison problems, a well-known method for distinguishing additive reasoning from multiplicative, are compared to their reasoning when calculating uncontextualised multiplicative tasks. Despite recognising the multiplicative structure of multiplicative comparison problems a significant proportion of students calculated multiplicative problems additively. Therefore, multiplicative comparison problems are insufficiant on their own as indicators of multiplicative reasoning.

• 2015. Kerstin Larsson. Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, 295-301

Equal groups and rectangular arrays are examples of multiplicative situations that have different qualities related to students' understanding of the distributive and the commutative properties. These properties are, inter alia, important for flexible mental calculations. In order to design effective instruction we need to investigate how students construct understanding of these properties. In this study sixth grade students were invited to reason with a peer about calculation strategies for multiplication with the goal of explaining and justifying distributivity. Their discussions demonstrate that the representation of multiplication as equal groups helps them to explain and justify distributivity. At the same time this representation hinders their efficient use of commutativity.

• 2015. Kerstin Larsson, Kerstin Pettersson. Proceeding of ICMI STUDY 23, 559-566

In this study of arithmetical reasoning, which extends earlier work, we explore what properties students, when working in pairs, discern in additive and multiplicative co-variation problems that help them to distinguish between problem types. Results showed that pairs who solved each problem appropriately discerned mathematically significant properties such as speed, starting time and distance. Pairs who over-used additive reasoning focused on the distance difference without considering speed. While speed is considered to be a difficult quantity, here it seems to help students distinguish between multiplicative and additive situations.

• 2013. E. Levenson, R. Barkai, Kerstin Larsson. Tasks and tools in elementary mathematics, 188-195

Explanations are an integral part of mathematics education in primary school. This paper investigates some of the possible functions of explanations according to curriculum documents in Israel and Sweden and provides a way of classifying those functions. Findings indicated that explanations may have several various functions depending on the context in which they are requested or given.

Show all publications by Kerstin Larsson at Stockholm University

Last updated: January 30, 2019

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