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The Seventh Nordic Conference onMathematics Education

NORMA 14 TurkuJune 3–6, 2014

PROGRAMME AND ABSTRACTS

UNIVERSITY OF TURKU, FINLANDDEPARTMENT OF TEACHER EDUCATION

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Conference Scientific Committee:

Chair Markku S. Hannula, University of Helsinki, ([email protected])

Members: Jorryt van Bommel, Karlstad University; Martin Carlsen, Univer-sity of Agder; Bettina Dahl Søndergaard, Aalborg University; Guðný HelgaGunnarsdóttir, University of Iceland; Cecilia Kilhamn, University of Gothen-burg; Jüri Kurvits, Tallinn University & Tallinn University of Technology;Tomi Kärki, University of Turku; Birgit Pepin, Sør-Trøndelag UniversityCollege; Lisser Rye Ejersbo, Aarhus University; Harry Silfverberg, Univer-sity of Turku

Local Organizing Committee:

Chair Harry Silfverberg, University of Turku ([email protected])

Members: Aija Ahtineva, Satu Kankare, Tomi Kärki, Anu Tuominen, Uni-versity of Turku

Conference Secretary Services: University of Turku Congress Office,http://congress.utu.fi

c©Harry Silfverberg (Ed.)

CONTENTS 3

Contents

1 Schedule 1

2 Plenary lessons 3

3 Regular papers 73.1 Tuesday June 3 13:30-14:50 Session 1a Room EDU2

Chair: Markus Hähkiöniemi . . . . . . . . . . . . . . . . 73.2 Tuesday June 3 13:30-14:50 Session 1b Room EDU3

Chair: Kjellrun Hiis Hauge . . . . . . . . . . . . . . . . . 83.3 Tuesday June 3 13:30-14:50 Session 1c Room EDU244

Chair: Per Nilsson . . . . . . . . . . . . . . . . . . . . . . 93.4 Wednesday June 4 9:00-10:20 Session 2a; Room EDU2

Chair: Raymond Bjuland . . . . . . . . . . . . . . . . . . 103.5 Wednesday June 4 9:00-10:20 Session 2b Room EDU3

Chair: Janne Fauskanger . . . . . . . . . . . . . . . . . . 113.6 Wednesday June 4 9:00-10:20 Session 2c Room EDU244

Chair: Ragnhild Johanne Rensaa . . . . . . . . . . . . . 123.7 Thursday June 5 9:00-10:20 Session 3a; Room EDU2

Chair: Markku S. Hannula . . . . . . . . . . . . . . . . . 133.8 Thursday June 5 9:00-10:20 Session 3b; Room EDU3

Chair: Guðný Helga Gunnarsdóttir . . . . . . . . . . . 143.9 Thursday June 5 9:00-10:20 Session 3c; Room EDU244

Chair: Andreas Ryve . . . . . . . . . . . . . . . . . . . . 153.10 Thursday June 5 13:00-14:20 Session 4a; Room EDU2

Chair: Tomi Kärki . . . . . . . . . . . . . . . . . . . . . . 163.11 Thursday June 5 13:00-14:20 Session 4b; Room EDU3

Chair: Maria L. Johansson . . . . . . . . . . . . . . . . 173.12 Thursday June 5 13:00-14:20 Session 4c; Room EDU244

Chair: Anu Tuominen . . . . . . . . . . . . . . . . . . . . 183.13 Friday June 6 9:00-10:20 Session 5a; Room EDU2

Chair: Anna-Maija Partanen . . . . . . . . . . . . . . . 193.14 Friday June 6 9:00-10:20 Session 5b; Room EDU3

Chair: Uffe Thomas Jankvist . . . . . . . . . . . . . . . 203.15 Friday June 6 9:00-10:20 Session 5c; Room EDU244

Chair: Arne Jakobsen . . . . . . . . . . . . . . . . . . . . 21

4 Short communications 234.1 Tuesday June 3 15:20-17:10 Session 1a Room EDU3

Chair: Mette Andresen . . . . . . . . . . . . . . . . . . . 234.2 Tuesday June 3 15:20-17:10 Session 1b Room EDU244

Chair: Ole Enge . . . . . . . . . . . . . . . . . . . . . . . . 27

CONTENTS 4

4.3 Wednesday June 4 13:00-14:30 Session 1c Room EDU244Chair: Annette Hessen Bjerke . . . . . . . . . . . . . . . 30

4.4 Thursday June 5 14:40-16:00 Session 2a Room EDU3Chair: Ann-Sofi Röj-Lindberg . . . . . . . . . . . . . . . 33

4.5 Thursday June 5 14:40-16:00 Session 2b Room EDU244Chair: Lovisa Sumpter . . . . . . . . . . . . . . . . . . . 36

5 Symposium Wednesday June 4 13:00-14:30 Room EDU2 395.1 The theme of the symposium . . . . . . . . . . . . . . . . . . 395.2 Symposium paper: Eva Norén . . . . . . . . . . . . . . . . . . 405.3 Symposium paper: Katarina With & Yvette Solomon . . . . . 405.4 Symposium paper: Lovisa Sumpter . . . . . . . . . . . . . . . 41

6 Working groups 426.1 Tuesday June 3 15:20-16:20 Working group 1 Room EDU2

Chairs: Guðný Gunnarsdóttir & Guðbjörg Pálsdóttir 426.2 Wednesday June 4 13:00-14:00 Working group 2 Room EDU3

Chairs: Simon Goodchild & Frode Rønning . . . . . . . 446.3 Thursday June 5 14:40-15:40 Working group 3 Room EDU2

Chair:Reidar Mosvold . . . . . . . . . . . . . . . . . . . . 47

7 Map of the conference venue 50

Index

1 SCHEDULE 1

1 Schedule

Tuesday June 3

Time Halls/restaurants EDU 2 EDU 3 EDU 244

10:00-‐12:00

Registration and coffee (or self-‐paid lunch)/ Entrance hall of the Educarium building

12:00-‐12:20 Opening session

12:20-‐13:30 Plenary lecture 1

Erno Lehtinen

13:30-‐14:50 Regular papers 1a Regular papers 1b Regular papers 1c

U. Jankvist & M. Niss E. Hägerstedt et al. R. Bjuland et al.

M. Sjöblom R. Rensaa J. Kristinsdóttir

14:50-‐15:20 Coffee

15:20-‐17:10 Working group 1 Short communic. 1a Short communic. 1bChairs: G. Gunnarsdóttir & G. Pálsdóttir

M. Hannula-‐Sormunen et al.

A.-‐S. Röj-‐LindbergResearch on curriculum materials

E. Esteva & M. S. Hannula

Y. Solomon & A. Bjerke et al.

G. Rodríguez Padilla et al.

N. Pongsakdi, T. Laine & E. Lehtinen

A. PetterssonH. Kaarstein & G. Nortvedt

I. Kaldo & M. Hannula B. Gustafsson

17:10-‐18:30Get-‐together party/ Entrance hall of the Publicum building

Wednesday June 4

Time Halls/restaurants EDU 2 EDU 3 EDU 2449:00-‐10:20 Regular papers 2a Regular papers 2b Regular papers 2c

G. Gunnarsdóttir & G. Pálsdóttir

R. Mosvold & P.-‐E. Sæbbe K. Hauge & R. Herheim

L. Ahl et al.M. Johansson & A. Wernberg et al.

P. Nilsson

10:20-‐10:50 Coffee


Morten Misfeldt

12:00-‐13:00Lunch/ Restaurant Macciavelli (EDU)

13:00-‐14:20Symposium (Chairing by Yvette Solomon)

Working group 2 Short communic. 1c

E. Norén (Reg. paper)Chairs: S. Goodchild & F. Rønning

A.-‐M. PartanenWith & Solomon (Reg. paper)

Teaching Mathematics at higher education

R. Wester

L. Sumpter (Reg. paper)E.-‐L. Erixon & M. Bjerneby Häll

Excursions: The Historical walking tour 16:00-‐18:00; The cruise 19:00-‐23:00

The Seventh Nordic Conference on Mathematics Education University of Turku, Department of Teacher Education

1 SCHEDULE 2

Thursday June 5


O. Enge & A. Valenta T. Højgaard & U. Jankvist M. HähkiöniemiH. Palmér & J. van Bommel

R. Herheim & T. E. Rangnes

J. Neuman et al.

10:20-‐10:50 Coffee


Heidi Strømskag

12:00-‐13:00Lunch/ Restaurant Macciavelli (EDU)

13:00-‐14:20 Regular papers 4a Regular papers 4b Regular papers 4cJ. Fauskanger & R. Mosvold

M. Carlsen J. Ärlebäck & H. M. Doerr

A. Jakobsen & M. Kazima L. Køhrsen & M. Misfeldt B. Kleve

14:20-‐14:40 Coffee

14:40-‐16:00 Working group 3 Short communic. 2a Short communic. 2b

Chair: Reidar Mosvold J. McMullen et al. L. RussellPotential uses of social media in and for

B. Kleve & I. Solem L. Medvedeva & P. VosA.-‐T. Bofah & M. S. Hannula

A. H. Bjerke

B. Brezovszky et al.A. Bergwall & M. Knutsson

16:15-‐16:45 Nordina-‐info

16:45-‐17:45 Norme General Assemply

19:30-‐23:00 Conference Dinner Brewery Restaurant Koulu ("School")

Friday June 5


A. Lorange I. Grave & B. Pepin C. V. Berg

M. Andresen L. Hoelgaard & A. Ryve K. Rø

H. Silfverberg

10:20-‐10:50 Coffee


Helen Doerr

12.00-‐12.15 Closing session

Lunch/Macciavelli

2 PLENARY LESSONS 3

2 Plenary lessons

HOW STUDENTS OWN TENDENCY TO FOCUSSPONTANEOUSLY ON MATHEMATICALLY

RELEVANT PHENOMENA PREDICTSMATHEMATICAL DEVELOPMENT?

Erno Lehtinen

Centre for Learning Research, University of Turku

According to the results of many longitudinal studies, inter-individualdifferences in mathematical achievement tend to increase in thecourse of formal schooling. Instead of attributing this entirelyto the lack of (stable) abilities we should focus on the dynamicdevelopmental factors, which might explain different learning tra-jectories. Our own studies from last fifteen years have highlightedthe role of students’ own focusing tendencies in the mathematicaldevelopment. In our early studies we noticed that young childrenhave generalized and relatively stable differences in their tendencyto spontaneously focus on number of objects and events in theireveryday surrounding. Longitudinal studies showed that these dif-ferences were in strong mutual interaction with early developmentof number concept and were a domain specific predictor of math-ematical learning during early school years. Our recent studieshave revealed that later in their development students have similarinter-individual differences in their tendency to spontaneously no-tice quantitative relations situations that are not explicitly math-ematical. First longitudinal studies on the “spontaneous focusingon quantitative relations” show that this tendency is a strong pre-dictor of later learning of rational number concept. Earlier inter-vention studies show that it is possible to enhance children’s spon-taneous focusing on numerosity in a way, which has subsequenteffects on the learning of number skills. In the presentation I willdiscuss if it is also possible to have similar intervention effects onthe spontaneous focusing on quantitative relations.

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2 PLENARY LESSONS 4

A MODELING PERSPECTIVE ON THEMATHEMATICAL WORK OF TEACHING

Helen M. Doerr

Syracuse UniversityMathematics & Mathematics Education

While much research over the past three decades has demonstratedthe positive impact of mathematical modeling on student learning,progress has been slow in the widespread adoption of mathematicalmodeling as a classroom practice. A key factor in any change inclassroom practice is the role of the teacher. Recently, research-ers have investigated approaches to modeling that move beyondsingle modeling tasks to sequences of modeling tasks that facilit-ate the development of learners’ mathematical ideas and modelingcompetencies. The mathematical work of teaching sequences ofmodeling tasks places new demands on the learners and new chal-lenges for the teacher. The nature of teaching practices and themathematical knowledge needed will be taken up in this present-ation.

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STUDENTS’ MATHEMATICAL ACTIVITYCONSTRAINED BY THE MILIEU : A CASE OF

ALGEBRAHeidi Strømskag

Sør-Trøndelag University CollegeFaculty of Teacher and Interpreter Education

The importance of algebra is widely acknowledged through its roleas the language in which generalisation of quantity and relation-ships of patterns can be expressed, manipulated, and reasonedabout. Students, however, experience serious difficulties in learn-ing the symbolic language of algebra, algebraic thinking and gen-eralisation. This is well documented in the research literature.Research on students’ processes of pattern generalisation suggeststhat it is not generalisation tasks in themselves that are difficult;the problems that students encounter are rather due to the waytasks are designed and limitations of the teaching approaches em-ployed. It is therefore relevant to gain insights into how design oftasks and the way pattern generalisation is taught influence theoutcome of students’ engagement with tasks on shape patterns. I

2 PLENARY LESSONS 5

shall discuss this with data from a case study of student teachers’engagement with tasks on patterns generalisation at a universitycollege.

In the reported study, the addressed research question was: Whatfactors constrain students’ establishment of algebraic generality inshape patterns? The theory of didactical situations in mathemat-ics has been used to identify constraints to students’ generalisationprocesses. Research participants are two groups of three studentteachers in the first academic year on a teacher education pro-gramme for primary and lower secondary school in Norway, andtwo teacher educator of mathematics. Data sources are: tran-scripts from video-recorded lessons of first-year student teachers’collaborative engagement with mathematical tasks (with teacherinvolvement); the mathematical tasks they solved; and, conversa-tions with the mathematics teacher who had designed the tasks.

The identified constraints are conceptualised in terms of three ana-lytic categories, emerging from an open coding process. The firstcategory is about features of the milieu that imply inadequatefeedback for the students in adidactical situations; the second cat-egory is about challenges the students face when they shall trans-form into algebraic notation relationships that they have expressedinformally; and, the third category is about challenges related tostudents’ justification of formulae they have developed. I will showhow elements of the material and intellectual reality (the milieu)that the students act upon in the adidactical situation have limit-ations with respect to the knowledge at stake (e.g., the conceptsof mathematical statement and formula). Here, I will show howthe tasks are designed in a way that constrains the devolutionprocess and makes it unclear for the students what they are sup-posed to do when solving the tasks. Further, I will show how thedistinctiveness of recursive and explicit approaches to generality isconfused, in the tasks and in conversions between the participants.

Further, I will present how the categories are developed; how con-cepts and models from the theory of didactical situations are usedto conceptualise the data and develop the three core categories.Results from the study point at important factors with respect todesign of tasks on algebraic generalisation of shape patterns, andto teaching of this topic. I will discuss this from an epistemologicalpoint of view, where I relate it to the research literature on theteaching and learning of elementary algebra.

2 PLENARY LESSONS 6

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CREATIVITY AND MATHEMATICS TEACHINGMorten Misfeldt

Aalborg UniversityICT and Design for learning

Creativity and innovation are important 21 century skills and math-ematics education is considered a major factor in contributing tothe development of these skills. However it is far from clear ex-actly how we as mathematics educators should respond to need forcontributing to the development of creativity and innovation withour students. One reason is that it is not clear what such creativeand innovative skills are in relation to mathematics, and how weshould teach for it and evaluate it.In my talk I will focus on understanding what mathematical innov-ation and creativity "is" in the relevant domains (e.g. disciplinary,professional, scholastic, and informal domains) and how it is trans-lated into the mathematical classroom.I will describe a framework that allows us to study how teachersand students frame the activities in the classroom towards differ-ent situated understandings of mathematical innovation and cre-ativity, in relation to domains such as industry and commerce,mathematics as a discipline, out of school activities, internal schol-astic conceptions of mathematics ect. I will show how differentconceptions of mathematical innovation and creativity are domin-ating in different parts of the mathematics education literature,and give examples of how the different conceptions are simultan-eously present in situations where mathematics is taught.

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3 REGULAR PAPERS 7

3 Regular papers

3.1 Tuesday June 3 13:30-14:50 Session 1a Room EDU2Chair: Markus Hähkiöniemi

DESIGNING A RESEARCH-BASED ‘MATHSCOUNSELLOR’ PROGRAM FOR DANISH UPPER

SECONDARY TEACHERSUffe Thomas Jankvist1 & Mogens Niss2

1Aarhus University; 2Roskilde University

The paper addresses how decades of mathematics education re-search results can inform practice by describing a developmentalresearch project on designing and implementing an in-service up-per secondary school teacher education program in Denmark. Theprogram aims to educate a “task force” of so-called “maths counsel-lors”; mathematics teachers whose purpose it is to identify studentswith learning difficulties in mathematics, investigate the nature ofthese difficulties, and carry out interventions to assist the studentsin overcoming them. We describe the considerations made in rela-tion to designing (and implementing for the first time) the programas well as the resulting components of the program.

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COORDINATING THE IC-MODEL WITH AFRAMEWORK ON COMMUNICATION IN ANALYSING

STUDENT-TO-STUDENT INTERACTIONS INMATHEMATICSMarie Sjöblom

Malmö University

The aim of this paper is to investigate possibilities for coordinatingtwo theories in order to analyse interactions in a group of four stu-dents completing a mathematics task in upper secondary school.The investigation suggests that the theories can be coordinated,but their interpretations of the interactions provide informationon different levels. Alrø and Skovsmose’s IC-model gives a moregeneral picture of what is happening in the interaction betweenstudents, whereas Fuentes’s framework gives details to what ishappening in the different dialogic acts in the IC-model.

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3 REGULAR PAPERS 8

3.2 Tuesday June 3 13:30-14:50 Session 1b Room EDU3Chair: Kjellrun Hiis Hauge

TEACHERS’ EXPERIENCE FROM USINGINTERACTIVE E-BOOKS IN THE CLASSROOM

Esbjörn Hägerstedt1 & Linda Mannila1Tapio Salakoski2,Ralph-Johan Back1

1Åbo Akademi University, Turku, Finland, 2University of Turku,Turku, Finland

The availability of computers and tablets at school level has in-creased during recent years. Nevertheless, studies show that teach-ers experience a lack of pedagogically viable material to use to-gether with the technology in the classroom. This is the case inparticular for mathematics. In this paper we discuss teachers’ ex-perience from using a given kind of interactive learning material intheir mathematics classroom for the first time. Our findings sug-gest that teachers appreciated the opportunity to use new, flexibleand interactive instructional methods for teaching and coachingstudents as well as the possibility to modify the material them-selves. Challenges experienced were e.g. technical problems andthe increase in time needed for teaching (both for getting used tothe new material as well as using new tools etc.).

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ENGINEERING STUDENTS’ USE OF WEB LECTURESIN A LINEAR ALGEBRA COURSE

Ragnhild Johanne Rensaa

Narvik University College

The present paper investigates engineering students’ use of recor-ded lectures published on the web as part of their studying andlearning of linear algebra. The study shows that students utilizethe free access to web lectures preferably by consulting sequentialparts. However, there is a preference to attend live lectures ratherthan watch lectures in real time on the web.

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3 REGULAR PAPERS 9

3.3 Tuesday June 3 13:30-14:50 Session 1c Room EDU244Chair: Per Nilsson

DIALOGUES OF STUDENT TEACHERS DEVELOPINGLESSON PLANS OF MATHEMATICS IN FIELD

PRACTICERaymond Bjuland, Reidar Mosvold & Janne Fauskanger

University of Stavanger

Previous studies indicate that lesson study can be used to stimulatethe development of effective learning environments in prospectiveteacher education. In this paper, we present and discuss the resultsfrom a Norwegian project where lesson study was implemented inthe field practice period in prospective teacher education. We usea dialogical approach to analyze data from a pre-lesson mentoringsession where three student teachers and one mentor teacher par-ticipated. Even though the lesson study intervention had seriouslimitations, the results indicate an increased focus on content andlearning. More focus on knowledge of the particular content to betaught is, however, necessary.

SUPPORTIVE MATHEMATICS LEARNINGCOMMUNITY

Jónína Vala Kristinsdóttir

University of Iceland – School of Education

The study reported on here is a part of a three years collaborat-ive project with seven 5th to 7th grade classroom teachers. Theimplementation of the policy of inclusive education in Iceland andthe growth of migration has welcomed previously excluded stu-dents into schools. As a consequence, teachers are currently facedwith new challenges to differentiate teaching. The study aims atlearning to understand how teachers meet new challenges in theirmathematics classes. It is a qualitative collaborative inquiry intomathematics teaching where teachers research their mathematicsteaching together with a teacher educator. The narrative presen-ted here is of a social pedagogue who works with classroom teach-ers and is representative of the learning that developed withinour community. She gained confidence in teaching mathematics asshe participated in workshops and developed her understanding ofmathematics. The results indicate that collaborative research cansupport teachers in developing their practice when meeting newchallenges in their work.

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3.4 Wednesday June 4 9:00-10:20 Session 2a; Room EDU2Chair: Raymond Bjuland

HOW DO TEACHERS USE TEACHER GUIDES INMATHEMATICS?

Guðný Helga Gunnarsdóttir and Guðbjörg Pálsdóttir

University of Iceland

Curriculum materials in mathematics are an important tool forteachers in preparation, instruction and evaluation. The aim ofthis study is to determine how Icelandic teachers use teacher guidesin preparing for their mathematics teaching and analyse how theysupport the teacher learning. Five teachers in lower grades (1-6)were interviewed and asked about their use of teacher guides. Theguides the teachers were using and the interviews were analysedaccording to a framework developed by Hemmi, Koljonen, Hoel-gaard, Ahl and Ryve. The framework was developed for analysingteacher guides but in this study we also test whether it can beused to analyse the interviews. The study is done in collaborationwith researchers in Sweden and Finland. The Icelandic teachersused two different types of teacher guides which provide differentopportunities to develop professionally. These findings indicatethat the structure and content of the teacher guides influence howthe teachers think of and prepare their teaching. They also sup-port the idea that teacher guides can play an important part inteachers’ professional development.

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HOW IS MATHEMATICS TEACHER GUIDES USEDFOR SUPPORT AND INSPIRATION IN TEACHING?

Linda Ahl, Tuula Koljonen & Lena Hoelgaard

Mälardalen University, Sweden

In this study we investigate how teachers use mathematics teacherguides for support and inspiration in teaching, due to their exper-ience, intentions and abilities. We aim to broaden the knowledgeof how teachers use mathematics teacher guides. Our rationale isthat teacher guides have potential for representing ideas, convey-ing practices, reinforcing cultural norms, and influencing teachers.

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Our second aim is to try out if a framework for designing edu-cative curriculum material can serve as an analytical tool. Theresults show that less experienced teachers demand for a widerscope of content in the teacher guide. More experienced teachersdemand for support in design of teaching. All teachers in our studywant the teacher guide to provide connections between theory andpractice. The framework for writing educative curriculum mater-ials worked out as an analytical tool and it covered all contentdiscussed in interviews.

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3.5 Wednesday June 4 9:00-10:20 Session 2b Room EDU3Chair: Janne Fauskanger

TASKS OF TEACHING AS A FOUNDATION FORINVESTIGATING KINDERGARTEN TEACHERS’

MATHEMATICAL COMPETENCEReidar Mosvold & Per-Einar Sæbbe


Research on the knowledge for teaching mathematics in schoolhas received much attention in the last decades. In comparison,research on kindergarten teachers’ mathematical competence hasbeen scarce. In this paper, we discuss the extent to which thetheories of mathematical knowledge for teaching (MKT) can in-form studies of Norwegian kindergarten teachers’ mathematicalcompetence. Based on discussions of a vignette from a Norwegiankindergarten context, we argue that tasks of teaching can serve asa foundation for such studies, and we also suggest that this is apoint where the theories of MKT and mathematical competenciesintersect.

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PRESCHOOL TEACHERS’ PERCEPTIONS OF THEROLE OF VIDEOS IN PROFESSIONAL DEVELOPMENTOla Helenius1, Maria L. Johansson2, Troels Lange3, Tamsin

Meaney3, Eva Riesbeck3 & Anna Wernberg3

1NCM; 2Luleå University of Technology; 3Malmö University,Sweden

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This paper presents the results of a pilot study using question-naires on the role of video case studies in professional developmentmaterial for preschool and preschool class teachers in Sweden. Al-though the analysis of the results show that some questions inthe questionnaire need adapting, generally it seems that it is pos-sible to find out information about the impact of specific aspectsof a PD programme. The results of the pilot study suggest thatteachers found videos particularly useful in developing their un-derstandings of mathematics in preschools and children’s learningof mathematics in preschools. They found it difficult to make con-nections between the videos and the relationships that they weredeveloping with other preschool teachers, with the children andwith others at their preschools.

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3.6 Wednesday June 4 9:00-10:20 Session 2c Room EDU244Chair: Ragnhild Johanne Rensaa

REFLECTIONS ON UNCERTAINTY ASPECTS IN ASTUDENT PROJECT ON TRAFFIC SAFETY

Kjellrun Hiis Hauge & Rune Herheim

Bergen University College

This paper explores concepts from post-normal science togetherwith Skovsmose’s reflection steps to aid analyses relevant for crit-ical citizenship. In particular, it focuses on the characterising ofuncertainty in knowledge production and on how uncertainty islinked to societal value aspects. A student project on traffic safetyin their local area is described and analysed. The community wherethis took place has experienced cars driving off the road and intothe sea. The findings suggest that the students handle differentsorts of uncertainty and reflect in accordance with several of thereflection steps. Thereby, they practice key competences for crit-ical citizenship. However, the paper concludes that the uncertaintyconcepts may be more useful for issues involving higher complexitythan the analysed student project.

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BUILDING A LOCAL THEORY FOR THE LEARNINGOF EXPERIMENTAL PROBABILITY

Per Nilsson

3 REGULAR PAPERS 13

Örebro University

The approach of this paper builds on the assumption that thereis a need to develop local, domain specific instructional theoriesfor the learning of probability. The aim of the present paper is toexplore the qualitative hypothesis of building such a theory on thecombination of students’ own experimentations with samples andprinciples of variation. By using data from 12-13-year old studentsinvestigating the probability of obtaining a certain colour whenpicking, at random, one piece from a bag with six different coloursof the candy, the paper shows how variations in students’ ownexperimentations with samples can be used as means to explore

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3.7 Thursday June 5 9:00-10:20 Session 3a; Room EDU2Chair: Markku S. Hannula

STUDENT TEACHERS’ WORK ON REASONING ANDPROVING

Ole Enge and Anita Valenta

Sør-Trøndelag University College, Norway

In this study we are analysing student teachers’ justifications ofan algebraic conjecture. The study is based on student teach-ers’ written work on investigation and justification of a statementabout relation between multiples of 6 and multiples of 3. Our re-search question concerns the type of justifications student teachersprovide, the characteristic properties of their justifications and inparticular the way they represent the generality in their work.

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HOW TO SOLVE IT - ON FOCAL PROJECTS ANDEFFECTIVE COMMUNICATION

Hanna Palmér1 & Jorryt van Bommel2

1Linnaeus University Sweden, 2Karlstad University Sweden

This paper reports on a design research study of the implement-ation and development of mathematics teaching through problemsolving in lower primary school. The focus is on the communic-ation between students working with problem solving in groups.

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In the paper episodes of two groups of students working with thesame problem solving task are analysed. When analysing the epis-odes the interaction between the problem solvers rather than onthe learning of each individual problem solver are foregrounded.The results show that students’ expectations about the rules of theactivity are of importance for the communication in the groups tobecome effective.

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3.8 Thursday June 5 9:00-10:20 Session 3b; Room EDU3Chair: Guðný Helga Gunnarsdóttir

EDUCATING MATHEMATICS TEACHER EDUCATORS:A COMPETENCY-BASED COURSE DESIGN

Tomas Højgaard & Uffe Thomas Jankvist

Department of Education, Aarhus University, Denmark

The paper argues for a three-dimensional course design structurefor future mathematics teacher educators. More precisely we de-scribe the design and implementation of a course basing itselfon: the two mathematical competencies of modelling and problemtackling, this being the first dimension; the two mathematical top-ics of differential equations and stochastics, this being the seconddimension; and finally a third dimension the purpose of which isto deepen the two others by means of a didactical perspective.

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MATHEMATICAL AGENCY IN A TRAFFIC SAFETYPROJECT

Rune Herheim & Toril Eskeland Rangnes

Bergen University College, Norway

This paper concerns students’ mathematical agency and teach-ers’ facilitation of such agency in a multidisciplinary project ontraffic safety. The concept of agency is explored. The conversa-tions between students and a teacher are analysed, with emphasison students’ empowerment and the two concepts ‘shared agency’and ‘dance of agency’. Characteristics of students’ agency andteacher’s facilitation of agency are identified and reflected uponwith a focus on critical argumentation.

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3.9 Thursday June 5 9:00-10:20 Session 3c; Room EDU244Chair: Andreas Ryve

USING QUESTIONING DIAGRAMS TO STUDYTEACHER-STUDENT INTERACTION

Markus Hähkiöniemi

University of Jyväskylä, Finland

Previous studies have often created question categories and studiedfrequencies of types of questions. The aim of this study is to de-velop a visual representation to capture how teacher questioningproceeds during a lesson. A group of 29 Finnish student teach-ers participated in a programme about inquiry-based mathematicsteaching in grades 7–12. As part of the programme, they plannedand implemented inquiry-based mathematics lessons. Data wascollected by video recording the lessons. Data was analyzed bycoding teacher questions into probing, guiding, factual and otherquestions. Questioning diagrams representing the flow of questionswere created and used in identifying questioning patterns. Ana-lysis of teacher-student interaction gives further insights into thequestioning patterns.

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MATHEMATICS TEXTBOOKS’ IMPACT ONCLASSROOM INSTRUCTION: EXAMINING THE

VIEWS OF 278 SWEDISH TEACHERSJannika Neuman1, Kirsti Hemmi1, Andreas Ryve1,2 & Marie

Wiberg2

1Mälardalen University, Sweden; 2Umeå University, Sweden

For mathematics teachers to achieve an instruction where studentshave the opportunity to develop different mathematical compet-encies is difficult without access to adequate support. The mostcommonly used supportive tools are by far mathematics textbooks.However, in Sweden, there is very little research available on thecharacteristics of these materials. In this paper we aim to examinethe relationship between teachers’ (K–6) perceived support fromthe curriculum materials and their mathematics instruction, look-ing for patterns associated with commonly used textbooks. Ouranalysis of teachers’ responses to a questionnaire (n=278) showedmajor differences regarding perceived support for teachers using

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different textbooks. This pattern was also evident when the teach-ers were to report about their mathematics instruction.

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3.10 Thursday June 5 13:00-14:20 Session 4a; Room EDU2Chair: Tomi Kärki

THE DIFFICULTIES OF MEASURING TYPES OFMATHEMATICS TEACHERS’ KNOWLEDGE

Janne Fauskanger & Reidar Mosvold


We present a critical discussion concerning the results from ana-lyses of the connections between types of knowledge that are meas-ured by the teachers’ responses to multiple-choice and open-endedquestions. The data material consists of 30 teachers’ responsesto multiple-choice items and corresponding open-ended items. Weused directed content analysis in our analysis of data, and cognitivetypes of teachers’ content knowledge were used as analytical frame-work. The results indicate that the connection between teachers’responses to the multiple-choice items and the open-ended itemsis not always straightforward. In this paper, we discuss possibleexplanations for this.

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MATHEMATICAL KNOWLEDGE FOR TEACHINGAMONG PROSPECTIVE TEACHERS IN MALAWI

Arne Jakobsen1 & Mercy Kazima2

1University of Stavanger, Norway; 2University of Malawi, Malawi

In this article we report on base line data that informed the de-velopment of a five-year project of improving quality and capacityof mathematics teacher education in Malawi (Kazima & Jakob-sen, 2013). 29 mathematics teacher educators at three differentteacher colleges in Malawi answered a questioner about differentaspects of prospective teachers mathematical knowledge for teach-ing (MKT) – with a special focus on the subject matter knowledge.Our findings indicate that prospective teachers struggle with thesame topics as Malawi pupils – as reported in two reports by TheSouthern and Eastern Africa Consortium for Monitoring Educa-tional Quality (SACMEQ II and SACMEQ III). We also find that

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what prospective teachers struggle least with in College, is repor-ted to be most difficult for them to teach at schools.

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3.11 Thursday June 5 13:00-14:20 Session 4b; Room EDU3Chair: Maria L. Johansson

UPPER SECONDARY STUDENTS APPROPRIATINGTHE TOOL OF HARMONIC OSCILLATION: THE ISSUE

OF RESISTANCEMartin Carlsen

University of Agder, Norway

This study analyses four upper secondary school students’ collab-orative small-group problem solving in order to illustrate the roleresistance may play in a process of appropriating the mathemat-ical tool of harmonic oscillation. From a sociocultural perspectivestudents’ appropriation of mathematical tools is characterised byresistance. The study reveals that resistance unfolds as problemsof recalling facets of the mathematical tool and difficulties in hold-ing various elements together when using the tool in a mathemat-ical problem context. The students experience difficulties in mak-ing sense of the relationships between mathematically theoreticaldescriptions of parameters involved in a functional expression ofharmonic oscillation and their counterparts in a problem situation.

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AN ETHNOMATHEMATICAL STUDY OF PLAY INMINECRAFT

Louis Køhrsen1 & Morten Misfeldt2

1Metropolitan University College; 2Aalborg University

This paper explores how children engaged in playing Minecraftin an afterschool program develop mathematical approaches. Theinvestigation is framed as ethnomathematical in the sense that,rather than searching for specific curricular concepts, it exploresthe problem situations and explanatory systems that children de-velop. Aesthetics, symmetry, collaboration, copying, and efficientbuilding strategies all lead to local problem-solving and explanat-ory systems and can therefore be characterised as steps towards

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an ethnomathematics. In the explored example, collaborationbetween the children and the afterschool program’s attitude to-wards children’s collaborative gaming are crucial factors in the wayMinecraft supports the development of mathematical thinking.

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3.12 Thursday June 5 13:00-14:20 Session 4c; Room EDU244Chair: Anu Tuominen

PRESERVING STUDENTS’ INDEPENDENCE BYENCOURAGING STUDENTS’ SELF-EVALUATION

Jonas B. Ärlebäck 1 & Helen M. Doerr2

1Linköping University, Sweden; 2Syracuse University, USA

Over the past twenty years, reform efforts in mathematics teach-ing have emphasized the importance of listening to and develop-ing student ideas in order to achieve the conceptual understandingneeded for problem solving and mathematical reasoning. As teach-ers have worked to enact practices that build on student ideas, theyhave encountered many tensions and dilemmas. In this paper, weput forward the notion that supporting and preserving studentindependence should be a central principle in guiding teachingpractices, potentially providing new ways to address the tensionsand dilemmas of in the moment decision making and actions. Weprovide empirical evidence of teaching practices that encouragestudents’ self-evaluation of their modelling activities in ways thatpreserve their independence as learners and problem solvers.

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MATHEMATICS IN A LITERACY PERSPECTIVE:META AWARENESS ALSO FOR THE WEAK STUDENTS

Bodil Kleve

Oslo and Akershus University College of Applied Sciences

In this paper the increasing social inequalities in Norwegian edu-cational system are taken as a starting point. It is a theoreticalpaper in which it is argued for higher metaawareness for all pupils.Taking a didactic meta perspective, a literacy perspective the ar-gument is presented on three levels which together build on theperspective of metaawareness. First, the level of discourse, primar-ily concerning cultural relations and communities of meaning, is

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considered. The next level is genre, concerning both common cul-tural texts and practices and how meanings are framed in linguisticforms. Finally, arguments regarding the modes of thought are con-sidered. The latter is substantiated by data from own classroomresearch in order to argue that both modes of thought are neededfor all pupils in mathematics.

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3.13 Friday June 6 9:00-10:20 Session 5a; Room EDU2Chair: Anna-Maija Partanen

RADFORD’S LAYERS OF OBJECTIFICATION ASDESIGN PRINCIPLES IN PROVING ACTIVITIES

Andreas Lorange

NLA University College, Norway

The aim of this paper is to give an example of how Radford’s fac-tual, contextual and symbolic layers of objectification can be usedas design principles in connection with proving activities related toarithmetic relations. Because concrete actions are central in Rad-ford’s description of the factual layer of objectification, physicalartefacts will be important in the design of the learning activities.In this case study I follow four groups of teacher students in theirfirst year of their education, and the analysis of their response tothe learning activities is based upon a semiotic-cultural framework.

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STUDENTS’ STRATEGIES FOR MODELLING A FERRISWHEEL

Mette Andresen

Department of Mathematics, University of Bergen, Norway

This study of students’ strategies for modelling was based on anepisode where two upper secondary students in an inquiry basedsetting model the movement of a Ferris wheel with the use of Geo-Gebra. The aim of the study was to identify students’ strategiesfor creative inquiry and to learn about their beliefs.

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3.14 Friday June 6 9:00-10:20 Session 5b; Room EDU3Chair: Uffe Thomas Jankvist

TEACHERS’ USE OF RESOURCES IN AND FORMATHEMATICS TEACHING

Ingvild Lambert Grave & Birgit Pepin

Sør–Trøndelag University College, Trondheim, Norway

There is an increasing amount of resources available for teachingand learning mathematics, traditional as well as digital. How-ever, we know relatively little about how teachers work with themin detail. In this study we have studied how four Norwegianprimary teachers used resources in/for their mathematics teach-ing. Anchored in the analyses of lesson observations, interviewsand particular documents, three (out of five) “usage categories”are discussed in this paper: (1) management of teaching object-ives; (2) teachers‘ use of resources for inspiration; and (3) resourcesteachers use for student work. These categories emphasize the im-portance of understanding interactions between teachers and re-sources; and the ways resources influence many different aspectsof teachers’ work.

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TEACHING BY THE BOOK: WHAT KIND OFCLASSROOM PRACTICE DO THREE DIFFERENT

TEACHER GUIDES FOR YEAR 1 PROMOTE?Lena Hoelgaard & Andreas Ryve

Mälardalen University

This paper investigates three Swedish commercial mathematicsteaching materials for Year1 covering more than 80% of the mar-ket. We specifically focus on the teacher guides and the classroompractice they construe. By taking an educative curriculum mater-ial perspective, the analysis of these three popular mathematicsteaching materials reveals substantial differences in its support fordesigning the classroom practice.

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3.15 Friday June 6 9:00-10:20 Session 5c; Room EDU244Chair: Arne Jakobsen

PRE-SERVICE MATHEMATICS TEACHERS ASRESEARCHERS: THE CENTRALITY OF INQUIRY

Claire Vaugelade Berg

University of Agder, Kristiansand, Norway

This paper reports on a developmental research project which ideasare implemented in an innovative course in mathematics teachereducation. One of the aspects of the course is to invite pre-serviceteachers to act both as teachers and researchers and to reflect ontheir experiences. Results emphasise the importance of a dialect-ical relationship between theory and practice where inquiry plays acentral role. Implications for designing teacher education programare discussed.

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DEVELOPING AN IDENTITY AS A SECONDARYSCHOOL MATHEMATICS TEACHER: A PROSPECTIVE

TEACHER’S NARRATIVEKirsti Rø

University of Agder, Norway

The paper discusses the case of Benedicte, a prospective secondaryschool mathematics teacher undergoing a one-year teacher train-ing program at university. A narrative interview conducted at theend of the first semester of her teacher training reveals a story ofa student teacher in mathematics acting as a broker when crossingboundaries between communities of practice in university teachereducation and school. The case of Benedicte is further an ex-ample of learning during boundary crossing in terms of reflection,which appears as changes in her relationship with mathematicsand mathematics teaching.

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THE HIDDEN AND SALIENT MESSAGES OF THEMATHEMATICS CURRICULUM ABOUT THE

CHANGES IN THE CULTURE OF MATHEMATICSEDUCATION

Silfverberg Harry

University of Turku, Finland

The study examines by textual and linguistic analysis at to whatextent the Finnish mathematics curriculum texts reflect and pro-mote (1) the social turn in mathematics education, and (2) thedifferent components of student’s mathematical proficiency likeprocedural fluency, conceptual understanding, strategic compet-ence, adaptive reasoning and productive disposition. The mainmeans in the linguistic analysis is a so-called verb analysis.

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4 SHORT COMMUNICATIONS 23

4 Short communications

4.1 Tuesday June 3 15:20-17:10 Session 1a Room EDU3Chair: Mette Andresen

CHILDREN’S SPONTANEOUS FOCUSING ONNUMEROSITY AND QUANTITATIVE RELATIONS AS

BUILDING BLOCKS OF MATHEMATICALDEVELOPMENT FROM PRESCHOOL TO THE END OF

PRIMARY SCHOOLMinna M. Hannula-Sormunen1,2, Jake McMullen1 & Erno

Lehtinen1

1Centre for Learning Research and Department of TeacherEducation, University of Turku; 2Turku Institute for Advanced

Studies, University of Turku

Only a part of the development of cognitive skills, such as math-ematical skills takes place during formal learning situations, whilemany opportunities to practice and further develop recently learntskills occur in informal, unguided situations.This brief overview of two separate longitudinal studies will de-tail basic methods and theoretical ideas of investigating individualdifferences in preschool children’s spontaneous focusing on numer-osity (SFON) and spontaneous focusing on quantitative relations(SFOR) in relation to natural and rational number concepts (Han-nula & Lehtinen, 2005; McMullen, Hannula-Sormunen & Lehtinen,in press). These studies are based on a notions that using of num-ber skills such as exact number recognition and proportional reas-oning in natural surroundings is not a totally automatic act andthe amount of practice young children acquire in using their earlynumber skills may differ substantially according to how frequentlythey spontaneously focus their attention on quantitative proper-ties (Hannula & Lehtinen, 2005).A 7-year longitudinal study examined how children’s spontaneousfocusing on numerosity (SFON) and counting skills assessed atthe age of 6 years predict their school mathematics achievement,particularly rational number concept, at the age of 12. The par-ticipants were 36 Finnish children. The results demonstrate thatSFON and counting skills before school age school mathematics,and also rational number understanding in grade 5, even after non-verbal IQ is controlled for.In the second longitudinal study, 25 first graders completed meas-ures of SFOR tendency and a measure of fraction knowledge three


years later. SFOR was found to predict fraction knowledge, sug-gesting that it plays a role in the development of fraction know-ledge.

Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusingon numerosity and mathematical skills of young children. Learn-ing and Instruction, 15, 237-256.McMullen, J., Hannula-Sormunen, M. M., & Lehtinen, E. (inpress). Spontaneous focusing on quantitative relations in the de-velopment of children’s fraction knowledge. Cognition and Instruc-tion.

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A STUDY OF STUDENT ATTENTION IN CLASS USINGMOBILE GAZE TRACKING TECHNOLOGY –

PRELIMINARY RESULTSEnrique Garcia Moreno Esteva & Markku S. Hannula

University of Helsinki, Finland

We will report on a preliminary study of student attention in classmade with the use of mobile gaze tracking technology which will becarried out in the early stages of 2014. Our interest is in trackingstudent attention to various foci, such as a student’s work area, apeer’s work area during collaboration, and the teacher’s present-ation area. We are particularly interested in tracking attentionwhen electronic devices such as tablets and phones are used inclass. Our use of mobile gaze tracking allows us to conduct thestudy in a social environment (classroom as opposed to a labor-atory setting), for which there is little precedent. Mobile gazetracking experiments give rise to questions such as:

• How does the student attention shift between the followingthree main areas of interest: own work, peer (and peer’swork), teacher (board, screen).

• What kinds of attention pathways are related to engaged/productivelearning vs. disengaged student activities?

• What characteristics of the learning environment promotesuch shifts?

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DOES ACCOUNTING FOR MATH MOTIVATION ANDGAMING BACKGROUNDS ADD UP WHEN USING A

SERIOUS GAME IN THE CLASSROOM?Gabriela Rodrìguez Padilla, Boglarka Brezovszky, Tomi

Jaakkola, Jake McMullen & Erno Lehtinen

Centre for Learning Research and Department of TeacherEducation, University of Turku

Serious Games are digital games designed specifically to producelearning outcomes. Number Navigation Game is a Serious Gamewhich aims to develop flexibility and adaptivity in arithmetic strategies.The present study aims to find out what students’ gaming back-grounds and math motivational backgrounds are, and whetherthese have an effect on students’ performance in NNG. Changes instudents’ engagement, self-efficacy beliefs, and beliefs in the pos-itive value of the game will also be studied. This is an ongoinglarge-scale intervention in which forty 4th-6th grade classroomsacross Finland play NNG for ten weeks. Methods used will be:1) pre- and post- surveys on gaming histories and experiences, 2)gaming diaries filled out throughout the intervention, 3) game logdata, and 4) semi-structured interviews with students.

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STUDENTS’ CONCEPT IMAGES ABOUT LINEARFUNCTIONS and four critical points that affect the

graphical viewAnnika Pettersson

Karlstad University

The study is an on-going study which purpose is to better under-stand upper secondary school students’ learning about relationsbetween algebraic and graphical representations of linear func-tions. The graphical representation of linear functions, y=cx+m,are affected by; the parameters c and m, if the coordinate systemis homogenous and also of the domain. The study is a case studyof students working with designed tasks in GeoGebra. The screenand the students’ work have been captured by video and followedup by stimulated recall interviews. The analysis of the data is inprogress. The research questions are: Which concept images (Vin-ner,1983) do the students show about;


1. the relation between parameters and the graphical and algeb-raic representation of linear functions?2. the relation between domain of definition and the graphical andalgebraic representation of linear functions?3. how a change of the scale of the x-axis change the graphical andalgebraic representation of linear functions?

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GENDER DIFFERENCES FAVOURING FEMALES INESTONIAN UNIVERSITY STUDENTS’ VIEWS OF

MATHEMATICSIndrek Kaldo1 & Markku S. Hannula2

1Tallinn University, Estonia; 2University of Helsinki, Finland

This study reports on first-year Estonian university students’ viewsof mathematics. The data were collected from 970 university stu-dents of different disciplines. The participants completed a Likert-type questionnaire that was compiled from previously publishedinstruments. Our research question are: 1) Which are the cor-relations between the variables on the structure of affect; 2) Arethe correlations between different affective variables equal for bothgenders; 3) Do the means between the variables differ for malesand females? The results reveal the importance of Mastery GoalOrientation as central to the structure of their views of mathem-atics. In this study, in five of six dimensions, females hold a morepositive view of mathematics than do male students. Performance-Approach Goal Orientation was the only dimension in which wefound no statistically significant gender difference. In all the otherdimensions, the female respondents expressed a more positive af-fect towards mathematics: They showed a more powerful masteryorientation, valued mathematics more, felt more competent, per-ceived their teacher more positively, and cheated less frequently.

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4.2 Tuesday June 3 15:20-17:10 Session 1b Room EDU244Chair: Ole Enge

POSITIONING TALK AND STORYLINES IN THREEINTRODUCTORY ALGEBRA CLASSROOMS: A

TENTATIVE ANALYSISAnn-Sofi Röj-Lindberg

Åbo Akademi University, Vasa, Finland

Within the on-going VIDEOMAT project videotaped informationhas been collected from four consecutive lessons in three grade 6classrooms in Finland. Among the clearly visible commonalitiesbetween the classrooms found so far are the same teaching con-tent (equations of an arithmetic type), the same textbook and adominance of individual work over group work (Partanen & Kil-hamn, 2013). Analyses of pronouns in talk within the teacher-ledsections of the first lessons show, however, clear differences in thesocial spaces where students could potentially take part in col-lective classroom dialogues (Rowland, 1999). In two classroomsonly 3-4 % of the pronouns used appeared within student-talk. Inthe third class the proportion was close to 30 % (Röj-Lindberg,Partanen & Björkqvist, 2013). The questions I intend to addressis whether this difference reflect different discursive practices, and,whether the difference might as well be interpreted as an indicationof different possibilities to develop mathematical identities consti-tuted through differences in the positioning acts. I will present atentative analyses based on positioning as interactive or reflexiveand defined as “the discursive process whereby selves are located inconversations as observably and subjectively coherent participantsin jointly produced story lines”(Davies & HarrÈ, 1990). Accord-ing to Davies and HarrÈ (1990) the very persons, students andteachers, who engage in discursive practices are also the productsof these practices. Analyses of episodes from each of the threeclassrooms will be discussed.REFERENCESDavies, B., & HarrÈ, R. (1990). Positioning: The discursive pro-duction of selves. Journal for the Theory of Social Behavior, 20,43-63.Partanen, A.-M., & Kilhamn, C. (2013). Distribution of lessontime in introductory algebra classes from four countries. Paperpresented at Symposium of the Finnsh Mathematics and ScienceEducation Research Association in Vasa, Finland, 6-8 November,2013.


Rowland, T. (1999). Pronouns in mathematics talk: power, vague-ness and generalisation. For the Learning of Mathematics, 19(2),19-26.Röj-Lindberg, A.-S., Partanen, A.-M. & Björkqvist, O. (2013).Introduction to equations: Three cases as part of a video study.Poster presented at CERME 8, Antalya, Turkey, 6-10 February,2013.

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“BECOMING EDUCATIONALLY WISE”:MATHEMATICS PRE-SERVICE TEACHERS AND THE

VALUE OF PEER LEARNINGElisabeta Eriksen, Bjørn Smestad, Camilla Rodal,

Yvette Solomon & Annette Hessen Bjerke

Oslo and Akershus University College of Applied Sciences(HiOA), Oslo, Norway

This is part of a larger action research project investigating first-year pre-service teachers’ (PSTs’) experience of school placementat our University College. Various interventions were put in placeon the basis of the findings from our base-line data, which high-lighted PSTs’ difficulties in translating theory into practice; spe-cifically, they did not see the value of the university mathematicscourse as preparation for teaching. However, we found that ad-ditional assessment aimed at enhancing PSTs’ reflection on theconnection between their mathematics pedagogy course and theirteaching in the classroom did not have the benefits that we hopedfor. PSTs continued to express dissatisfaction. Therefore, our nextintervention aimed to use third-year PSTs to mediate reflectionson theory and practice on the assumption that near peers might beable to connect more with the problems the first-years were hav-ing, and give more credibility to our programme. Here we describethis intervention.

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EXPERIENCES FROM DEVELOPING A TOOL TOINVESTIGATE RELATIONSHIPS BETWEEN TEACHERFACTORS AND STUDENT ACHIEVEMENT GAIN IN

MATHEMATICSHege Kaarstein & Guri A. Nortvedt


Department of Teacher Education and School Research,University of Oslo, Norway

Identifying teacher factors that influence student achievement gainis an important part of the quest for effective education. Thispaper presents experiences from an attempt to develop an assess-ment tool to investigate the relationship between three teacherfactors—background, orientation and mathematics pedagogical con-tent knowledge (MPCK)—and students’ achievement gain in math-ematics. The two research questions for the study are: (1) Howcan teacher factors and student achievement gain in mathematicsbe operationalised and measured? (2) What is the relationshipbetween teacher factors and student achievement gain in mathem-atics?

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STUDENT TEACHERS’ REASONING ABOUT THEMATHEMATICAL CONTENT IN PUPILS’ SOLUTIONS

Birgit Gustafsson

Mid Sweden University

The focus of this study is to investigate student teachers’ inter-pretation of the mathematical content in first year upper second-ary school pupils’ solutions of two algebra problem solving tasks.The student teachers were gathered together in six groups with2-3 students in each group, and were asked to discuss and assessthe solutions of two algebra tasks, taken from released PISA 2003tasks. Altogether around 90 pupils solved the two tasks. Based ona first analysis of the solutions, where different solution strategieswere identified, a sample of solutions was chosen and given to thestudent teachers. Each group of student teachers got four solu-tions of each task, representing different strategies, to discuss andassess. My aim of this work is to answer the following researchquestion: What characterizes student teachers’ interpretation ofand communication about secondary school pupils’ solution of al-gebra tasks?

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4.3 Wednesday June 4 13:00-14:30 Session 1c Room EDU244Chair: Annette Hessen Bjerke

POSITIONING THEORY IN CONCEPTUALIZINGIMPLICIT NEGOTIATION OF EPISTEMIC SOCIAL

NORMSAnna-Maija Partanen

University of Lapland, Finland

The Finnish data of the VIDEOMAT project includes video record-ings of lessons from three sixth grade classrooms in the Swedish-speaking part of Finland when equations were introduced to thestudents. During four consecutive lessons, the three teachers of theclasses taught the same content and used the same textbook. Theepistemic expectations for the students were, however, different inthe classrooms when new topics were introduced. For example,in one of the classrooms students were mostly expected to answersimple and concrete questions or reproduce the steps of solvingequations just taught to them. In another classroom, the students


spontaneously posed their own questions and they were even askedto critically examine a solution to an exam question producedby another (unknown) student. I am planning a study on thistopic. A tentative research question would be: What kind of epi-stemic expectations were established for the students in the threeclassrooms? The emergent perspective of Cobb and Yackel (1996)presents classroom social norms as agreed expectations; obligationsand rights, for teacher and students about their own role, other’srole, and the general nature of mathematical activity at school (p.211). I call epistemic social norms those social norms which areabout roles of teacher and students in knowing and learning. Intheir framework, Cobb and Yackel (1996) emphasize explicit ne-gotiation of norms suitable for inquiry mathematics. I see thatwe need to understand both implicit negotiation, or production,and explicit negotiation of norms to be able to support teachersin developing their own classroom cultures. Harré and Langen-hove (1999) suggest that positioning theory offers a more dynamicand process like approach for analyzing mutual expectations ofinteracting people than the concept of role. I am interested inthe possibilities for studying the moment-by-moment assignmentsof rights and obligations this social constructionist framework of-fers. In my mind, this is the same as implicit negotiation of socialnorms. In the presentation, I am going to discuss how the produc-tion of epistemic social norms could be conceptualized using thepositioning theory.

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SOCIAL AND SOCIO-MATHEMATICAL NORMS ANDSTUDENTS’ PERCEPTIONS OF TEACHING

PRACTICESRichard Wester

Malmö University, Sweden

Professional development of mathematics teachers in Sweden hasconcentrated on supporting them to adopt teaching practices whichare less-textbook focussed and require students to be more activelyengaged. Although many teachers have been involved in extens-ive professional development of the kind advocated as best prac-tice by mathematics education researchers (Rodgers, et al., 2007),the impact on classrooms seems to be minimal. In my research,a cohort of Year 9 students were certain that their mathematics


classes were taught in a new way. This particular class of stu-dents were the first cohort to experience a new curriculum and anew grading system which were implemented to support teacherchange, so it was perhaps not surprising that they were very awareof the differences with what had been established practice previ-ously. However, recognition of these differences did not result inan acceptance that these new practices were appropriate ones. Forthe analysis, I have used Cobb and Yackel’s (1996) framework ofsocial and socio-mathematical norms. Originally, this frameworkwas used to analyse mathematics classroom interactions so thatthe taken-as-granted ways of behaving could be recognised andtheir role in determining what occurred in the classroom betterunderstood. In my research, the framework has proved useful inidentifying differences in the students and the teacher’s percep-tions of the appropriateness of the new teaching practices. Al-though it was clear that these differences were likely to producedtensions in the classroom, it is difficult to connect these to con-clusions about the “resistance” that students have to new teach-ing practices. Therefore, the questions that I want to explore inthis short communication are: Are social and socio-mathematicalnorms useful constructs in analysing interview data about math-ematics teaching? And if so, do they need to be modified in anyway to better understand the impact of tensions between teachersand students’ perceptions?

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MATHEMATICS TEACHERS’ MEANING MAKING INAN ONLINE PROFESSIONAL DEVELOPMENT COURSE

Eva-Lena Erixon & Maria Bjerneby Häll

Dalarna University, Sweden

In an ongoing research project we analyse the content of teachers’discussions in an online context, commenting on each other’s video-taped lessons in mathematics. The teachers take part in a continu-ing professional development course for mathematics teachers inprimary school and secondary school. In the first step of ana-lysis we use the framework “Community of inquiry” by Garrison(2011, p. 22). This theoretical framework consists of three interde-pendent elements: social presence, cognitive presence and teach-ing presence; each element defined by categories and indicators toguide the coding of transcripts. A major part of the research usingthis framework has focused on the element of social presence but


few studies have been focusing on all three elements at the sametime. There is still much to understand, from both a theoreticaland practical perspective, regarding interaction between teachingpresence, social presence and cognitive presence, according to Gar-rison (2011, p. 61).

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THE EFFECTS OF WORD PROBLEM ENRICHMENTPROGRAMME ON STUDENTS’ REALISTIC

MATHEMATICAL MODELING: A PILOT STUDYNonmanut Pongsakdi1, Teija Laine2 & Erno Lehtinen1

1Centre for Learning Research and Department of TeacherEducation, University of Turku, 2Centre for Teacher Training

(Turun Matikkamaa), City of Turku Finland

Although a tendency of elementary school students applying super-ficial strategy and excluding realistic considerations during math-ematical modeling has been discussed and studied over decades,this issue still remains as extant literature from various countriescontinuously reports the failure of students to make proper use ofrealistic thinking and reasoning skills in their solution processes.This article provides an overview of a pilot study of word prob-lem enrichment intervention programme (WPE) in support of stu-dents’ realistic mathematical modeling and problem solving skills,and information about the intervention’s effects. The interventioneffectiveness was investigated using a word problem test which in-cluded four problem items. Fourth-, and sixth-graders (N = 170)from elementary schools located in southwest Finland participatedin the study. Results of interaction effects on students’ problemsolving achievement between an experimental group (WPE) anda control group (Traditional) provide support for the hypothesisthat the enriching word problems used in mathematics teachingby supporting teachers in developing their own innovative tasksis promising method to improve students’ realistic mathematicalmodeling and problem solving skills.

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4.4 Thursday June 5 14:40-16:00 Session 2a Room EDU3Chair: Ann-Sofi Röj-Lindberg

SPONTANEOUS FOCUSING ON QUANTITATIVE


RELATIONS PREDICTS THE REPRESENTATION OFRATIONAL NUMBER MAGNITUDES

Jake McMullen1, Minna M. Hannula-Sormunen2 &Erno Lehtinen1

1Centre for Learning Research and Department of TeacherEducation, University of Turku; 2Turku Institute for Advanced

Studies, University of Turku

Despite their crucial importance, most students have serious diffi-culties in learning about rational numbers (McMullen et al., 2014).Much is known about the difficulties students face with under-standing rational number concepts; however, there is little evid-ence of relevant contributors to learning about these topics. Dif-ferences in the spontaneous focusing of attention on mathematicalaspects have been found to be key contributors to the develop-ment of mathematical skills. In particular, Spontaneous Focus-ing On quantitative Relations (SFOR) has been found to predictthe development of rational number conceptual knowledge in lateprimary school children (McMullen et al., in press). Recent re-search has investigated the role of magnitude representations inthe development of understanding of rational numbers (Siegleret al., 2011). The present study aims to investigate the role ofconceptual knowledge of rational numbers and SFOR tendencyin rational number. This study reports on 251 Finnish students(136 Female) who were in grades three through five at the begin-ning of the study. At the first time point, in winter 2012 parti-cipants completed measures of SFOR and rational number concep-tual knowledge. At a second time point, in spring 2013, measuresof arithmetic fluency, non-verbal intelligence, and a number lineestimation task, which included fractions and decimals as well aswhole numbers, were completed. Preliminary results reveal thatSFOR tendency predicts fraction estimation proficiency, but notdecimal or whole number, even after taking into account rationalnumber conceptual knowledge, arithmetic fluency, and non-verbalintelligence.

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FINDING IN-BETWEEN FRACTION, A CONTINGENTMOMENT IN GRADE 7

Bodil Kleve & Ida Heiberg Solem


Oslo and Akershus University College of Applied Sciences,Norway

Earlier research have suggested ways in which teachers may re-spond when a student suggests how to find a fraction between twogiven fractions (Bishop, 1976; Rowland & Zazkis, 2013; Stylian-ides & Sylianides, 2010). However, data from classroom discus-sions have not been presented from these studies. In a mathem-atics lesson about fractions, decimal numbers and percentages ina7th grade in Norway, which we observed, this problem aroused,and data from this classroom event create the background for thispresentation. We will discuss how the teacher, Kim, orchestrateda whole class discussion when searching for a fraction between3/5 and 4/5. Focus in our presentation will be how this situationopened up for students’ contributions and different hypothesesabout adding nominators and denominators to find an in-betweenfraction. Our research questions are:

• What mathematizing activities took place in discussing theuse of ’mediant’ (add numerators and denominators) to findan in-between fraction?

• How did the teacher’s mathematical knowledge in teachingsurface in the discussion?

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SELF-CONCEPT AND MOTIVATION INMATHEMATICS

Emmanuel Adu-Tutu Bofah and Markku S. Hannula

Stockholm University, Sweden

The purpose of the study is to determine the extent to which stu-dents’ self-concept in mathematics could be explained from stu-dents’ math self-confidence, teacher quality, and family encour-agement in mathematics. The data involves 12th-grade students(N = 2034, M = 18.49, SD = 1.25; 58.2% girls). The resultsindicated that self-confidence, teacher quality and family encour-age are significant predictors of students self-concept. Moreover,student self-confidence mediate between students family encour-agement and teacher quality.

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NUMBER NAVIGATION DIGITAL STRATEGY GAMEFOR TRAINING ADAPTIVE EXPERTISE WITH

ARITHMETIC PROBLEM SOLVINGBoglárka Brezovszky, Jake McMullen, Gabriela Rodriguez &

Erno Lehtinen

Centre for Learning Research, Department of Teacher Education,University of Turku, Finland

Providing students with adaptive and flexible environments for ex-ploration with various number patterns can be a promising methodfor developing arithmetic flexibility and adaptive expertise witharithmetic problem solving (Threlfall, 2009). Digital games havea large potential for creating these environments; however, up todate, there are very few complex games that would target morethan the drill and practice of already acquired basic calculation flu-ency (Devlin, 2011). Number Navigation Game (NNG) is a digitalstrategy game which was developed with the aim to promote thedevelopment of adaptive expertise with flexible arithmetic problemsolving. Pilot studies conducted with NNG show promising resultsregarding players’ engagement in strategic exploration with variousalternative number-operation combinations and number patternsduring gameplay (Brezovszky et al., 2013). Preliminary analysesof additional pilot data suggest a connection between high levels ofstrategic exploration during gameplay and paper-pencil measuresof adaptive expertise with arithmetic. A large-scale randomizedexperimental study is currently conducted with the aim to provideevidence of the effects of gameplay with NNG on the developmentof arithmetic problem solving. Participants are 600 4th-6th gradestudents from Western-Finland area. Teachers are randomly di-vided into experimental and control groups. Both groups com-plete paper-pencil tests measuring arithmetic operation produc-tion, arithmetic conceptual understanding, and arithmetic fluencybefore and after the 10 weeks training with NNG. Students playindividually or in pairs for avg. 30 minutes per session, 2 times aweek. Detailed log data on students’ game performance and pro-gress is also collected. Preliminary results of the experiment willbe presented and discussed in more detail during the conference.

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4.5 Thursday June 5 14:40-16:00 Session 2b Room EDU244Chair: Lovisa Sumpter

EXPLORING THE EFFECT OF A SYSTEMATIC


VARIED LESSON DESIGN AS A TEACHING METHODIN MATHEMATICSLaurence Russell

MidSweden University

The study presented in this paper explores the student percep-tion of a specific lesson design and teaching method in compulsoryschool mathematics. The initial research goal is to answer thequestion of whether students find the lesson design a favorableteaching method and if it therefore affects knowledge achievementand improves self-concept such as motivation and the desire tolearn mathematics.

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WHEEL ALGEBRA: LEARNING MATHEMATICS WITHA DOUBLE-WINCH TOOL

Liubov Medvedeva & Pauline Vos

University of Agder, Kristiansand, Norway

Many studies show that algebra is perceived by pupils as an ab-stract, difficult to understand subject with almost no connectionsto every-day reality. Therefore, the motivation for this researchwas to find out what helps to make this abstract topic more mean-ingful to pupils and how we can assist them in discovering thatalgebra can be useful for establishing connections between differ-ent variables. Using mechanical tools with pairs of weights thatmove with different velocities could be promising for instructionalpurposes. First of all, the different velocities of the weights makevariables and their relationship tangible. Secondly, pupils knowsome physical properties of the tool from non-mathematical life ex-periences, and this can support their learning of algebra. Thirdly,the unknown properties of the device arouse curiosity thus helpingto keep the pupils motivated. Finally the pupils can be activelyengaged by investigating something themselves.

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DEVELOPING AN INSTRUMENT: SELF-EFFICACY INTEACHING MATHEMATICS

Annette Hessen Bjerke


Oslo and Akershus University College of Applied Sciences(HiOA), Norway

Building on Bandura’s original definition of self-efficacy, Tschannen-Moran and Hoy (2001) defined self-efficacy in teaching as a teacher’s“judgment of his or her capabilities to bring about desired out-comes of student engagement and learning,. . . ” (p. 783). Applyingthis definition to teaching mathematics, a ‘Self-efficacy in teachingmathematics’ (SETM) instrument, designed for use with element-ary pre-service teachers (PSTs), was developed and validated usingRasch modelling. The SETM-instrument was developed as part ofan ongoing study, where the intended use of the instrument is two-fold. First, it provides part of data needed to describe novice PSTs’self-efficacy as a potential teacher in mathematics. Additionally, itwill play a role in assessing how PSTs’ SETM develops after nearlytwo years of teacher training in mathematics.

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STUDENTS’ VIEWS ON MATHEMATICALCHALLENGES IN WORKING AS A TEACHER

Andreas Bergwall & Malin Knutsson

Örebro University and Mälardalen University, Sweden

Many frameworks for teacher knowledge describe the work of amathematics teacher as highly complex and therefore requires spe-cialized competences (e.g. Rowland & Ruthven, 2011). At thesame time, countries around the world have difficulties in recruit-ing highly qualified students to teacher education. Furthermore,teacher educators often express that prospective teachers questionthe amount and level of mathematics that they have to learn. Re-search on views about teaching often focuses on teachers’ views(Philipp, 2007). Less is known about students’ views about work-ing as a teacher and how those might influence their choice of aprofession. The focus of this study is on the views that studentshave on mathematical challenges associated with the work of amathematics teacher, when compared to other occupations.

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5 SYMPOSIUM WEDNESDAY JUNE 4 13:00-14:30 ROOM EDU2 39

5 Symposium Wednesday June 4 13:00-14:30 RoomEDU2

5.1 The theme of the symposium

GENDER AND MATHEMATICS IN THE NORDICCOUNTRIES: WHERE ARE WE NOW?

Eva Norén1, Yvette Solomon2,3(Chair), Lovisa Sumpter4 &Katarina With2,5

1Stockholm University, 2Høgskolen i Oslo og Akershus, OsloNorway, 3Manchester Metropolitan University, Manchester UK,

4Höskolan Dalarna, Sweden, 5Veitvet Skole, Oslo, Norway

OBJECTIVESIn this symposium we explore issues of gender in mathematics inthe Nordic countries. We interrogate the impact of equity dis-courses on access to mathematics in Sweden and Norway. Ouraim is to ask ‘Where are we now?’: what progress has been madein enacting gender equity in the Nordic countries with regard tomathematics education? What might the threats be to genderequity?OVERVIEW AND SIGNIFICANCEResearch in mathematics education reports that many girls andwomen develop identities of exclusion, even when they are suc-cessful, and that women’s participation in mathematics can beseen as relating to how their mathematical identities function andoperate (or are perceived to function and operate) within the so-cial and discursive structure of mathematics activities (Solomon,2008; 2012). However, the Nordic countries are seen as significantleaders in the area of gender equity. In this symposium we ex-amine the extent to which equity discourses impact on identities,positioning, and participation.STRUCTUREThis symposium will consist of three papers which address differentphases of our engagement with mathematics. We begin with EvaNorén’s paper focusing on children’s early experience of classroomdiscourse: “Positioning of Girls and Boys in a Primary Mathem-atics Classroom”. Katarina With and Yvette Solomon’s paper“Choosing Mathematics in Norway and England: Discourses ofGender, Equity and Choice”, focuses on students’ account of choos-ing post-compulsory mathematics. We close with Lovisa Sumpter’spaper focusing on women’s sense of belonging in post-graduate re-search mathematics and academia, “Why Sarah Left Academia”.


We will invite the audience to participate in a final discussion on‘Where are we now?”

ReferencesSolomon, Y. (2008). Mathematical literacy: developing identitiesof inclusion. New York: Routledge.Solomon, Y. (2012). Finding a voice? Narrating the female self inmathematics. Educational Studies in Mathematics, 80, 171-183.

5.2 Symposium paper: Eva Norén

POSITIONING OF GIRLS AND BOYS IN A PRIMARYMATHEMATICS CLASSROOM

Eva Norén

Stockholm University

This paper deals with how various discourses impact on girls andboys positions as active and engaged mathematics learners in a firstgrade classroom. Students and teachers may themselves adopt aposition exercising a specific discourse, or they may assign posi-tions to others. The discursive practices in this classroom encour-aged the boys’ positions as engaged mathematics learners morethan the girls even though girls’ experiences from out of schoolwere valued as starting points for learning mathematics.

5.3 Symposium paper: Katarina With & Yvette Solomon

CHOOSING MATHEMATICS IN NORWAY ANDENGLAND: DISCOURSES OF GENDER, EQUITY AND

CHOICEKatarina With1,2 & Yvette Solomon2,3

1Veitvet Skole, Oslo Norway, 2Høgskolen i Oslo og Akershus, OsloNorway, 3Manchester Metropolitan University, Manchester UK

In many countries, including Norway and England, there is aconcern about the low number of students continuing with post-compulsory mathematics, and especially the low number of girls.Drawing on socio-cultural perspectives on the construction of iden-tity, this paper explores the role of cultural models in choosingpost-compulsory mathematics in the context of contrasts betweenNorwegian and English education systems, practices and policies.


Specifically, we seek to interrogate the extent to which a Norwe-gian public discourse of egalitarianism, particularly gender equity,impacts on girls’ and boys’ accounts of choosing mathematics. Weconclude that there are more similarities than differences betweenthe two countries, and note the potential impact of neo-liberaldiscourses in eroding Norwegian equity discourses.

5.4 Symposium paper: Lovisa Sumpter

WHY SARAH LEFT ACADEMIALovisa Sumpter

School of Education and Humanities, Dalarna University, Sweden

This paper explores why some Swedish female mathematicians de-cide not to work in academia. The stories of four women weremerged into one narrative. Sarah describes the life as a femalePhD student in a mathematics department as a positive experi-ence. The reasons why she decided not to stay at the universitywere (1) the difficulty of getting a job, and (2) her wanting towork with applications and problem solving more than developingtheory.

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6 WORKING GROUPS 42

6 Working groups

6.1 Tuesday June 3 15:20-16:20Working group 1 Room EDU2Chairs: Guðný Gunnarsdóttir & Guðbjörg Pálsdóttir

WORKING GROUP ON RESEARCH ON CURRICULUMMATERIALS

Guðný Helga Gunnarsdóttir & Guðbjörg Pálsdóttir

University of Iceland

A network for research on mathematics textbooks in the Nordiccountries has been operating during the last three years (2011-2014). The network is funded by NordForsk. The network con-sists of researchers from Estonia, Finland, Iceland, Latvia, Norway,Sweden and some international experts from the Netherlands andGermany. The network is lead by professor Barbro Grevholm, Uni-versity of Agder (Grevholm, 2011). The network has collaboratedand organized seminars and workshops on mathematics textbooksresearch every year and the last workshop will be held in Reykjavík in May 2014.

The main aim of the network was to increase the Nordic and Balticcollaboration in research on mathematics textbooks with implic-ations for teachers’ teaching, students’ learning, and decisions bypolicymakers and publishing houses. Researchers in the networkhave collaborated in many ways and the network is now workingon papers to be published in a thematic issue of NOMAD.

Members of the network are interested in continuing their col-laboration and want to invite others to join the group. The aim ofthe working group is to provide insight into the work of the net-work and to discuss how researchers in this area can continue theircollaboration now when the period of funding by NordForsk is fin-ished. The network has gathered material and information aboutdifferent aspects of textbooks and curriculum materials, their his-tory and usage. Now when IT is getting more accessible to bothteachers and students it is important to follow and do researchon the development of curriculum materials In the working groupparticipants in the network will present some of their work. Theorganizers will introduce some ideas about how to proceed andstart up discussions about possibilities for future collaboration inthis area.

6 WORKING GROUPS 43

References

Grevholm, B. (2011). Network for research on mathematics text-books in the Nordic countries. Nordic Studies in MathematicsEducation, 16(4), 101–112.

6 WORKING GROUPS 44

6.2 Wednesday June 4 13:00-14:00 Working group 2 RoomEDU3Chairs: Simon Goodchild & Frode Rønning

TEACHING MATHEMATICS AT HIGHER EDUCATIONSimon Goodchild1 & Frode Rønning2

1University of Agder; 2Norwegian University of Science andTechnology

An increasing attention towards learning and teaching of mathem-atics in higher education, also in research, can be observed (Abdul-wahed, Crawford, & Jaworski, 2012). This is to some extent motiv-ated by the society’s need and desire to educate more people in Sci-ence, Technology and Mathematics combined with a concern aboutthe level of performance of students as they transfer from schoolto higher education. International studies (e.g. TIMSSAdvanced)show that both Norwegian and Swedish students1 perform wellbelow the international average in mathematics (Mullis, Martin,Robitille, & Foy, 2009). In higher education one can observe a con-siderable drop out rate in study programmes requiring strong com-petencies in mathematics, and typically the mathematics coursesin the programmes are seen as particularly challenging. Recentlyseveral new projects have been launched in Norway to addressissues concerned with teaching and learning of mathematics inhigher education, Two examples of such projects are the Centre forResearch, Innovation and Coordination of Mathematics Teaching:MatRIC, based at the University of Agder and run in collaborationwith partners, and the project Kvalitet, tilgjengelighet og differen-siering i grunnutdanningen i matematikk2: KTDiM, based at theNorwegian University of Science and Technology (NTNU). Tradi-tionally teaching of university mathematics has been much aboutpresenting the subject matter, without much variety in modes ofpresentation. Acknowledging that students come to higher educa-tion with different background and motivation, one will come tothe conclusion that a stereotype way of teaching will have diffi-culties providing adequate education to a group of students thatshow increasing variation (Henderson & Broadbridge, 2007). Thesteadily increasing range of possibilities in using technology (video,digital and web-based technologies) seems to offer interesting op-tions when it comes to adapt to students’ varying background andmotivation. The aim of this workshop is to discuss and work onsome issues related to the teaching of mathematics in higher edu-cation, and to identify some questions that are worthwhile lookingcloser into. Some questions could be

6 WORKING GROUPS 45

– What are the necessary features of mathematics at highereducation that distinguishes the subject from students’ priorexperience in school?

– How do the special characteristics of mathematics influencemathematical1 2 education at higher education?

– What are the ’conditions’ of/for innovation in mathematicsteaching, learning and assessment at higher education?

Another goal is to establish a network of researchers in mathemat-ics education who are focusing on the issues and quality of teachingand learning mathematics in higher education. The workshop willbe organised according to the following points.

1. The Workshop commences with a very short presentation ofthe activities of MatRIC and NTNU/ KTDiM and openingfor other participants to provide brief descriptions of pro-jects in teaching higher education mathematics at their insti-tutions/centres. This will lead the research questions outlineabove. (15 minutes)

2. Small group discussion focusing on the proposed questions(25 minutes).

3. Summarizing from group discussion and initial planning ofa network that will work towards a symposium on TeachingMathematics at higher education for the next NORMA con-ference. (20 minutes)

In preparation for the workshop participants may familiarize them-selves with the document “A Framework for Mathematics Cur-ricula in Engineering Education” (Alpers, 2013).

References

Abdulwahed, M., Jaworski, B., & Crawford, A. R. (2012). In-novative approaches to teaching mathematics in higher education:A review and a critique. Nordic Studies in Mathematics Educa-tion, 17(2), 49-68.

Alpers, B. (Ed.). (2013). A framework for mathematics curriculain engineering education. Brussels: SEFI. Retrieved fromhttp : //www.sefi.be/wpcontent/uploads/Competency%20based%20

1No other Nordic countries participated in TIMSS-Advanced 2008.2Quality, availability and differentiation in basic teaching of mathematics.

6 WORKING GROUPS 46

curriculum%20incl%20ads.pdf

Henderson, S., & Broadbridge, P. (2007). Mathematics for 21stcentury engineering students. In Proceedings of the 2007 AaeEConference, Melbourne (pp. 1-8). Retrieved fromhttp : //ww2.cs.mu.oz.au/aaee2007/papers/invHend.pdf

Mullis, I. V. S., Martin, M. O., Robitaille, D. F., & Foy, P. (2009).TIMSS Advanced 2008 International Report: Findings from IEA’sStudy of Achievement in Advanced Mathematics and Physics inthe Final Year of Secondary School. Chestnut Hill, MA: TIMSS& PIRLS International Study Center.

6 WORKING GROUPS 47

6.3 Thursday June 5 14:40-15:40 Working group 3 RoomEDU2 Chair:Reidar Mosvold

POTENTIAL USES OF SOCIAL MEDIA IN AND FORMATHEMATICS EDUCATION RESEARCH

Reidar Mosvold

University of Stavanger, Norway

“Everyone” uses social media, and Twitter and Facebook are ex-amples of popular social networks. In this working group, possib-ilities and pitfalls for using social media in and for mathematicseducation research will be discussed.INTRODUCTION Social media has become increasingly popularin the last years, and academics have also (slowly) started adoptingit – mainly to connect with other people (e.g., Gruzd, Staves, &Wilks, 2012). Social media and networks are mainly about commu-nication, and the novelty of social media lies in the virtual natureof the communities and networks in which the communication andinterchange of information takes place. Although social networkshave a recent origin, the very idea of communicating in settingsother than face to face is, of course, far from recent. Research-ers – and human beings in general – have embraced this idea forcenturies. An example is the scientific journal – although we donot always think of it as a virtual community. Indeed there aredifferences between publishing an article in e.g. Educational Stud-ies in Mathematics and publishing a 140 character long message(tweet) on Twitter. The differences are, however, mainly relatedto the qualities of the output media – or virtual community – andnot so much to the communication act itself. It can be argued,and rightfully so, that publishing a scientific article is more time-consuming and challenging than publishing brief messages on socialnetworks like Twitter, Facebook, Google+, etc. Both activities arestill, however, acts of communication, and both acts of communic-ation take place in some kind of virtual community or network.Since our activities, as researchers, evolve around acts of commu-nication, we should carefully consider the benefits and pitfalls ofthe different possible arenas in which our scientific communicationcan take place. Media consumers and creators have adopted socialnetworks in general and Twitter in particular en masse (Lasorsa,Lewis, & Holton, 2012), but researchers in mathematics educa-tion seem to be more reluctant adopters. Some studies investigatethe use of education researchers’ use of social media in general(Gruzd et al., 2012; Veletsianos & Kimmons, 2013) and Twitter

6 WORKING GROUPS 48

in particular (e.g., Veletsianos, 2012). In mathematics educationresearch journals, however, little attention is given to these top-ics. With this background, I propose to organize a working groupat NORMA 14 with a focus on discussing potential uses of socialmedia in and for mathematics education research. I suggest thatTwitter – which is one of the largest and most common social net-works – can serve as a starting point (but not an end point) forthe discussion. The following research question will be raised inthe working group: What are the potentials (and pitfalls) of us-ing social media in and for mathematics education research? OR-GANISATION OF THE WORKING GROUP The working groupsession will be initiated by a short presentation of some issues thathave been raised in research on Twitter in relation to education ingeneral – since virtually no research so far has been reported onuse of Twitter in mathematics education. In this short synthesisof previous research, the following themes will be highlighted:

• research on teachers’ and education researchers’ use of Twit-ter

• research on Twitter networking

• research on the content of tweets (Twitter messages)

With this overview of the existing research on Twitter use in edu-cation as a background and illustrative example, a discussion ofpossible uses of social media in and for mathematics educationresearch will be initiated. The following topics are proposed fordiscussion:

• possibilities (and pitfalls) of using social media for networkingand collaboration in mathematics education

• possibilities (and pitfalls) of using social media for commu-nication and mining of research

• possibilities (and pitfalls) of conducting research on social me-dia (e.g., Twitter content) or uses of social media

• possible theoretical and/or methodological approaches for re-search on social media

An overall aim of the activities in the working group is to explorepossibilities for initiating collaborative research and writing pro-jects on the topic, and the final part of the working group sessionwill be used for discussing this.

6 WORKING GROUPS 49

References

Gruzd, A., Staves, K., & Wilk, A. (2012). Connected scholars:Examining the role of social media in research practices of facultyusing the UTAUT model. Computers in Human Behavior, 28,2340–2350.

Lasorsa, D.L., Lewis, S.C., & Holton, A. (2012). NormalizingTwitter: Journalism practice in an emerging communication space.Journalism Studies, 13(1), 19–36.

Veletsianos, G. (2012). Higher education scholars’ participationand practices on Twitter.Journal of Computer Assisted Learning,28(4), 336–349.

Veletsianos, G. & Kimmons, R. (2013). Scholars and faculty mem-bers’ lived experiences in social networks. Internet and HigherEducation, 16, 43–50.

7 MAP OF THE CONFERENCE VENUE 50

7 Map of the conference venue

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Index

Ahl Linda, 10Ahtineva Aija, 2Andresen Mette, 19, 23

Back Ralph-Johan, 8Berg Claire Vaugelade, 21Bergwall Andreas, 38Bjerke Annette, 30, 37Bjerneby Häll Maria, 32Bjuland Raymond, 9Bofah Adu-Tutu, 35van Bommel Jorryt, 2, 13Brezovszky Boglarka, 25, 36

Carlsen Martin, 2, 17

Dahl Søndergaard Bettina, 2Doerr Helen, 4, 18

Ejersbo Lisser, 2Enge Ole, 13, 27Eriksen Elisabeta, 28Erixon Eva-Lena, 32Esteva Garcia, 24

Fauskanger Janne, 9, 11, 16

Goodchild Simon, 44Grave Ingvild, 20Gunnarsdóttir Guðný, 2, 10,

14, 42Gustafsson Birgit, 30

Hannula Markku S., 2, 13,24, 26, 35

Hannula-Sormunen Minna,23, 34

Hauge Kjellrun, 12Helenius Ola Lena, 11Hemmi Kirsti, 15Herheim Rune, 12, 14Hägerstedt Esbjörn, 8Hähkiöniemi Markus, 7, 15

Højgaard Tomas, 14Hoelgaard Lena, 10, 20

Jakobsen Arne, 16, 21Jankvist Uffe, 7, 14, 20Johansson Maria, 11, 17

Kaarstein Hege, 28Kaldo Indrek, 26Kankare Satu, 2Kazima Mercy, 16Kilhamn Cecilia, 2Kleve Bodil, 18, 34Knutsson Malin, 38Koljonen Tuula, 10Kristinsdóttir Jónína, 9Kurvits Jüri, 2Køhrsen Louis, 17Kärki Tomi, 2, 16

Laine Teija, 33Lange Troels, 11Lehtinen Erno, 3, 23, 25, 33,

34Lorange Andreas, 19

Mannila Linda, 8McMullen Jake, 23, 25, 34Meaney Tamsin, 11Medvedeva Liubov, 37Misfeldt Morten, 6, 17Mosvold Reidar, 9, 11, 16, 47

Neuman Jannika, 15Nilsson Per, 12Niss Mogens, 7Norén Eva, 39, 40Nortvedt Guri, 28

Palmér Hanna, 13Partanen Anna-Maija, 19Partanen Anna-Maija , 30Pepin Birgit, 2, 20

51

INDEX 52

Pettersson Annika, 25Pongsakdi Nonmanut, 33Pálsdóttir Guðbjörg, 2, 10,

42

Rangnes Toril, 14Rensaa Ragnhild, 8, 12Riesbeck Eva, 11Rodal Camilla, 28Rodrìguez Padilla Gabriela,

25, 36Russell Laurence, 37Ryve Andreas, 15, 20Rø Kirsti, 21Röj-Lindberg Ann-Sofi, 27,

33Rønning Frode, 44

Sæbbe Per-Einar, 11

Salakoski Tapio, 8Silfverberg Harry, 2, 22Sjöblom Marie, 7Smestad Bjørn, 28Solem Ida, 34Solomon Yvette, 28, 39, 40Strømskag Heidi, 4Sumpter Lovisa, 36, 39, 41

Tuominen Anu, 2, 18

Valenta Anita, 13Vos Pauline, 37

Wernberg Anna, 11Wester Richard, 31Wiberg Marie, 15With Katarina, 39, 40

Ärlebäck Jonas, 18

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