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Johansson, Helenaorcid.org/0000-0002-5981-3722

Open this publication in new window or tab >>Grade 6 teachers’ objectification of the algebra discourse### Johansson, Helena

### Kilhamn, Cecilia

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Proceedings of the 43^{rd} Conference of the International Group for the Psychology of Mathematics Education / [ed] Graven, M., Venkat, H., Essien, A. & Vale, P, Pretoria, South Africa: PME , 2019, Vol. 4, p. 51-51Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Pretoria, South Africa: PME, 2019
##### National Category

Educational Sciences
##### Identifiers

urn:nbn:se:miun:diva-36817 (URN)978-0-6398215-6-6 (ISBN)
##### Conference

The 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, July 7-12, 2019.
#####

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Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-13Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.

Nationellt Centrum för Matematikutbildning, NCM, Göteborgs Universitet.

In tackling the well-known challenges of learning algebra, Sfard (2008) highlights the need for objectification of mathematical discourse. Teachers can support students in this objectification by modelling the discourse they want students to develop (Sfard, 2016). Our study uses Sfard’s (2008) definition of objectification in order to analyse grade 6 teachers’ algebra discourse. The purpose is to understand if and how objectification occurs in the discourse when algebra is introduced, and how this might influence students’ understanding of algebra. Data consist of video recordings from three Swedish teachers’ introductory lessons in algebra with 12-year old students, with four consecutive introductory algebra lessons for each teacher. The recordings are from a larger international video study. Teachers’ discourse about algebraic entities was analysed concerning word-use, visual mediators, routines, and endorsed narratives (Sfard, 2008). Preliminary results show that there were mainly three algebraic entities that were in focus in the lessons, described as equations, expressions and variables. Generally, we note that as more formal algebraic symbols were introduced and used by two of the teachers, the more objectified became their discourse. This objectification did not occur in the third teacher’s discourse, which lacked an early introduction of formal symbols. This could imply that symbols reinforce objectification. Particularly, the progression of the objectification process concerning expressions was very prominent over the course of one teacher’s four lessons. The word use clearly changed from treating the introduced symbols as processes, where an expression was “to describe something with the help of a variable”; to objects, where an expression was “a system of symbols” that “could be used in an equation”. A more comprehensive discussion of the results, including routines and endorsed narratives, will be included in our presentation.

Open this publication in new window or tab >>Objectification of upper-secondary teachers’ verbal discourse in relation to symbolic expressions### Johansson, Helena

### Österholm, Magnus

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028, article id 100722Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Keywords

Alienation, Mathematical learning, Mathematical symbols, Natural language, Reification, Word use
##### National Category

Other Mathematics Didactics
##### Identifiers

urn:nbn:se:miun:diva-36841 (URN)10.1016/j.jmathb.2019.100722 (DOI)
#####

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##### Note

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Umeå universitet, Umeå.

Research literature points to the importance of objectification when learning mathematics, and thereby in the discourse of mathematics. To increase the field's understanding of aspects and degrees of objectification in various mathematical discourses, our study uses the combination of two sub-processes of objectification in order to analyse upper-secondary teachers’ word use in relation to any type of mathematical symbols. Our results show that the verbal discourse around symbols is very objectified. This can put high demands on students understanding of their teacher, since it might be needed that the students have reached a certain degree of objectification in their own thinking in order to be able to participate in a more objectified discourse. The results also show that there exist patterns in the variation of the degree of objectification, in particular that the discourse tends to be more objectified when more familiar symbols are used. This exploratory study also reveals several phenomena that could be the focus of more in-depth analyses in future studies.

Available online 3 August 2019

Available from: 2019-08-13 Created: 2019-08-13 Last updated: 2019-08-13Bibliographically approvedOpen this publication in new window or tab >>Glömska eller ytliga fysikkunskaper: Fördjupad analys av svenska elevers sjunkande fysikresultat i TIMSS Advanced 2015### Johansson, Helena

### Oskarsson, Magnus

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.### Nyström, Peter

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##### Abstract [sv]

##### Place, publisher, year, edition, pages

Stockholm: Skolverket, 2018. p. 64
##### Series

Övriga trycksaker
##### National Category

Didactics Other Natural Sciences
##### Identifiers

urn:nbn:se:miun:diva-32694 (URN)978-91-7559-315-9 (ISBN)
#####

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Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2019-08-06Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.

Göteborgs Universitet.

TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps-och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Resultaten visade att Sverige förbättrat sina resultat i matematik medan resultaten i fysik försämrats. Dessa resultat brukar normalt följas åt och denna rapport undersöker möjliga orsaker till de sjunkande fysikresultaten i TIMSS Advanced.

Open this publication in new window or tab >>Teachers’ and students’ perception of the gap between secondary and tertiary mathematics### Johansson, Helena

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.### Österholm, Magnus

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.### Flodén, Liselott

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.### Heidtmann, Pia

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2018 (English)In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L., Umeå, Sweden: PME , 2018, Vol. 5, p. 77-77Conference paper, Oral presentation with published abstract (Refereed)
##### Place, publisher, year, edition, pages

Umeå, Sweden: PME, 2018
##### National Category

Educational Sciences
##### Identifiers

urn:nbn:se:miun:diva-36816 (URN)
##### Conference

The 42nd Conference of the International Group for the Psychology of Mathematics Education, Umeå, Sweden, July 3-8, 2018
#####

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Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-13Bibliographically approved

Open this publication in new window or tab >>Dependence between creative and non-creative mathematical reasoning in national physics tests### Johansson, Helena

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 22, no 2, p. 93-119Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Creative mathematical reasoning, Descriptive statistics, Imitative reasoning, Mathematical Reasoning Requirements, National tests, Physics tasks, Upper secondary school.
##### National Category

Didactics Other Mathematics
##### Identifiers

urn:nbn:se:miun:diva-32687 (URN)
#####

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Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17Bibliographically approved

Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.

It is known from previous studies that a focus on rote learning and procedural mathematical reasoning hamper students’ learning of mathematics. Since mathematics is an integral part of physics, it is assumed that mathematical reasoning also influences students’ success in physics. This paper aims to study how students’ ability to reason mathematically affects their success on different kinds of physics tasks. A descriptive statistical approach is adopted, which compares the ratio between conditional and unconditional probability to solve physics tasks requiring different kinds of mathematical reasoning. Tasks from eight Swedish national physics tests for upper secondary school, serve as a basis for the analysis. The result shows that if students succeed on tasks requiring creative mathematical reasoning, the probability to solve the other tasks on the same test increases. This increase is higher than if the students succeed on tasks not requiring creative mathematical reasoning. This result suggests that if students can reason mathematically creatively, they have the ability to use their knowledge in other novel situations and thus become more successful on tests.

Open this publication in new window or tab >>Upper-secondary teachers' objectification of symbols by their use of language### Johansson, Helena

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.### Österholm, Magnus

Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2017 (English)In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H., Singapore: PME , 2017, Vol. 1, p. 215-215Conference paper, Oral presentation with published abstract (Refereed)
##### Place, publisher, year, edition, pages

Singapore: PME, 2017
##### National Category

Educational Sciences
##### Identifiers

urn:nbn:se:miun:diva-36818 (URN)
##### Conference

The 41st Conference of the International Group for the Psychology of Mathematics Education, Singapore, July, 17-22, 2017
#####

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Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-13Bibliographically approved

Open this publication in new window or tab >>Hur samstämmiga är svenska styrdokument och nationella prov med ramverk och uppgifter i TIMSS Advanced 2015?### Nyström, Peter

### Kjellson Lind, Annika

### Dahlberg, Ulrica

### Johansson, Helena

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2016 (Swedish)Report (Other academic)
##### Abstract [sv]

##### Place, publisher, year, edition, pages

Stockholm: Skolverket, 2016. p. 130
##### Series

Övriga trycksaker
##### National Category

Didactics Other Natural Sciences Other Mathematics
##### Identifiers

urn:nbn:se:miun:diva-32693 (URN)978-91-7559-259-6 (ISBN)
#####

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Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17Bibliographically approved

Göteborgs Universitet.

Umeå Universitet.

Göteborgs Universitet.

Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.

TIMSS Advanced (Trends in Mathematics and Science Study ) är en internationell studie som undersöker gymnasieelevers kunskaper i avancerad matematik och fysik. TIMSS Advanced har genomförts tre gånger, 1995, 2008 och 2015, och Sverige har deltagit varje gång. I 2015 års studie deltog svenska elever i årskurs 3 på naturvetenskaps- och teknikprogrammet som slutfört eller håller på att slutföra kursen matematik 4 respektive fysik 2. Studien ger möjlighet att analysera förändringar i motsvarande elevgruppers kunskaper över tid inom dessa områden, men också möjlighet att jämföra svenska resultat med resultat från andra länder. TIMSS Advanced 2015 har genomförts av Skolverket i samarbete med Nationellt Centrum för Matematikutbildning (NCM) vid Göteborgs universitet. Skolverket har sammanställt en nationell huvudrapport med resultaten från TIMSS Advanced 2015. En viktig utgångspunkt för tolkning och analys av resultaten är att veta i vilken utsträckning svenska elever fått möjlighet att lära sig det som prövas i TIMSS Advanced. I denna rapport analyseras därför samstämmigheten mellan TIMSS Advanced 2015 och svenska ämnesplaner, nationella prov och bedömningsstöd. Mot bakgrund av ämnenas kopplingar mellan varandra genomförs också en analys som särskilt fokuserar på inslaget av matematik i fysikuppgifterna.

Open this publication in new window or tab >>Mathematical Reasoning: In physics and real-life context### Johansson, Helena

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2015 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Göteborg: Chalmers University of Technology and University of Gothenburg, 2015
##### Keywords

Creative mathematical reasoning, Descriptive statistics, Differential item functioning, Figurative context, Imitative reasoning, Mathematical Reasoning Requirements, Mathematics tasks, National tests, Physics tasks, Real-life context, T-test, Upper secondary school
##### National Category

Didactics Other Mathematics
##### Identifiers

urn:nbn:se:miun:diva-32696 (URN)978-91-628-9431-3 (ISBN)978-91-628-9432-0 (ISBN)
##### Opponent

### Blomhøj, Morten

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##### Supervisors

### Andersson, Mats

### Boesen, Jesper

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Available from: 2018-01-18 Created: 2018-01-17 Last updated: 2018-01-18Bibliographically approved

Göteborgs universitet, Institutionen för matematiska vetenskaper.

This thesis is a compilation of four papers in which mathematical reasoning is examined in various contexts, in which mathematics is an integral part. It is known from previous studies that a focus on rote learning and procedural mathematical reasoning hamper students’ learning of mathematics. The aims of this thesis are to explore how mathematical reasoning affects upper secondary students’ possibilities to master the physics curricula, and how real-life contexts in mathematics affect students’ mathematical reasoning. This is done by analysing the mathematical reasoning requirements in Swedish national physics tests; as well as by examining how mathematical reasoning affects students’ success on the tests/tasks. Furthermore, the possible effect of the presence of real-life contexts in Swedish national mathematics tasks on students’ success is explored; as well as if the effect differs when account is taken to mathematical reasoning requirements. The framework that is used for categorising mathematical reasoning, distinguishes between imitative and creative mathematical reasoning, where the latter, in particular, involves reasoning based on intrinsic properties. Data consisted of ten Swedish national physics tests for upper secondary school, with additional student data for eight of the tests; and six Swedish national mathematics tests for upper secondary school, with additional student data. Both qualitative and quantitative methods were used in the analyses. The qualitative analysis consisted of structured comparisons between representative student solutions and the students’ educational history. Furthermore, various descriptive statistics and significance tests were used. The main results are that a majority of the physics tasks require mathematical reasoning, and particularly that creative mathematical reasoning is required to fully master the physics curricula. Moreover, the ability to reason mathematically creatively seems to have a positive effect on students’ success on physics tasks. The results indicate additionally, that there is an advantage of the presence of real-life context in mathematics tasks when creative mathematical reasoning is required. This advantage seems to be particularly notable for students with lower grades.

Roskilde University, Denmark.

Göteborgs universitet och Chalmers tekniska högskola, Institutionen för matematik.

Göteborgs universitet, Nationellt centrum för matematikutbildning.

Open this publication in new window or tab >>Relation between mathematical reasoning ability and national formal demands in physics courses### Johansson, Helena

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education / [ed] Kim Beswick, Tracey Muir, & Jill Wells, Hobart, Australia: PME , 2015, Vol. 3, p. 121-128Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Hobart, Australia: PME, 2015
##### Keywords

Creative mathematical reasoning, Imitative reasoning, Mathematical Reasoning Requirements, National tests, Physics tasks, Upper secondary school
##### National Category

Didactics Other Mathematics
##### Identifiers

urn:nbn:se:miun:diva-32689 (URN)9781326664312 (ISBN)
##### Conference

The 39th Conference of the International Group for the Psychology of Mathematics Education, Hobart, Australia, July 13 - 18, 2015
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Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17Bibliographically approved

Göteborgs Universitet, Institutionen för Matematiska vetenskaper.

It is widely accepted that mathematical competence is of great importance whenlearning physics. This paper focuses on one aspects of mathematical competence,namely mathematical reasoning, and how this competency influences students’ successin physics. Mathematical reasoning required to solve tasks in physics tests, within anational tests system, is separated in imitative and creative mathematical reasoning.The result shows that students lacking the ability to reason mathematically creativelyare more likely not to do well on national physics test, thus not fully mastering thephysics curricula. It is further discussed how the high demands of creativemathematical reasoning in physics tests stand in contrast to what is known about theeducational practices in mathematics and physics in upper secondary school

Open this publication in new window or tab >>Mathematical Reasoning in Physics Tests: Requirements, Relations, Dependence### Johansson, Helena

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##### Abstract [en]

##### Place, publisher, year, edition, pages

Göteborg: Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, 2013
##### Series

Preprint ; 2013:18
##### Keywords

Mathematical reasoning, imitative reasoning, creative mathematical reasoning, physics tests, physics tasks, upper secondary school, Mantel-Haenszel procedure
##### National Category

Didactics Other Mathematics
##### Identifiers

urn:nbn:se:miun:diva-32697 (URN)
##### Opponent

### Pettersson, Kerstin

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##### Supervisors

### Andersson, Mats

### Boesen, Jesper

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Available from: 2018-01-18 Created: 2018-01-17 Last updated: 2018-01-18Bibliographically approved

Göteborgs universitet, Institutionen för matematiska vetenskaper.

By analysing and expanding upon mathematical reasoning requirements in physics tests, this licentiate thesis aims to contribute to the research studying how students’ knowledge in mathematics influence their learning of physics. A sample of physics tests from the Swedish National Test Bank in Physics was used as data, together with information of upper secondary students’ scores and grades on the tests. First it was decided whether the tasks in the tests required mathematical reasoning at all and if they did, that reasoning was characterised. Further, the relation between students’ grades and mathematical reasoning requirements was examined. Another aim in this thesis is to try out if the Mantel-Haenszel procedure is an appropriate statistical method to answer questions about if there is a dependence between students’ success on different physics tasks requiring different kinds of mathematical reasoning. The results show that 75% of the tasks in the physics tests require mathematical reasoning and that it is impossible to pass six out of eight tests without mathematical reasoning. It is also revealed that it is uncommon that a student gets a higher grade than Pass without solving tasks that require the student to come up with not already familiar solutions. It is concluded that the Mantel-Haenszel procedure is sensitive to the number of students each teacher accounts for. If there are not too few students, the procedure can be used. The outcome indicates that there is a dependence between success on tasks requiring different kinds of reasoning. It is more likely that a student manages to solve a task that requires the produce of new reasoning if the student has solved a task that is familiar from before.

Högskolan i Skövde, Institutionen för vård och natur.

Göteborgs universitet och Chalmers tekniska högskola.

Göteborgs universitet, Nationellt centrum för matematikutbildning.