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1. Teaching Inverse Functions at Tertiary level Attorps, Iiris PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1289",{id:"formSmash:items:resultList:0:j_idt1289",widgetVar:"widget_formSmash_items_resultList_0_j_idt1289",onLabel:"Attorps, Iiris ",offLabel:"Attorps, Iiris ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1292",{id:"formSmash:items:resultList:0:j_idt1292",widgetVar:"widget_formSmash_items_resultList_0_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Björk, KjellUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.Radic, MirkoUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.Viirman, OlovUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Teaching Inverse Functions at Tertiary level2013In: CERME 8: Proceedings of the Eight Congress of the European Society for Research in Mathematics Education, Antalya: Middle East Technical University , 2013, p. 2524-2533Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:0:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_0_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This study is a part of an ongoing research that attempts to explain the relationship between the teachers’ instructional practise and students’ learning in the context of functions and function inverses. The question in this paper is how the use of technology as a pedagogical tool may contribute to the understanding of the inverse function concept. An engineering student group (n =17) was taught functions and inverse functions with the assistance of GeoGebra. In our theoretical framework we apply Variation theory together with the theory of Concept image and Concept definition. The data were gathered by doing a pre and post test concerning inverse functions. Our experiment revealed that students’ concept images in the post test were more developed compared with the results in the pre test.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. "I'm still making dots for them" Hernandez-Martinez, Paul PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1289",{id:"formSmash:items:resultList:1:j_idt1289",widgetVar:"widget_formSmash_items_resultList_1_j_idt1289",onLabel:"Hernandez-Martinez, Paul ",offLabel:"Hernandez-Martinez, Paul ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1292",{id:"formSmash:items:resultList:1:j_idt1292",widgetVar:"widget_formSmash_items_resultList_1_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Swinburne University of Technology.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Thomas, StephanieLoughborough University.Viirman, OlovUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. University of Agder.Rogovchenko, YuriyUniversity of Agder.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); "I'm still making dots for them": mathematics lecturers' views on their mathematical modelling practices2021In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 51, no 2, p. 165-177Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:1:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_1_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Using Cultural-Historical Activity Theory, we analyze lecturers’ views on the aims and teaching practices of mathematical modelling (MM) education in Norway and England. We aim to expose the tensions that exist within the activity of teaching MM at university, such as those between multiple, sometimes competing, aims for teaching MM, or between the lecturers’ professional identities and the structure of university degrees. Our conceptualization of these tensions might help lecturers consider how to overcome obstacles in their own contexts.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. Research Forum Heyd-Metzuyanim, Einat PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1289",{id:"formSmash:items:resultList:2:j_idt1289",widgetVar:"widget_formSmash_items_resultList_2_j_idt1289",onLabel:"Heyd-Metzuyanim, Einat ",offLabel:"Heyd-Metzuyanim, Einat ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1292",{id:"formSmash:items:resultList:2:j_idt1292",widgetVar:"widget_formSmash_items_resultList_2_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Technion, Israel Institute of Technology.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Adler, JillUniversity of the Witwatersrand.Lavie, IritHaifa University.Nachlieli, TalliLevinsky College.Tabach, MichalTel Aviv University.Robertson, Sally-AnnRhodes University.Graven, MellonyRhodes University.Viirman, OlovUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Research Forum: Rituals and explorations in mathematical teaching and learning2019In: Proceedings: 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1) / [ed] Mellony Graven, Hamsa Venkat, Anthony A Essien and Pamela Vale, 2019, Vol. 1, p. 137-164Conference paper (Refereed)4. An exploration of students’ discourse using Sim2Bil within group work Hogstad, Ninni Marie PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1289",{id:"formSmash:items:resultList:3:j_idt1289",widgetVar:"widget_formSmash_items_resultList_3_j_idt1289",onLabel:"Hogstad, Ninni Marie ",offLabel:"Hogstad, Ninni Marie ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1292",{id:"formSmash:items:resultList:3:j_idt1292",widgetVar:"widget_formSmash_items_resultList_3_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Viirman, OlovUniversity of Agder.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); An exploration of students’ discourse using Sim2Bil within group work: A commognitive perspective2017Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:3:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_3_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper reports on critical aspects of three engineering students’ discourse in group work using a digital tool called Sim2Bil while solving mathematical tasks. Applying a commognitive perspective, where mathematical discourse is characterized by words used, visual mediators applied, narratives developed and routines established, we investigate how these characteristics are influenced by the technological environment. It is found that all of the aspects of the students’ discourse are influenced by Sim2Bil. For instance, a “trial and error” routine directly connected to the use of the tool is present in the students’ discourse.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. Commognitive analyses of the learning and teaching of mathematics at university level Nardi, Elena PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1289",{id:"formSmash:items:resultList:4:j_idt1289",widgetVar:"widget_formSmash_items_resultList_4_j_idt1289",onLabel:"Nardi, Elena ",offLabel:"Nardi, Elena ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1292",{id:"formSmash:items:resultList:4:j_idt1292",widgetVar:"widget_formSmash_items_resultList_4_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); School of Education and Lifelong Learning, University of East Anglia, Norwich, UK.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ryve, AndreasSchool of Education, Culture and Communication, Mälardalen University, Västerås, Sweden.Stadler, ErikaDepartment of Mathematics and Science Education, Stockholm University, Stockholm, Sweden.Viirman, OlovUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. Department of Mathematics, Karlstad University, Karlstad, Sweden.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus2014In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 16, no 2, p. 182-198Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:4:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_4_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards 'scaling-up' the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as "legitimate peripheral participation" from the theory of Communities of Practice and "didactic contract" from the Theory of Didactic Situations.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:4:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 6. Mathematics lecturers' views on the teaching of mathematical modelling Treffert-Thomas, Stephanie PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1289",{id:"formSmash:items:resultList:5:j_idt1289",widgetVar:"widget_formSmash_items_resultList_5_j_idt1289",onLabel:"Treffert-Thomas, Stephanie ",offLabel:"Treffert-Thomas, Stephanie ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1292",{id:"formSmash:items:resultList:5:j_idt1292",widgetVar:"widget_formSmash_items_resultList_5_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Loughborough University, UK.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Viirman, OlovUniversity of Agder, Norway.Hernandez-Martinez, PaulLoughborough University, UK.Rogovchenko, YuriyUniversity of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Mathematics lecturers' views on the teaching of mathematical modelling2017In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 22, no 4, p. 121-145Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:5:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_5_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The paper reports on the views and use of mathematical modelling (MM) in university mathematics courses in Norway from the perspective of lecturers. Our analysis includes a characterisation of MM views based on the modelling perspectives developed by Kaiser and Sriraman (2006). Through an online survey we aimed to identify the main perspectives held in higher education by mathematics lecturers and the underlying rationale for integrating (or not) MM in university courses. The results indicated that most respondents displayed a realistic perspective on MM when it came to their professional practice. There was a more varied response when it came to their views on MM in teaching. Regarding conditions influencing the use or non-use of MM in teaching, these mainly concerned the mathematical content and the institutional practices.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 7. Book review Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt1289",{id:"formSmash:items:resultList:6:j_idt1289",widgetVar:"widget_formSmash_items_resultList_6_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematical Sciences, University of Agder, Kristiansand, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Book review: Approaches to qualitative research in mathematics education: examples of methodology and methods2015In: Research in Mathematics Education, ISSN 1479-4802, E-ISSN 1754-0178, Vol. 17, no 3, p. 247-251Article, book review (Other academic)8. Characteristics of participation Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1289",{id:"formSmash:items:resultList:7:j_idt1289",widgetVar:"widget_formSmash_items_resultList_7_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. MatRIC, University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Characteristics of participation: A mathematician and a mathematics educator collaborating on a developmental research project2018In: Proceedings of INDRUM 2018 Second conference of the International Network for Didactic Research in University Mathematics / [ed] Viviane Durand-Guerrier, Reinhard Hochmuth, Simon Goodchild and Ninni Marie Hogstad, 2018, p. 442-451Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:7:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_7_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, a developmental research project involving offering mathematical modelling (MM) activities to university biology students is presented, and a particular aspect is studied, namely the project as a collaboration between mathematicians and mathematics educators. The aim of the paper is to investigate what characterizes their participation in the project, and how the characteristics of the project and its development might influence this participation. Interview data as well as observation data from the MM sessions are analysed, and findings show that the mathematics educator served as a broker influencing the practice of the mathematician. It is hoped that the findings of the study can be of use when planning future collaboration between mathematicians and mathematics educators.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. Different views Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1289",{id:"formSmash:items:resultList:8:j_idt1289",widgetVar:"widget_formSmash_items_resultList_8_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Different views: Teacher and engineering students on the concept of function2008In: Perspectives on Mathematical Knowledge: Proceedings of MADIF 6 / [ed] Christer Bergsten, Barbro Grevholm, Thomas Lingefjärd, Stockholm: SMDF , 2008, p. 97-106Conference paper (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:8:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_8_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This study analyses what kind of conceptions teacher students and engineering students have about the function concept, and how these conceptions differ between the two groups. The study was conducted through questionnaires, and 34 students at a Swedish university participated. The function concepts of the students have been classified according to modified versions of models presented by Vinner & Dreyfus, Sfard and DeMarois & Tall. The study shows that the students primarily have operational concepts of function, with only a couple of students having a structural function concept. The study also shows distinct differences between prospective compulsory school teachers and engineering students, where the former have less developed functional concepts.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Discourses of functions Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1289",{id:"formSmash:items:resultList:9:j_idt1289",widgetVar:"widget_formSmash_items_resultList_9_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Discourses of functions: University mathematics teaching through a commognitive lens2011In: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education / [ed] Marta Pytlak, Tim Rowland, Ewa Swoboda, Rzeszow, Poland, 2011, p. 2103-2112Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:9:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_9_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper excerpts from the lectures of three teachers at one university are analysed, using commognitive theory. Characteristic features of the teachers’ discourses about functions are presented. Definitions are found to be the central type of narrative, while theorems and proofs are largely absent, despite the fact that the teaching is of a traditional type, often connected to the “definition-theorem-proof” format. Three main categories of routines are found: substantiation, construction and motivation routines. It is also seen that the teachers are more concerned with questions of “why” to do things than “when” to do them.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Discursive practices of two university teachers on the concept of 'linear transformation' Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1289",{id:"formSmash:items:resultList:10:j_idt1289",widgetVar:"widget_formSmash_items_resultList_10_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Discursive practices of two university teachers on the concept of 'linear transformation'2011In: Developing Mathematical Thinking: Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 / [ed] Behiye Ubuz, Ankara: PME , 2011, p. 313-320Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:10:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_10_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper reports on an ongoing study focusing on the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper two excerpts of lectures on linear transformations are analysed, using commognitive theory. The two teachers' discursive uses of the terms 'linearity' and 'linear transformation' are described, and potential consequences for student learning are presented. One lecture displays a strong mathematical content while lacking contextualization, while the other is well grounded in everyday experience, but with a lack of attention to mathematical detail potentially detrimental to student learning.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1289",{id:"formSmash:items:resultList:11:j_idt1289",widgetVar:"widget_formSmash_items_resultList_11_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematical Sciences, University of Agder, Kristiansand, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis2015In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 8, p. 1165-1181Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:11:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_11_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard’s commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories –

*explanation*,*motivation*and*question*posing routines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines include*known mathematical facts*,*summary and repetition, different representations*, everyday language, and*concretization and metaphor*; the motivation routines include reference to*utility*,*the nature of mathematics*,*humour*and*result focus*; and the question posing routines include*control questions*, asking for*facts*,*enquiries*and*rhetorical*questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. The constitution of the nature of mathematics in the lecturing practices of three university mathematics teachers Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt1289",{id:"formSmash:items:resultList:12:j_idt1289",widgetVar:"widget_formSmash_items_resultList_12_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder, Faculty of Engineering and Science, Kristiansand, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The constitution of the nature of mathematics in the lecturing practices of three university mathematics teachers2015In: Proceedings of the ninth congress of the European mathematical society for research in mathematics education / [ed] K. Krainer & N. Vondrova, 2015, Vol. 1, p. 2263-2269Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:12:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_12_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The study reported in this paper investigates how notions of the nature of mathematical knowledge and mathematical objects are constituted through the teaching practices of three university mathematics teachers at a Swedish university. The data consists of video recorded lectures, and the analyses were informed by classifications presented by Lerman and Davis and Hersh. The results indicate that different epistemological and ontological positions are indeed constituted through the discourse. Although the discourse is generally highly objectified, the ways in which mathematical objects are introduced differ. Mostly the discourse was within an absolutist paradigm, but there were also examples of how the socio-historical nature of mathematical knowledge is emphasized.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. The development of the mathematical discourse of biology students working with mathematical modelling Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt1289",{id:"formSmash:items:resultList:13:j_idt1289",widgetVar:"widget_formSmash_items_resultList_13_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The development of the mathematical discourse of biology students working with mathematical modelling2016Conference paper (Refereed)15. The function concept and university mathematics teaching Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt1289",{id:"formSmash:items:resultList:14:j_idt1289",widgetVar:"widget_formSmash_items_resultList_14_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Karlstads universitet, Institutionen för matematik och datavetenskap.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The function concept and university mathematics teaching2014Doctoral thesis, comprehensive summary (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:14:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_14_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis concerns the teaching of mathematics at university level, with a particular focus on the teaching of the function concept. The main aim of the thesis is describing and analysing the teaching practices of university mathematics teachers regarding the function concept, and how this concept is constituted through these practices. To this end, video recordings of lectures by seven mathematics teachers at three Swedish universities were analysed using a discursive perspective, Sfard’s commognitive framework. The observed teaching was traditional in form, with teachers using “chalk talk” – simultaneously talking and writing on the board. The results show that the teaching practices of the teachers belong to two distinct but intertwined discourses – a mathematical discourse, and a discourse of mathematics teaching. Classifications of important aspects of these discourses are presented, and it is found that the teachers’ discursive practices, while sharing overall form, still display considerable differences. Other results include an analysis of the levels of objectification displayed by the teachers in their discursive constitution of the function concept. The study contributes to a small but growing body of empirical research on university mathematics teaching practice.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. The functions of function discourse Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt1289",{id:"formSmash:items:resultList:15:j_idt1289",widgetVar:"widget_formSmash_items_resultList_15_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The functions of function discourse: university mathematics teaching from a commognitive standpoint2014In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 45, no 4, p. 512-527Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:15:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_15_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of seven Swedish university teachers on the topic of functions, using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using “chalk talk”, and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level, in how the process of doing mathematics is made visible in the teachers’ teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. The many faces of function - students' understanding of the function concept Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt1289",{id:"formSmash:items:resultList:16:j_idt1289",widgetVar:"widget_formSmash_items_resultList_16_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The many faces of function - students' understanding of the function concept2007In: Conceptions and Beliefs in Mathematics and Science Education including MAVI XIII / [ed] Iiris Attorps, Eva Kellner, Gävle: University of Gävle , 2007, p. 87-97Conference paper (Other academic)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:16:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_16_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This study analyses what kind of conceptions teacher students and engineering students have about the function concept, and how these conceptions differ between the two groups. The study was conducted through questionnaires, and 34 students at a Swedish university participated. The function concepts of the students have been classified according to modified versions of models presented by Vinner & Dreyfus, Sfard and DeMarois & Tall. The result of the study shows that the students primarily have operational concepts of function, with only a couple of students having anything resembling a structural function concept. The study also shows distinct differences between prospective compulsory school teachers and engineering students, where the former have less developed functional concepts.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. The role of mathematics in the design of engineering programs Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt1289",{id:"formSmash:items:resultList:17:j_idt1289",widgetVar:"widget_formSmash_items_resultList_17_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The role of mathematics in the design of engineering programs: a case study of two Scandinavian universities2015In: Didactics of Mathematics in Higher Education asa Scientific Discipline19. The teaching of functions as a discursive practice Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt1289",{id:"formSmash:items:resultList:18:j_idt1289",widgetVar:"widget_formSmash_items_resultList_18_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The teaching of functions as a discursive practice: University mathematics teaching from a commognitive standpoint2012In: Proceedings of the 12^{th}international congress on mathematical education, 2012, p. 1559-1568Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:18:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_18_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper reports on a study of the teaching of functions in undergraduate courses in mathematics at three Swedish universities. In this paper excerpts from the lectures of the seven participating teachers are analysed, using commognitive theory. Characteristic features of the teachers’ discourses about functions are presented, focusing on routines – repetitive patterns characteristic of the discourse. The discursive practices are found to contain two intertwined discourses – mathematical discourse and discourse of mathematics teaching. Routines specific to the mathematical discourse are construction and substantiation routines, while the didactical routines include motivation, explanation, activation and recall routines.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:18:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 20. What we talk about when we talk about functions Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt1289",{id:"formSmash:items:resultList:19:j_idt1289",widgetVar:"widget_formSmash_items_resultList_19_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. Karlstad University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); What we talk about when we talk about functions: Characteristics of the function concept in the discursive practices of three university teachers2013In: Proceedings of the eighth congress of the European mathematical society for research in mathematics education, 2013, p. 2466-2475Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:19:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_19_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The study reported in the present paper forms part of an ongoing project regarding the teaching of functions in undergraduate courses at three Swedish universities. The theoretical framework underlying the project is Sfard’s commognitive theory. In the present study, three lectures in calculus from two different universities are analyzed, focusing on the characterizations of the function concept presented by the discursive practices of the teachers. All three teachers are found to make extensive use of the principle of variation, but differences are found for instance in the emphasis put on different realizations of functions, and on the role of domain and range. Also, according to the type of content of the lectures, differences between more process-oriented and more object-oriented discourses of functions can be seen.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 21. Different views - some Swedish mathematics students' concept images of the function concept Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt1289",{id:"formSmash:items:resultList:20:j_idt1289",widgetVar:"widget_formSmash_items_resultList_20_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt1292",{id:"formSmash:items:resultList:20:j_idt1292",widgetVar:"widget_formSmash_items_resultList_20_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Attorps, IirisUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.Tossavainen, TimoUniversity of Eastern Finland.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Different views - some Swedish mathematics students' concept images of the function concept2010In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 15, no 4, p. 5-24Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:20:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_20_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This study analyses what kind of concept images a group of engineering and teacher students have of the function concept, and how these concept images are related to the historical development of this concept. The study was conducted using questionnaires, and 34 students at a Swedish university participated. It is found that the students primarily rely on operational conceptions of the function concept, with only a minority of students possessing structural conceptions. The definitions given by the students mostly resemble an 18

^{th}or 19^{th}century view of functions. The study also indicates that the character of the definitions given in the textbooks used by the students affect their concept images.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:20:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 22. Using mathematical modelling activities to motivate biology students to learn mathematics Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt1289",{id:"formSmash:items:resultList:21:j_idt1289",widgetVar:"widget_formSmash_items_resultList_21_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt1292",{id:"formSmash:items:resultList:21:j_idt1292",widgetVar:"widget_formSmash_items_resultList_21_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Goodchild, SimonUniversity of Agder, Norway.Rogovchenko, YuiryUniversity of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Using mathematical modelling activities to motivate biology students to learn mathematics2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education / [ed] C. Csíkos, A. Rausch & J. Szitányi, 2016, Vol. 1, p. 262-Conference paper (Refereed)23. From ritual to exploration Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt1289",{id:"formSmash:items:resultList:22:j_idt1289",widgetVar:"widget_formSmash_items_resultList_22_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt1292",{id:"formSmash:items:resultList:22:j_idt1292",widgetVar:"widget_formSmash_items_resultList_22_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nardi, ElenaUniversity of East Anglia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); From ritual to exploration: The evolution of biology students’ mathematical discourse through mathematical modelling activities2017In: Proceedings of CERME10 / [ed] Thérèse Dooley, Ghislaine Gueudet, 2017, p. 2274-2281Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:22:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_22_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We report analyses from a collaborative, developmental research project between two Norwegian centres of excellence in higher education (MatRIC and bioCEED) in which biology-related mathematical modelling (MM) activities are introduced to biology students as a means to motivate their appreciation for, and competence in, mathematics. This phase of the project involved four sessions with 11 first-semester students. We report data and analyses from two activities: Yeast Growth and Digoxin. Our commognitive analyses trace the evolution of the students’ mathematical discourse in two episodes, revealing a scaffolding story about the gradual transition from ritualized to exploratory engagement with MM, and pointing to the crucial role played by the teacher in this process. We conclude with discussing some implications of our analysis for the design and use of MM activities for students of Biology, and other non-mathematics specialisms.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:22:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 24. Negotiating different disciplinary discourses Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt1289",{id:"formSmash:items:resultList:23:j_idt1289",widgetVar:"widget_formSmash_items_resultList_23_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt1292",{id:"formSmash:items:resultList:23:j_idt1292",widgetVar:"widget_formSmash_items_resultList_23_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Kristiansand, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nardi, ElenaSchool of Education, University of East Anglia, Norwich, UK.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Negotiating different disciplinary discourses: Biology students’ ritualized and exploratory participation in mathematical modelling activities2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 2, p. 233-252Article in journal (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:23:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_23_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:23:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Download full text (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_23_j_idt1552_0_j_idt1555",{id:"formSmash:items:resultList:23:j_idt1552:0:j_idt1555",widgetVar:"widget_formSmash_items_resultList_23_j_idt1552_0_j_idt1555",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:23:j_idt1552:0:fullText"});}); 25. Ritualised and exploratory graphing routines in mathematical modelling Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt1289",{id:"formSmash:items:resultList:24:j_idt1289",widgetVar:"widget_formSmash_items_resultList_24_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt1292",{id:"formSmash:items:resultList:24:j_idt1292",widgetVar:"widget_formSmash_items_resultList_24_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics. MatRIC, University of Agder, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Nardi, ElenaUniversity of East Anglia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ritualised and exploratory graphing routines in mathematical modelling: The Digoxin task2018In: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1) / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg, and Lovisa Sumpter, 2018, Vol. 4, p. 363-370Conference paper (Refereed)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt1327_0_j_idt1328",{id:"formSmash:items:resultList:24:j_idt1327:0:j_idt1328",widgetVar:"widget_formSmash_items_resultList_24_j_idt1327_0_j_idt1328",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The project we report from in this paper explores whether and how, biology students’ competence and confidence in – as well as appreciation for – mathematics in their discipline can be improved through greater integration of mathematics and biology in their study programme. Here, we examine biology students’ mathematical discourse as they engage with a biology-related Mathematical Modelling (MM) activity, the Digoxin task. We report commognitive analyses of data collected during sessions in which biology-related MM activities were introduced to undergraduate biology students (four sessions with 12 first-semester students).We focus on the interplay between students’ ritualised and exploratory engagement with the activity, particularly concerning graphing routines, and consider pedagogical implications.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:24:j_idt1327:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 26. What to do when there is no formula? Navigating between less and more familiar routines for determining velocity in a calculus task for engineering students. Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt1289",{id:"formSmash:items:resultList:25:j_idt1289",widgetVar:"widget_formSmash_items_resultList_25_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt1292",{id:"formSmash:items:resultList:25:j_idt1292",widgetVar:"widget_formSmash_items_resultList_25_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Pettersson, IrinaUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); What to do when there is no formula? Navigating between less and more familiar routines for determining velocity in a calculus task for engineering students.2019In: Calculus in upper secondary and beginning university mathematics – Conference proceedings. Kristiansand, Norway: MatRIC / [ed] J. Monaghan, E. Nardi and T. Dreyfus, 2019, p. 167-170Conference paper (Refereed)27. Programming in mathematics teacher education Viirman, Olov PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt1289",{id:"formSmash:items:resultList:26:j_idt1289",widgetVar:"widget_formSmash_items_resultList_26_j_idt1289",onLabel:"Viirman, Olov ",offLabel:"Viirman, Olov ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt1292",{id:"formSmash:items:resultList:26:j_idt1292",widgetVar:"widget_formSmash_items_resultList_26_j_idt1292",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Pettersson, IrinaUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.Björklund, JohanUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.Boustedt, JonasUniversity of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Computer science.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Programming in mathematics teacher education: A collaborative teaching approach2018Conference paper (Refereed)

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