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Nilsson, Per, Professor
Publications (10 of 39) Show all publications
Iversen, K. & Nilsson, P. (2019). Lower secondary school students’ reasoning about compound probability in spinner tasks. Journal of Mathematical Behavior
Open this publication in new window or tab >>Lower secondary school students’ reasoning about compound probability in spinner tasks
2019 (English)In: Journal of Mathematical Behavior, ISSN 0732-3123, E-ISSN 1873-8028Article in journal (Refereed) In press
Abstract [en]

In this paper we investigate the different ways in which students in lower secondary school (14–15 year-olds) reason about compound stochastic events (CSE). We ask students during clinical interviews to respond to CSE-tasks in a spinner context, where two linked spinners dis-play equal or different sizes of red and white areas. We seek to enrich our knowledge of how students make sense of CSE by not focusing exclusively on sample-space grounded reasoning. We open up the analysis to how students’reasoning can reflect aspects of multiplicative reasoning in relation to The Product Law of Probability. Our results show that students have difficulty in applying well-grounded combinatorial reasoning as well as multiplicative reasoning to the tasks, but they do show intuitive reasoning that reflect aspects of The Product Law of Probability. Two ways of reasoning identified in the current study are area-based part-whole reasoning and lowest-chance reasoning.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Compound stochastic events, Reasoning, Sample-space, Product law of probability
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-76011 (URN)10.1016/j.jmathb.2019.100723 (DOI)
Available from: 2019-09-02 Created: 2019-09-02 Last updated: 2019-09-03Bibliographically approved
Nilsson, P. (2018). An Inferentialist Perspective on How Note-taking can Constrain the Orchestration of Math-Talk. Scandinavian Journal of Educational Research
Open this publication in new window or tab >>An Inferentialist Perspective on How Note-taking can Constrain the Orchestration of Math-Talk
2018 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170Article in journal (Refereed) Epub ahead of print
Abstract [en]

The aim of this study is to investigate relationships between note-taking and the orchestrating of math-talk in whole-class teaching. A lesson on (average) velocity in a Swedish Grade 6 has been observed. Taking an inferentialist stance on human understanding, the study conceptualizes teaching and learning from the perspective of how students come to be engaged in the language practice of giving and asking for reasons. The study shows how note-taking supports a teacher-student relationship where the teacher produces content and the students’ participation is reduced to consume content. It shows how note-taking can support descriptive math-talk of concepts and symbols and step-by-step procedural math-talk, connected to the goal of providing students examples of tasks, similar to the tasks in their textbook.

Place, publisher, year, edition, pages
Routledge, 2018
Keywords
Note-taking, math-talk, inferentialism, teacher control
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-70673 (URN)10.1080/00313831.2018.1520740 (DOI)
Funder
Swedish Research Council, 721-2012-4811
Available from: 2018-12-10 Created: 2018-12-10 Last updated: 2018-12-12Bibliographically approved
Nilsson, P. & Schindler, M. (2018). The nature and use of theories in statistics education: looking back, looking forward. In: M. A. Sorto, A. White, & L. Guyot (Ed.), Looking back, looking forward: . Paper presented at Tenth International Conference on Teaching Statistics, Kyoto, Japan, 8-13 July, 2018. Voorburg, The Netherlands: The International Statistical Institute
Open this publication in new window or tab >>The nature and use of theories in statistics education: looking back, looking forward
2018 (English)In: Looking back, looking forward / [ed] M. A. Sorto, A. White, & L. Guyot, Voorburg, The Netherlands: The International Statistical Institute, 2018Conference paper, Published paper (Refereed)
Abstract [en]

Theories have a significant role for scientific work—also for statistics education research (SER). This paper elaborates on the use of theories in SER, based on findings of a literature review on the nature and use of theories in SER. In particular, we address theoretical issues and possible directions to further theory development in SER. Subsequently, we discuss five themes that in our view need further attention in SER. 

Place, publisher, year, edition, pages
Voorburg, The Netherlands: The International Statistical Institute, 2018
National Category
Didactics
Identifiers
urn:nbn:se:oru:diva-68409 (URN)
Conference
Tenth International Conference on Teaching Statistics, Kyoto, Japan, 8-13 July, 2018
Funder
Swedish Research Council, 721-2012-4811
Available from: 2018-08-08 Created: 2018-08-08 Last updated: 2018-08-13Bibliographically approved
Nilsson, P., Eckert, A. & Pratt, D. (2017). Challenges and opportunities in experimentation-based instruction in probability. In: Batanero, C. & Chernoff, E.J. (Ed.), Teaching and Learning Probability: Advances in Probability Education Research. Springer Netherlands
Open this publication in new window or tab >>Challenges and opportunities in experimentation-based instruction in probability
2017 (English)In: Teaching and Learning Probability: Advances in Probability Education Research / [ed] Batanero, C. & Chernoff, E.J., Springer Netherlands, 2017Chapter in book (Other academic)
Place, publisher, year, edition, pages
Springer Netherlands, 2017
National Category
Didactics
Identifiers
urn:nbn:se:oru:diva-62190 (URN)9783319728704 (ISBN)
Available from: 2017-11-08 Created: 2017-11-08 Last updated: 2017-11-24Bibliographically approved
Nilsson, P., Ryve, A. & Larsson, M. (2017). Characterizing theories aimed at supporting teachers’ mathematical classroom practices. In: CERME 10: 10th Congress of European Research in Mathematics Education. Paper presented at 10th Congress of European Research in Mathematics Education (CERME 10), Dublin, Ireland, February 1-5, 2017. CERME
Open this publication in new window or tab >>Characterizing theories aimed at supporting teachers’ mathematical classroom practices
2017 (English)In: CERME 10: 10th Congress of European Research in Mathematics Education, CERME , 2017Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we draw upon examples from a recently published systematic literature review (Ryve et al, 2015) on productive classroom practice to contribute to the research on the nature of theories for action in mathematics education. By relating the results from the review to theories and literature on educational policy research, professional development research and implementation research we construct a framework for categorizing theories aiming at supporting teachers’ actions in mathematical classroom practices.

Place, publisher, year, edition, pages
CERME, 2017
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-62189 (URN)
Conference
10th Congress of European Research in Mathematics Education (CERME 10), Dublin, Ireland, February 1-5, 2017
Available from: 2017-11-08 Created: 2017-11-08 Last updated: 2019-03-29Bibliographically approved
Eckert, A. & Nilsson, P. (2017). Introducing a symbolic interactionist approach on teaching mathematics: The case of revoicing as an interactional strategy in the teaching of probability. Journal of Mathematics Teacher Education, 20(1), 31-48
Open this publication in new window or tab >>Introducing a symbolic interactionist approach on teaching mathematics: The case of revoicing as an interactional strategy in the teaching of probability
2017 (English)In: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 20, no 1, p. 31-48Article in journal (Refereed) Published
Abstract [en]

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Interactional teaching strategy, Teaching, Symbolic interactionism, Revoicing, Probability
National Category
Didactics Educational Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-48204 (URN)10.1007/s10857-015-9313-z (DOI)000397225200003 ()2-s2.0-84939247092 (Scopus ID)
Available from: 2016-02-11 Created: 2016-02-11 Last updated: 2019-03-26Bibliographically approved
Schindler, M., Hußmann, S., Nilsson, P. & Bakker, A. (2017). Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Mathematics Education Research Journal, 29(4), 471-492
Open this publication in new window or tab >>Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis
2017 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 29, no 4, p. 471-492Article in journal (Refereed) Published
Abstract [en]

Negative numbers are among the first formalizations students encounter in their mathematics learning that clearly differ from out-of-school experiences. What has not sufficiently been addressed in previous research is the question of how students draw on their prior experiences when reasoning on negative numbers and how they infer from these experiences. This article presents results from an empirical study investigating sixth-grade students’ reasoning and inferring from school-based and out-of-school experiences. In particular, it addresses the order relation, which deals with students’ very first encounters with negative numbers. Here, students can reason in different ways, depending on the experiences they draw on. We study how students reason before a lesson series and how their reasoning is influenced through this lesson series where the number line and the context debts-and-assets are predominant. For grasping the reasoning’s inferential and social nature and conducting in-depth analyses of two students’ reasoning, we use an epistemological framework that is based on the philosophical theory of inferentialism. The results illustrate how the students infer their reasoning from out-of-school and from school-based experiences both before and after the lesson series. They reveal interesting phenomena not previously analyzed in the research on the order relation for integers. 

Place, publisher, year, edition, pages
Springer, 2017
Keywords
Negative numbers; Negative integers; Reasoning; Prior experiences; Contexts; Inferentialism
National Category
Didactics
Identifiers
urn:nbn:se:oru:diva-60735 (URN)10.1007/s13394-017-0202-x (DOI)000417402300006 ()2-s2.0-85037051473 (Scopus ID)
Available from: 2017-09-11 Created: 2017-09-11 Last updated: 2018-08-06Bibliographically approved
Nilsson, P., Schindler, M. & Bakker, A. (2017). The nature and use of theories in statistics education. In: Ben-Zvi, D.; Makar, K.; Garfield, J. (Ed.), International Handbook of Research in Statistics Education: . Springer
Open this publication in new window or tab >>The nature and use of theories in statistics education
2017 (English)In: International Handbook of Research in Statistics Education / [ed] Ben-Zvi, D.; Makar, K.; Garfield, J., Springer, 2017Chapter in book (Other academic)
Place, publisher, year, edition, pages
Springer, 2017
Series
Springer International Handbooks of Education
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-62191 (URN)9783319661933 (ISBN)
Projects
Developing experimentation-based probability education: Inferentialism, contextualization and variation in collaboration
Available from: 2017-11-08 Created: 2017-11-08 Last updated: 2018-08-10Bibliographically approved
Bergman-Ärlebäck, J., Blomberg, P. & Nilsson, P. (2015). An instructional design perspective on data-modelling for learning statistics and modelling. In: Ola Helenius, Arne Engström, Tasmin Meaney, Per Nilsson, Eva Norén, Judy Sayers, Magnus Österholm (Ed.), Development of mathematics teaching: Design, Scale, Effects: Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar. Paper presented at The Ninth mathematics Education Research Seminar (MADIF 9), Umeå, Sweden, Februar 4-5, 2014 (pp. 37-46). Svensk Förening för Matematisk Didaktisk Forskning (SMDF)
Open this publication in new window or tab >>An instructional design perspective on data-modelling for learning statistics and modelling
2015 (English)In: Development of mathematics teaching: Design, Scale, Effects: Proceedings of MADIF 9, The Ninth mathematics Education Research Seminar / [ed] Ola Helenius, Arne Engström, Tasmin Meaney, Per Nilsson, Eva Norén, Judy Sayers, Magnus Österholm, Svensk Förening för Matematisk Didaktisk Forskning (SMDF) , 2015, p. 37-46Conference paper, Published paper (Refereed)
Abstract [en]

This theoretical and methodological paper discusses the emerging theoretical framing and methodological considerations in our efforts to develop a theoretical approach supporting instructional design for teaching and learning statistics and mathematical modelling. From an instructional design point of view aligned with the goals in governing curricula documents and real classroom constraints, we argue for the integration of the models and modelling perspective on teaching and learning mathematics with a data-modelling approach to facilitate students’ learning statistics and mathematical modelling. An application of the framework is given and future research discussed.

Place, publisher, year, edition, pages
Svensk Förening för Matematisk Didaktisk Forskning (SMDF), 2015
Series
Skrifter från SMDF ; 10
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-53873 (URN)
Conference
The Ninth mathematics Education Research Seminar (MADIF 9), Umeå, Sweden, Februar 4-5, 2014
Available from: 2016-12-12 Created: 2016-12-12 Last updated: 2019-04-11Bibliographically approved
Nilsson, P. (2015). Building a local theory for the learning of experimental probability. In: Harry Silfverberg, Tomi Kärki and Markku S. Hannula (Ed.), Nordic research in mathematics education: Proceedings of NORMA14, Turku, June 3–6, 2014. Paper presented at The Seventh Nordic Conference on Mathematics Education (NORMA 14), Turku, Finland, June 3-6, 2014 (pp. 318-328). Turku: University of Turku, Department of Teacher Education
Open this publication in new window or tab >>Building a local theory for the learning of experimental probability
2015 (English)In: Nordic research in mathematics education: Proceedings of NORMA14, Turku, June 3–6, 2014 / [ed] Harry Silfverberg, Tomi Kärki and Markku S. Hannula, Turku: University of Turku, Department of Teacher Education , 2015, p. 318-328Conference paper, Published paper (Refereed)
Abstract [en]

The approach of this paper builds on the assumption that there is a need to develop local, domain specific instructional theories for the learning of probability. The aim of the present paper is to explore the qualitative hypothesis of building such a theory on the combination of students’ own experimentations with samples and principles of variation. By using data from 12-13-year old students investigating the probability of obtaining a certain colour when picking, at random, one piece from a bag with six different colours of the candy, the paper shows how variations in students’ own experimentations with samples can be used as means to explore and support students’ understanding of critical features of experimental probability. 

Place, publisher, year, edition, pages
Turku: University of Turku, Department of Teacher Education, 2015
Series
Studies in Subject Didactics, ISSN 1799-9596 ; 10
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-53874 (URN)978-952-5993-17-2 (ISBN)
Conference
The Seventh Nordic Conference on Mathematics Education (NORMA 14), Turku, Finland, June 3-6, 2014
Available from: 2016-12-12 Created: 2016-12-12 Last updated: 2017-10-18Bibliographically approved
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