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Nilsson, P. & Eckert, A. (2023). Design principles for simulation-based learning of hypothesis testing in secondary school. Mathematical Thinking and Learning
Open this publication in new window or tab >>Design principles for simulation-based learning of hypothesis testing in secondary school
2023 (English)In: Mathematical Thinking and Learning, ISSN 1098-6065, E-ISSN 1532-7833Article in journal (Refereed) Epub ahead of print
Abstract [en]

This study contributes to the call for influencing practice by increasing attention to how learning environments can be designed to support learning in statistical inference. We report on a design experiment in secondary school (students 14-16 years old), that resulted in a set of lessons with the learning goal of teaching students how to apply concepts and principles of hypothesis testing for making an inference as to whether or not students in secondary school can taste the difference between two brands of cola soda. The design experiment resulted in four design principles for a simulation-based approach for learning hypothesis testing in secondary school. The design principles highlight the combination of practical and digital simulations of samplings. They stress the need for using random generators that allow for high reliability in collecting sample data and introduce a simulation-based method for determining p-values, i.e., to quantify how likely or surprising a sample result, or a result more extreme, is under a null hypothesis.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2023
Keywords
Hypothesis testing, Secondary school, Design principles; Informal inferential statistics; Statistics education.
National Category
Didactics Probability Theory and Statistics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-118037 (URN)10.1080/10986065.2022.2161288 (DOI)000906252000001 ()2-s2.0-85145446378 (Scopus ID)
Funder
Swedish Institute for Educational Research
Available from: 2022-12-21 Created: 2022-12-21 Last updated: 2024-02-05
Alstad, E., Berre, M. & Nilsson, P. (2023). Exploring spherical units as perceptual clues in enumerating 3D arrays. Mathematics Education Research Journal
Open this publication in new window or tab >>Exploring spherical units as perceptual clues in enumerating 3D arrays
2023 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

This study continues an investigation of how spherical units, compared to cubical units, can facilitate students’ units-locating and organizing units in composites. We analyze how Norwegian grade 3 students enumerate 3D arrays with cubical and spherical units. Our results show how spherical units can act as perceptual clues that facilitate cognitive processes, underlying students’ strategies in the enumeration of 3D arrays. In particular, the results show how spherical units facilitate the units-locating process, which, in turn, supports processes of organizing-by-composites and spatial structuring of the array, in the action of developing a proper iterative strategy such as layer-based thinking.

Place, publisher, year, edition, pages
Springer, 2023
Keywords
Perceptual clues; Enumerating units; 3D arrays; Spherical units
National Category
Didactics Mathematics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123470 (URN)10.1007/s13394-023-00466-w (DOI)001022434400001 ()2-s2.0-85164007373 (Scopus ID)
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2024-02-05
Alstad, E., Berre, M. & Nilsson, P. (2023). Exploring units-locating in enumerating units of 3D arrays: linking units-locating to units-representation. Mathematics Education Research Journal, 35(3), 583-605
Open this publication in new window or tab >>Exploring units-locating in enumerating units of 3D arrays: linking units-locating to units-representation
2023 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 35, no 3, p. 583-605Article in journal (Refereed) Published
Abstract [en]

The aim of the present study is to explore strategies in enumerating units of three dimensional (3D) arrays. We analyse enumeration strategies of students in grade 3 (ages 8 to 9) in situations of cubical and spherical representations of units of 3D arrays. By exploring students’ strategies in these two situations, we find that difficulties in enumerating units in 3D arrays can be traced to difficulties in units-locating, with the consequence of applying double and triple counting. Our results also indicate that spherical units can serve as perceptual clues in units-locating and in assembling units into relevant composites. With input from our findings, we suggest research to investigate the following three hypotheses: (i) spherical units can turn students away from double and triple counting, (ii) spherical units can support students’ units-locating process and their ability to assemble units into relevant composites and (iii) teaching of enumerating 3D arrays should start with spherical units before cubical units.

Place, publisher, year, edition, pages
Springer Nature, 2023
Keywords
3D arrays, Units-locating, Enumerating, Perceptual clues, Units-representation
National Category
Didactics
Research subject
Education, Didactics
Identifiers
urn:nbn:se:lnu:diva-123471 (URN)10.1007/s13394-021-00405-7 (DOI)2-s2.0-85119083075 (Scopus ID)
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-10-16Bibliographically approved
Nilsson, P. (2023). Hypothetical learning trajectory on informal hypothesis testing in a probability context. Statistics Education Research Journal, 22(2), Article ID 11.
Open this publication in new window or tab >>Hypothetical learning trajectory on informal hypothesis testing in a probability context
2023 (English)In: Statistics Education Research Journal, E-ISSN 1570-1824, Vol. 22, no 2, article id 11Article in journal (Refereed) Published
Abstract [en]

A design experiment where students in Grade 5 (11–12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space reasoning over idiosyncratic reasoning when the sample space was changed between color runs. In the second and third steps, students used degrees of variation in the distribution of the mode across samples to infer whether an unknown sample space was uniform. Students’ reasoning disclosed the logic: the larger the variation, the greater the reason for rejecting a uniform sample space.

Place, publisher, year, edition, pages
IASE/ISI, 2023
Keywords
Statistics education research; Informal statistical inference; Hypothesis testing; Inferentialism; Reasons, Sample-space
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123466 (URN)10.52041/serj.v22i2.425 (DOI)
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2024-02-28Bibliographically approved
Harvey, F. & Nilsson, P. (2022). Contradictions and their manifestations in professional learning communities in mathematics. Journal of Mathematics Teacher Education, 25(6), 697-723
Open this publication in new window or tab >>Contradictions and their manifestations in professional learning communities in mathematics
2022 (English)In: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 25, no 6, p. 697-723Article in journal (Refereed) Published
Abstract [en]

Professional learning communities (PLC) have increasingly attracted attention in research on teachers’ professional development. The aim of this study is to identify contradictions that can occur and be manifested in PLCs in mathematics. Identifying contradictions in PLCs are important, as the identification and resolution of contradictions are crucial to developing PLCs. We have conceptualized PLCs and contradictions within the Cultural Historical Activity Theory. Our data consist of two iterations of interviews with four teacher leader coaches with extensive experience of coaching teacher leaders of PLCs in mathematics. The study distinguishes 26 manifestations of contradictions, taking the overall forms of dilemmas and conflicts. Our results can be used in designing PLCs in mathematics: they can be used to make visible and increase participants’ awareness of contradictions involved in PLCs and thereby increase the possibility that the contradictions serve as sources of support rather than obstacles in the development of PLCs in mathematics.

Place, publisher, year, edition, pages
Springer Nature, 2022
Keywords
Activity systems; Professional learning communities; Contradictions; Manifestations; Mathematics
National Category
Didactics
Research subject
Education, Didactics
Identifiers
urn:nbn:se:lnu:diva-123472 (URN)10.1007/s10857-021-09513-4 (DOI)2-s2.0-85113775325 (Scopus ID)
Funder
Örebro University
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-08-25Bibliographically approved
Nilsson, P. (2020). A Framework for Investigating Qualities of Procedural and Conceptual Knowledge in Mathematics: An inferentialist perspective. Journal for Research in Mathematics Education, 51(5), 574-599
Open this publication in new window or tab >>A Framework for Investigating Qualities of Procedural and Conceptual Knowledge in Mathematics: An inferentialist perspective
2020 (English)In: Journal for Research in Mathematics Education, ISSN 0021-8251, E-ISSN 1945-2306, Vol. 51, no 5, p. 574-599Article in journal (Refereed) Published
Abstract [en]

This study introduces inferentialism and, particularly, the Game of Giving and Asking for Reasons (GoGAR), as a new theoretical perspective for investigating qualities of procedural and conceptual knowledge in mathematics. The study develops a framework in which procedural knowledge and conceptual knowledge are connected to limited and rich qualities of GoGARs. General characteristics of limited GoGARs are their atomistic, implicit, and noninferential nature, as opposed to rich GoGARs, which are holistic, explicit, and inferential. The mathematical discussions of a Grade 6 class serve the case to show how the framework of procedural and conceptual GoGARs can be used to give an account of qualitative differences in procedural and conceptual knowledge in the teaching of mathematics.

Place, publisher, year, edition, pages
National Council of Teachers of Mathematics, 2020
Keywords
Inferential connections, Inferentialism, Mathematical discussions, Procedural and conceptual knowledge, Reasons
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123482 (URN)10.5951/jresematheduc-2020-0167 (DOI)000587848500005 ()2-s2.0-85096578700 (Scopus ID)
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-09-11Bibliographically approved
Hjelte, A., Schindler, M. & Nilsson, P. (2020). Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review. Education Sciences, 10(10), Article ID 289.
Open this publication in new window or tab >>Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review
2020 (English)In: Education Sciences, E-ISSN 2227-7102, Vol. 10, no 10, article id 289Article, review/survey (Refereed) Published
Abstract [en]

Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under investigation is diverse—which goes along with a diversity of understandings of the term reasoning. The aim of this article is to provide an overview on kinds of mathematical reasoning that are addressed in mathematics education research. We conducted a systematic review focusing on the question: What kinds of reasoning are addressed in empirical research in mathematics education? We pursued this question by searching for articles in the database Web of Science with the term reason* in the title. Based on this search, we used a systematic approach to inductively find kinds of reasoning addressed in empirical research in mathematics education. We found three domain-general kinds of reasoning (e.g., creative reasoning) as well as six domain-specific kinds of reasoning (e.g., algebraic reasoning). The article gives an overview on these different kinds of reasoning both in a domain-general and domain-specific perspective, which may be of value for both research and practice (e.g., school teaching).

Place, publisher, year, edition, pages
MDPI, 2020
Keywords
mathematics education, mathematical reasoning, systematic literature review, kinds of reasoning
National Category
Didactics
Research subject
Mathematics
Identifiers
urn:nbn:se:lnu:diva-123478 (URN)10.3390/educsci10100289 (DOI)000585309400001 ()
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-08-08Bibliographically approved
Nilsson, P. (2020). Students’ Informal Hypothesis Testing in a Probability Context with Concrete Random Generators. Statistics Education Research Journal, 19(3), 53-73
Open this publication in new window or tab >>Students’ Informal Hypothesis Testing in a Probability Context with Concrete Random Generators
2020 (English)In: Statistics Education Research Journal, E-ISSN 1570-1824, Vol. 19, no 3, p. 53-73Article in journal (Refereed) Published
Abstract [en]

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning environment, and what role processes of data production play in their investigations. The study outlines aspects of students’ informal understanding of hypothesis testing. It shows how students with no formal education can follow the logic that a small difference in samples can be the effect of randomness, while a large difference implies a real difference in the underlying process. The students distinguish the mode and the size of differences in frequencies as signals in data and used these signals to give data-based reasons in processes of informal hypothesis testing. The study also highlights the role of data production and points to a need for further research on the role of data production in an informal approach to the teaching and learning of statistical inference.

Place, publisher, year, edition, pages
Voorburg, The Netherlands: IASE/ISI, 2020
Keywords
Statistics education research, Informal statistical inference, Informal hypothesis testing, Experimentation-based teaching, Probability distribution, Inferentialism
National Category
Didactics
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123486 (URN)10.52041/serj.v19i3.56 (DOI)
Funder
Swedish Research Council, 721-2012-4811
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2024-02-28Bibliographically approved
Nilsson, P. (2019). An Inferentialist Perspective on How Note-taking can Constrain the Orchestration of Math-Talk. Scandinavian Journal of Educational Research, 63(7), 1121-1133
Open this publication in new window or tab >>An Inferentialist Perspective on How Note-taking can Constrain the Orchestration of Math-Talk
2019 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 63, no 7, p. 1121-1133Article in journal (Refereed) Published
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, 2019
Keywords
Note-taking, math-talk, inferentialism, teacher control
National Category
Didactics
Research subject
Mathematics; Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123483 (URN)10.1080/00313831.2018.1520740 (DOI)000493920100009 ()2-s2.0-85054516852 (Scopus ID)
Funder
Swedish Research Council, 721-2012-4811
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-09-11Bibliographically approved
Nilsson, P. & Eckert, A. (2019). Color-coding as a means to support flexibility in pattern generalization tasks. In: U. T. Jankvist; M. van den Heuvel-Panhuizen; M. Veldhuis (Ed.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education: . Paper presented at Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht, the Netherlands, February 6-10, 2019 (pp. 614-621). Utrecht, Netherlands: European Society for Research in Mathematics Education
Open this publication in new window or tab >>Color-coding as a means to support flexibility in pattern generalization tasks
2019 (English)In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education / [ed] U. T. Jankvist; M. van den Heuvel-Panhuizen; M. Veldhuis, Utrecht, Netherlands: European Society for Research in Mathematics Education, 2019, p. 614-621Conference paper, Published paper (Refereed)
Abstract [en]

This study investigates how color-coding can support processes of flexibility in figural pattern generalization tasks. A lesson from a Grade 8 class serves the case for our investigation. The lesson is part of a larger research project, which is based on the iterative research methodology of design experiments and involves a total of six lessons, distributed over two classes (three lessons in each class). The study shows how coloring can encourage students to move from recursive strategies, like successive addition, and support processes of flexibility in linking algebraic expressions and the meaning of n to visual structures of an expanding figural pattern.

Place, publisher, year, edition, pages
Utrecht, Netherlands: European Society for Research in Mathematics Education, 2019
National Category
Didactics Algebra and Logic
Research subject
Mathematics, Mathematical Education
Identifiers
urn:nbn:se:lnu:diva-123488 (URN)
Conference
Eleventh Congress of the European Society for Research in Mathematics Education (CERME11), Utrecht, the Netherlands, February 6-10, 2019
Available from: 2023-08-08 Created: 2023-08-08 Last updated: 2023-09-12Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-6827-5508

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