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Seidouvy, A. & Schindler, M. (2019). An inferentialist account of students’ collaboration in mathematics education. Mathematics Education Research Journal
Open this publication in new window or tab >>An inferentialist account of students’ collaboration in mathematics education
2019 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

Collaboration is an increasingly popular topic in mathematics education due to its potential to foster students’learning. The purpose of this article is to draw attention to the semantic philosophical theory of inferentialism and its value for investigating students’ collaboration. We suggest that Brandom’s inferentialism can serve as a valuable theoretical resource to overcome certain issues of existing theoretical view-points on student collaboration. In particular, we argue that inferentialism may help to understand the individual and social nature of collaboration as intertwined. We illustrate our inferentialist approach using data from two scenes taken from video-recorded group work sessions from a fifth and seventh grade primary school class in Sweden. The topic in both classes was data generation in statistics.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Collaboration, Data generation, Inferentialism, Norms, Philosophy
National Category
Mathematics Didactics
Identifiers
urn:nbn:se:oru:diva-76042 (URN)10.1007/s13394-019-00267-0 (DOI)
Funder
Swedish Research Council, 2012-04811
Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
Seidouvy, A., Helenius, O. & Schindler, M. (2019). Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism. Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], 24(2), 25-47
Open this publication in new window or tab >>Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism
2019 (English)In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 24, no 2, p. 25-47Article in journal (Refereed) Published
Abstract [en]

Students’ peer collaboration efforts in mathematics and statistics is a topic that has increasingly gained attention in research. In any collaboration, authority relations play a role for how meaning is constituted: Whenever things are discussed and decision sare made, authority is involved in a sense that some arguments or persons may be more convincing and powerful than others. In this article, we investigate how authority changes dynamically in type and in distribution as groups of fifth grade students collaborate in data generation processes. We identify and categorize authority using an epistemological framework, which is based on the philosophical theory of inferentialism. The results show that the three different types of authority described in inferentialism are all identifiable in students’ collaborative work. We also find and categorize further types of authority connected to the statistics group work, some of which are hardly addressed in previous research.

Place, publisher, year, edition, pages
Göteborg, Sweden: NOMAD, 2019
National Category
Mathematics Didactics
Identifiers
urn:nbn:se:oru:diva-76046 (URN)
Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-05Bibliographically approved
Schindler, M. & Lilienthal, A. J. (2019). Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry. Educational Studies in Mathematics, 101(1), 123-139
Open this publication in new window or tab >>Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry
2019 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 1, p. 123-139Article in journal (Refereed) Published
Abstract [en]

Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in mathematics even though they may not apply in this domain. This article investigates to what extent the EMH applies in mathematics - geometry in particular - and aims to lift the discussion of what inferences can be validly made from eye-tracking data. We use a case study to investigate the need for a refinement of the use of the EMH. In a stimulated recall interview, a student described his original thoughts perusing a gaze-overlaid video recorded when he was working on a geometry problem. Our findings contribute to better a understanding of when and how the EMH applies in the subdomain of geometry. In particular, we identify patterns of eye movements that provide valuable information on students' geometry problem solving: certain patterns where the eye fixates on what the student is processing and others where the EMH does not hold. Identifying such patterns may contribute to an interpretation theory for students' eye movements in geometry - exemplifying a domain-specific theory that may reduce the inherent ambiguity and uncertainty that eye tracking data analysis has.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Eye tracking, Eye movements, Eye-mind hypothesis, Geometry
National Category
Educational Sciences
Identifiers
urn:nbn:se:oru:diva-73868 (URN)10.1007/s10649-019-9878-z (DOI)000463669800009 ()2-s2.0-85061182709 (Scopus ID)
Available from: 2019-04-23 Created: 2019-04-23 Last updated: 2019-04-23Bibliographically approved
Chadalavada, R. T., Andreasson, H., Schindler, M., Palm, R. & Lilienthal, A. (2018). Accessing your navigation plans! Human-Robot Intention Transfer using Eye-Tracking Glasses. In: Case K. &Thorvald P. (Ed.), Advances in Manufacturing Technology XXXII: Proceedings of the 16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, September 11–13, 2018, University of Skövde, Sweden. Paper presented at 16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, University of Skövde, Sweden, September 11–13, 2018 (pp. 253-258). Amsterdam, Netherlands: IOS Press
Open this publication in new window or tab >>Accessing your navigation plans! Human-Robot Intention Transfer using Eye-Tracking Glasses
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2018 (English)In: Advances in Manufacturing Technology XXXII: Proceedings of the 16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, September 11–13, 2018, University of Skövde, Sweden / [ed] Case K. &Thorvald P., Amsterdam, Netherlands: IOS Press, 2018, p. 253-258Conference paper, Published paper (Refereed)
Abstract [en]

Robots in human co-habited environments need human-aware task and motion planning, ideally responding to people’s motion intentions as soon as they can be inferred from human cues. Eye gaze can convey information about intentions beyond trajectory and head pose of a person. Hence, we propose eye-tracking glasses as safety equipment in industrial environments shared by humans and robots. This paper investigates the possibility of human-to-robot implicit intention transference solely from eye gaze data.  We present experiments in which humans wearing eye-tracking glasses encountered a small forklift truck under various conditions. We evaluate how the observed eye gaze patterns of the participants related to their navigation decisions. Our analysis shows that people primarily gazed on that side of the robot they ultimately decided to pass by. We discuss implications of these results and relate to a control approach that uses human eye gaze for early obstacle avoidance.

Place, publisher, year, edition, pages
Amsterdam, Netherlands: IOS Press, 2018
Series
Advances in Transdisciplinary Engineering, ISSN 2352-751X, E-ISSN 2352-7528 ; 8
Keywords
Human-Robot Interaction (HRI), Eye-tracking, Eye-Tracking Glasses, Navigation Intent, Implicit Intention Transference, Obstacle avoidance.
National Category
Computer Sciences
Research subject
Computer Science
Identifiers
urn:nbn:se:oru:diva-70706 (URN)10.3233/978-1-61499-902-7-253 (DOI)000462212700041 ()2-s2.0-85057390000 (Scopus ID)978-1-61499-901-0 (ISBN)978-1-61499-902-7 (ISBN)
Conference
16th International Conference on Manufacturing Research, incorporating the 33rd National Conference on Manufacturing Research, University of Skövde, Sweden, September 11–13, 2018
Projects
Action and Intention Recognition (AIR)ILIAD
Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2019-04-04Bibliographically approved
Seidouvy, A., Helenius, O. & Schindler, M. (2018). Data generation in statistics – both procedural and conceptual: An inferentialist analysis. In: J. Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren, & O. Olande (Ed.), Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11. Paper presented at The eleventh research seminar of the Swedish Society for Research in Mathematics Education (MADIF11), Karlstad, Sweden, January 23–24, 2018 (pp. 191-200). Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF
Open this publication in new window or tab >>Data generation in statistics – both procedural and conceptual: An inferentialist analysis
2018 (English)In: Perspectives on professional development of mathematics teachers: Proceedings of MADIF 11 / [ed] J. Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren, & O. Olande, Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018, p. 191-200Conference paper, Published paper (Refereed)
Abstract [en]

Data generation in statistics education is often conducted by the students them-selves; however, the question of what learning opportunities the data generation process offers has only been studied to a small extent. This paper investigates to what extent data generation is an observational and procedural vs. a conceptual activity. We inquire into this question based on an empirical study where eleven year old students measured the jump lengths of paper frogs. Our analysis draws on stu-dents’ discussions in group work, and it uses inferentialism as a background theory. Our results indicate that students’ discussions are conceptual to a certain extent and provide various learning opportunities for the students.

Place, publisher, year, edition, pages
Göteborg, Sweden: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2018
Series
Skrifter från Svensk Förening för MatematikDidaktisk Forskning, ISSN 1651-3274 ; 13
National Category
Mathematics Didactics
Identifiers
urn:nbn:se:oru:diva-76045 (URN)978-91-984024-2-1 (ISBN)
Conference
The eleventh research seminar of the Swedish Society for Research in Mathematics Education (MADIF11), Karlstad, Sweden, January 23–24, 2018
Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-20Bibliographically approved
Schindler, M. & Seidouvy, A. (2018). Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology. In: Gail Burrill, Dani Ben-Zvi (Ed.), Topics and Trends in Current Statistics Education Research: (pp. 153-171). Springer
Open this publication in new window or tab >>Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology
2018 (English)In: Topics and Trends in Current Statistics Education Research / [ed] Gail Burrill, Dani Ben-Zvi, Springer, 2018, p. 153-171Chapter in book (Refereed)
Abstract [en]

Informal statistical inference and informal inferential reasoning (IIR) are increasingly gaining significance in statistics education research. What has not sufficiently been dealt with in previous research is the social nature of students’ informal inferences. This chapter presents results from a study investigating seventh grade students’ IIR in an experiment with paper helicopters. It focuses on students’ reasoning on the best rotor blade length, addressing statistical correlation. We study how students draw inferences when working in a group; and how their inferences emerge socially in their IIR. For grasping the reasoning’s social nature and its normativity, we use inferentialism as background theory. The results illustrate how students’ informal inferences are socially negotiated in the group, how students’ perceived norms influence IIR, and what roles statistical concepts play in students’ IIR.

Place, publisher, year, edition, pages
Springer, 2018
Series
ICME-13 Monographs, ISSN 2520-8322, E-ISSN 2520-8330
Keywords
Generalization from data, Inferentialism, Informal inferential reasoning (IIR), Informal statistical inference (ISI), Informal statistical reasoning, Norms, Social
National Category
Mathematics Didactics
Identifiers
urn:nbn:se:oru:diva-76043 (URN)10.1007/978-3-030-03472-6_7 (DOI)978-3-030-03471-9 (ISBN)978-3-030-03472-6 (ISBN)
Funder
Swedish Research Council, 2012-04811
Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
Lilienthal, A. & Schindler, M. (2017). Conducting Dual Portable Eye-Tracking in Mathematical Creativity Research. In: Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H (Ed.), Proceedings the 41th Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at The 41th Conference of the International Group for the Psychology of Mathematics Education, Singapore, July 17 – 22, 2017 (pp. 233-233). Singapore: PME, 1
Open this publication in new window or tab >>Conducting Dual Portable Eye-Tracking in Mathematical Creativity Research
2017 (English)In: Proceedings the 41th Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H, Singapore: PME , 2017, Vol. 1, p. 233-233Conference paper, Published paper (Refereed)
Abstract [en]

Eye-tracking opens a window to the focus of attention of persons and promises to allow studying, e.g., creative processes “in vivo” (Nüssli, 2011). Most eye-tracking studies in mathematics education research focus on single students. However, following a Vygotskyan notion of learning and development where the individual and the social are dialectically interrelated, eye-tracking studies of collaborating persons appear beneficial for understanding students’ learning in their social facet. Dual eye-tracking, where two persons’ eye-movements are recorded and related to a joint coordinate-system, has hardly been used in mathematics education research. Especially dual portable eye-tracking (DPET) with goggles has hardly been explored due to its technical challenges compared to screen-based eye-tracking.In our interdisciplinary research project between mathematics education and computer science, we conduct DPET for studying collective mathematical creativity (Levenson, 2011) in a process perspective. DPET offers certain advantages, including to carry out paper and pen tasks in rather natural settings. Our research interests are: conducting DPET (technical), investigating opportunities and limitations of DPET for studying students’ collective creativity (methodological), and studying students’ collective creative problem solving (empirical).We carried out experiments with two pairs of university students wearing Pupil Pro eye tracking goggles. The students were given 45 min to solve a geometry problem in as many ways as possible. For our analysis, we first programmed MATLAB code to synchronize data from both participants’ goggles; resulting in a video displaying both students’ eye-movements projected on the task sheet, the sound recorded by the goggles, and additional information, e.g. pupil dilation. With these videos we expect to get insights into how students’ attentions meet, if students’ eye-movements follow one another, or verbal inputs, etc. We expect insights into promotive aspects in students’ collaboration: e.g., if pointing on the figure or intensive verbal communication promote students’ joint attention (cf. Nüssli, 2011). Finally, we think that the expected insights can contribute to existing research on collective mathematical creativity, especially to the question of how to enhance students’ creative collaboration.

Place, publisher, year, edition, pages
Singapore: PME, 2017
National Category
Didactics
Research subject
Computer Engineering; Computer Science
Identifiers
urn:nbn:se:oru:diva-64763 (URN)978-138-71-3608-7 (ISBN)
Conference
The 41th Conference of the International Group for the Psychology of Mathematics Education, Singapore, July 17 – 22, 2017
Available from: 2018-02-01 Created: 2018-02-01 Last updated: 2018-08-14Bibliographically approved
Schindler, M. & Lilienthal, A. (2017). Eye-Tracking and its Domain-Specific Interpretation: A Stimulated Recall Study on Eye Movements in Geometrical Tasks. In: Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H (Ed.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at Annual Meeting of the International Group for the Psychology of Mathematics Education, Singapore, Singapore, July 17 – 22, 2017 (pp. 153-160). Singapore: PME, 4
Open this publication in new window or tab >>Eye-Tracking and its Domain-Specific Interpretation: A Stimulated Recall Study on Eye Movements in Geometrical Tasks
2017 (English)In: Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education / [ed] Kaur, B., Ho, W.K., Toh, T.L., & Choy, B.H, Singapore: PME , 2017, Vol. 4, p. 153-160Conference paper, Published paper (Refereed)
Abstract [en]

Eye-tracking offers various possibilities for mathematics education. Yet, even in suitably visually presented tasks, interpretation of eye-tracking data is non-trivial. A key reason is that the interpretation of eye-tracking data is context-sensitive. To reduce ambiguity and uncertainty, we studied the interpretation of eye movements in a specific domain: geometrical mathematical creativity tasks. We present results from a qualitative empirical study in which we analyzed a Stimulated Recall Interview where a student watched the eye-tracking overlaid video of his work on a task. Our results hint at how eye movements can be interpreted and show limitations and opportunities of eye tracking in the domain of mathematical geometry tasks and beyond.

Place, publisher, year, edition, pages
Singapore: PME, 2017
National Category
Didactics
Research subject
Education
Identifiers
urn:nbn:se:oru:diva-64765 (URN)978-138-71-3613-1 (ISBN)
Conference
Annual Meeting of the International Group for the Psychology of Mathematics Education, Singapore, Singapore, July 17 – 22, 2017
Available from: 2018-02-01 Created: 2018-02-01 Last updated: 2018-08-14Bibliographically approved
Schindler, M. & Lilienthal, A. (2017). Eye-Tracking As A Tool For Investigating Mathematical Creativity. In: The 10th Mathematical Creativity and Giftedness International Conference: Proceedings. Paper presented at 10th International Conference on Mathematical Creativity and Giftedness (MCG), Nicosia, Cyprus, 24-26 April, 2017 (pp. 45-50). Nicosia, Cyprus: Department of Education, University of Cyprus
Open this publication in new window or tab >>Eye-Tracking As A Tool For Investigating Mathematical Creativity
2017 (English)In: The 10th Mathematical Creativity and Giftedness International Conference: Proceedings, Nicosia, Cyprus: Department of Education, University of Cyprus , 2017, p. 45-50Conference paper, Published paper (Refereed)
Abstract [en]

Mathematical creativity as a key ability in our increasingly automated and interconnected, high-technology based society and economy is increasingly in the focus of mathematics education research. The recent scientific discussion in this domain is shifting from a product view, on written solutions and drawings, to a process view, which aims to investigate the different stages of how students come up with creative ideas. The latter is, however, a challenge. In this theoretical-methodological paper, we present and discuss the opportunities that eye-tracking offers for studying creativity in a process view. We discuss in which way eye-tracking allows to obtain novel answers to the questions of how original ideas come up, how they evolve and what leads to the so-called Eureka!-moment. We focus on video-based eye tracking approaches, discuss pros and cons of screen-based and mobile eye tracking, and illustrate methods of data analysis and their benefits for research on mathematical creativity.

Place, publisher, year, edition, pages
Nicosia, Cyprus: Department of Education, University of Cyprus, 2017
Keywords
Mathematical Creativity, Eye-Tracking, Eye Movements, MSTs, geometry, proof
National Category
Didactics
Research subject
Education
Identifiers
urn:nbn:se:oru:diva-64766 (URN)978-9963-700-99-8 (ISBN)
Conference
10th International Conference on Mathematical Creativity and Giftedness (MCG), Nicosia, Cyprus, 24-26 April, 2017
Available from: 2018-02-01 Created: 2018-02-01 Last updated: 2018-09-06Bibliographically approved
Schindler, M. & Rott, B. (2017). Networking theories on giftedness: What we can learn from synthesizing Renzulli’s domain general and Krutetskii’s mathematics-specific theory. Education Sciences, 7(1)
Open this publication in new window or tab >>Networking theories on giftedness: What we can learn from synthesizing Renzulli’s domain general and Krutetskii’s mathematics-specific theory
2017 (English)In: Education Sciences, E-ISSN 2227-7102, Vol. 7, no 1Article in journal (Refereed) Published
Abstract [en]

Giftedness is an increasingly important research topic in educational sciences and mathematics education in particular. In this paper, we contribute to further theorizing mathematical giftedness through illustrating how networking processes can be conducted and illustrating their potential benefits. The paper focuses on two theories: Renzulli’s domain-general theory on giftedness as an interplay of creativity, above-average ability, and task commitment; and Krutetskii’s mathematics-specific theory on gifted students’ abilities. In a “proof of concept”, we illustrate how the abilities offered in Krutetskii’s theory can be mapped to the three traits described by Renzulli. This is realized through a mapping process in which two raters independently mapped the abilities offered by Krutetskii to Renzulli’s traits. The results of this mapping give first insights into (a) possible mappings of Krutetskii’s abilities to Renzulli’s traits and, thus, (b) a possible domain-specific specification of Renzulli’s theory. This mapping hints at interesting potential phenomena: in Krutetskii’s theory, above-average ability appears to be the trait that predominantly is addressed, whereas creativity and especially task-commitment seem less represented. Our mapping demonstrates what a mathematics-specific specification of Renzulli’s theory can look like. Finally, we elaborate on the consequences of our findings, restrictions of our methodology, and on possible future research.

Place, publisher, year, edition, pages
Basel, Switzerland: MDPI AG, 2017
Keywords
giftedness; theories; mathematics education; networking theories; domain-general; domain-specific
National Category
Didactics Learning
Identifiers
urn:nbn:se:oru:diva-55244 (URN)10.3390/educsci7010006 (DOI)000418288400006 ()
Available from: 2017-02-02 Created: 2017-02-02 Last updated: 2018-11-29Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9530-4151

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