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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
Lilienthal, A. J. & Schindler, M. (2019). Current Trends in Eye Tracking Research in Mathematics Education: A PME Literature Review: A PME Survey. In: 43rd Annual Meeting 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 (PME-43), Pretoria, South Africa, July 7 - 12, 2019 (pp. 62-62). , 4
Open this publication in new window or tab >>Current Trends in Eye Tracking Research in Mathematics Education: A PME Literature Review: A PME Survey
2019 (English)In: 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education, 2019, Vol. 4, p. 62-62Conference paper, Oral presentation with published abstract (Other academic)
Abstract [en]

Eye tracking (ET) is a research method that receives growing interest in mathematics education research (MER). This paper aims to give a literature overview, specifically focusing on the evolution of interest in this technology, ET equipment, and analysis methods used in mathematics education. To capture the current state, we focus on papers published in the proceedings of PME, one of the primary conferences dedicated to MER, of the last ten years. We identify trends in interest, methodology, and methods of analysis that are used in the community, and discuss possible future developments.

Keywords
Eye Tracking, Mathematics Education Research, Survey, PME
National Category
Educational Sciences Pedagogy
Research subject
Education
Identifiers
urn:nbn:se:oru:diva-79738 (URN)
Conference
Annual Meeting of the International Group for the Psychology of Mathematics Education (PME-43), Pretoria, South Africa, July 7 - 12, 2019
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-07Bibliographically approved
Schindler, M., Schaffernicht, E. & Lilienthal, A. J. (2019). Differences in Quantity Recognition Between Students with and without Mathematical Difficulties Analyzed Through Eye: Analysis Through Eye-Tracking and AI. In: M. Graven, H. Venkat, A. Essien & P. Vale (Ed.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education: . Paper presented at 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July, 2019 (pp. 281-288). PME, 3
Open this publication in new window or tab >>Differences in Quantity Recognition Between Students with and without Mathematical Difficulties Analyzed Through Eye: Analysis Through Eye-Tracking and AI
2019 (English)In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education / [ed] M. Graven, H. Venkat, A. Essien & P. Vale, PME , 2019, Vol. 3, p. 281-288Conference paper, Published paper (Refereed)
Abstract [en]

Difficulties in mathematics learning are an important topic in practice and research. In particular, researchers and practitioners need to identify students’ needs for support to teach and help them adequately. However, empirical research about group differences of students with and without mathematical difficulties (MD) is still scarce. Previous research suggests that students with MD may differ in their quantity recognition strategies in structured whole number representations from students without MD. This study uses eye-tracking (ET), combined with Artificial Intelligence (AI), in particular pattern recognition methods, to analyze group differences in gaze patterns in quantity recognition of N=164 fifth grade students.

Place, publisher, year, edition, pages
PME, 2019
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics
Identifiers
urn:nbn:se:oru:diva-79730 (URN)
Conference
43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July, 2019
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-06Bibliographically 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. & Lilienthal, A. J. (2019). Implicit intention transference using eye-tracking glasses for improved safety in human-robot interaction. In: : . Paper presented at International Conference on Social Robotics - Quality of Interaction in Socially Assistive Robots Workshop, Madrid, Spain, November 26th-29th, 2019.
Open this publication in new window or tab >>Implicit intention transference using eye-tracking glasses for improved safety in human-robot interaction
2019 (English)Conference paper, Oral presentation only (Refereed)
Abstract [en]

Eye gaze can convey information about intentions beyond what can beinferred from the trajectory and head pose of a person. We propose eye-trackingglasses as safety equipment in industrial environments shared by humans androbots. In this work, an implicit intention transference system was developed and implemented. Robot was given access to human eye gaze data, and it responds tothe eye gaze data through spatial augmented reality projections on the sharedfloor space in real-time and the robot could also adapt its path. This allows proactivesafety approaches in HRI for example by attempting to get the human'sattention when they are in the vicinity of a moving robot. A study was conductedwith workers at an industrial warehouse. The time taken to understand the behaviorof the system was recorded. Electrodermal activity and pupil diameter wererecorded to measure the increase in stress and cognitive load while interactingwith an autonomous system, using these measurements as a proxy to quantifytrust in autonomous systems.

Keywords
Human-robot interaction, intention communication, eye tracking, spatial augmented reality, electrodermal activity, stress, cognitive load.
National Category
Computer Sciences
Research subject
Computer Science
Identifiers
urn:nbn:se:oru:diva-79736 (URN)
Conference
International Conference on Social Robotics - Quality of Interaction in Socially Assistive Robots Workshop, Madrid, Spain, November 26th-29th, 2019
Projects
ILAID
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-14Bibliographically approved
Schindler, M., Bader, E., Lilienthal, A. J., Schindler, F. & Schabmann, A. (2019). Quantity Recognition in Structured Whole Number Representations of Students with Mathematical Difficulties: An Eye-Tracking Study. Learning Disabilities: A Contemporary Journal, 17(1), 5-28
Open this publication in new window or tab >>Quantity Recognition in Structured Whole Number Representations of Students with Mathematical Difficulties: An Eye-Tracking Study
Show others...
2019 (English)In: Learning Disabilities: A Contemporary Journal, ISSN 1937-6928, Vol. 17, no 1, p. 5-28Article in journal (Refereed) Published
Abstract [en]

Quantity recognition in whole number representations is a fundamental skill children need to acquire in their mathematical development. Despite the observed correlation to mathematics achievement, however, the abil-ity to recognize quantities in structured whole number representations has not been studied extensively. In this article, we investigate how stu-dents with mathematical difficulties (MD) differ from typically develop-ing (TD) students in quantity recognition in structured whole number representations. We use eye tracking (ET), which can help to identify stu-dents’ quantity recognition strategies. In contrast to methods that include collecting verbal answers and reports, ET avoids an additional verbal-ization step, which may be affected by poor language skills and by low meta-cognitive abilities or memory issues when monitoring, recalling,and explaining one’s thoughts. We present an ET study with 20 students of which ten were found to have MD in initial tests (using qualitative and quantitative diagnostics). We used ET glasses, which allow seeing the students’ view of the scene with an augmented visualization of the gaze point projected onto the scene. The obtained gaze-overlaid videos also include audio data and records of students’ answers and utterances. In our study, we did not find significant differences between the error rates of MD and TD students. Response times, however, were longer for students with MD. The analysis of the ET data brought students’ quantity recogni-tion strategies to light, some of which were not found in previous research. Our analyses revealed differences in the use of these quantity recognition strategies between MD and TD students. Our study illustrates the power of ET for investigating students’ quantity recognition strategies and the potential of ET to support MD students.

Place, publisher, year, edition, pages
Learning Disabilities Worldwide, 2019
Keywords
Mathematical Difficulties, Structured Whole Number Representations, Quantity Recognition, Abacus, Dot-Field, Eye Tracking
National Category
Educational Sciences Pedagogy
Research subject
Education
Identifiers
urn:nbn:se:oru:diva-79744 (URN)
Available from: 2020-02-03 Created: 2020-02-03 Last updated: 2020-02-07Bibliographically approved
Schindler, M. & Lilienthal, A. J. (2019). Students' Creative Process in Mathematics: Insights from Eye-Tracking-Stimulated Recall Interview on Students' Work on Multiple Solution Tasks. International Journal of Science and Mathematics Education
Open this publication in new window or tab >>Students' Creative Process in Mathematics: Insights from Eye-Tracking-Stimulated Recall Interview on Students' Work on Multiple Solution Tasks
2019 (English)In: International Journal of Science and Mathematics Education, ISSN 1571-0068, E-ISSN 1573-1774Article in journal (Refereed) Epub ahead of print
Abstract [en]

Students' creative process in mathematics is increasingly gaining significance in mathematics education research. Researchers often use Multiple Solution Tasks (MSTs) to foster and evaluate students' mathematical creativity. Yet, research so far predominantly had a product-view and focused on solutions rather than the process leading to creative insights. The question remains unclear how students' process solving MSTs looks like-and if existing models to describe (creative) problem solving can capture this process adequately. This article presents an explorative, qualitative case study, which investigates the creative process of a school student, David. Using eye-tracking technology and a stimulated recall interview, we trace David's creative process. Our findings indicate what phases his creative process in the MST involves, how new ideas emerge, and in particular where illumination is situated in this process. Our case study illustrates that neither existing models on the creative process, nor on problem solving capture David's creative process fully, indicating the need to partially rethink students' creative process in MSTs.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Creative process, Eye tracking (ET), Mathematical creativity, Multiple solution tasks (MSTs), Stimulated recall interview (SRI)
National Category
Educational Sciences
Identifiers
urn:nbn:se:oru:diva-78719 (URN)10.1007/s10763-019-10033-0 (DOI)000499961000001 ()
Note

Funding Agency:

Örebro University

Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2020-02-07Bibliographically 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
Show others...
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
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9530-4151

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