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  • 1.
    Bunz, Elsa
    et al.
    Örebro University, Örebro, Sweden.
    Chadalavada, Ravi Teja
    Örebro University, School of Science and Technology.
    Andreasson, Henrik
    Örebro University, School of Science and Technology.
    Krug, Robert
    Örebro University, School of Science and Technology.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Spatial Augmented Reality and Eye Tracking for Evaluating Human Robot Interaction2016In: Proceedings of RO-MAN 2016 Workshop: Workshop on Communicating Intentions in Human-Robot Interaction, 2016Conference paper (Refereed)
    Abstract [en]

    Freely moving autonomous mobile robots may leadto anxiety when operating in workspaces shared with humans.Previous works have given evidence that communicating in-tentions using Spatial Augmented Reality (SAR) in the sharedworkspace will make humans more comfortable in the vicinity ofrobots. In this work, we conducted experiments with the robotprojecting various patterns in order to convey its movementintentions during encounters with humans. In these experiments,the trajectories of both humans and robot were recorded witha laser scanner. Human test subjects were also equipped withan eye tracker. We analyzed the eye gaze patterns and thelaser scan tracking data in order to understand how the robot’sintention communication affects the human movement behavior.Furthermore, we used retrospective recall interviews to aid inidentifying the reasons that lead to behavior changes.

  • 2.
    Chadalavada, Ravi Teja
    et al.
    Örebro University, School of Science and Technology.
    Andreasson, Henrik
    Örebro University, School of Science and Technology.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Palm, Rainer
    Örebro University, School of Science and Technology.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Accessing your navigation plans! Human-Robot Intention Transfer using Eye-Tracking Glasses2018In: 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 (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.

  • 3.
    Joklitschke, Julia
    et al.
    University of Duisburg-Essen, Duisburg, Germany.
    Rott, Benjamin
    University of Duisburg-Essen, Duisburg, Germany.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Correlations between creativity in geometry and algebra2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (PME) / [ed] C. Csíkos, A. Rausch, & J. Szitányi, 2016, p. 181-Conference paper (Refereed)
  • 4.
    Joklitschke, Julia
    et al.
    University of Duisburg-Essen, Duisburg, Germany.
    Rott, Benjamin
    University of Duisburg-Essen, Duisburg, Germany.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Erfassung mathematischer Kreativität: Herausforderungen valider Untersuchungsmethoden2016In: Beiträge zum Mathematikunterricht 2016: Vorträge auf der 50. Tagung für Didaktik der Mathematik vom 07.03.2016 bis 11.03.2016 in Heidelberg, WTM Verlag, 2016, p. 497-501Conference paper (Other academic)
  • 5.
    Joklitschke, Julia
    et al.
    University of Duisburg-Essen, Duisburg, Germany.
    Rott, Benjamin
    University of Duisburg-Essen, Duisburg, Germany.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Measuring mathematical creativity: Towards a conformation and refinement of a test-instrument2016In: Problem solving in mathematics education: Proceedings of the 2015 joint 17th conference of ProMath and the 2nd GDM working group on problem solving / [ed] T. Fritzlar, D. Assmuss, A Kuzle, & B. Rott, Münster: WTM Verlag, 2016, p. 149-158Conference paper (Refereed)
  • 6.
    Lilienthal, Achim
    et al.
    Örebro University, School of Science and Technology.
    Schindler, Maike
    Örebro University, School of Science and Technology. University of Cologne, Cologne, Germany.
    Conducting Dual Portable Eye-Tracking in Mathematical Creativity Research2017In: 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 (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.

  • 7.
    Nilsson, Per
    et al.
    Örebro University, School of Science and Technology.
    Schindler, Maike
    University of Cologne, Cologne, Germany.
    Bakker, Arthur
    Utrecht University, Utrecht, The Netherlands.
    The nature and use of theories in statistics education2017In: International Handbook of Research in Statistics Education / [ed] Ben-Zvi, D.; Makar, K.; Garfield, J., Springer, 2017Chapter in book (Other academic)
  • 8.
    Schindler, Maike
    Technische Universität, Dortmund, Deutschland.
    Auf dem Weg zum Begriff der negativen Zahl: Empirische Studie zur Ordnungsrelation für ganze Zahlen aus inferentieller Perspektive.2014Doctoral thesis, monograph (Other academic)
    Abstract [de]

    Grundmuster von Begriffsbildungsprozessen von Schülerinnen und Schülern einer Beschreibung und Analyse zugänglich zu machen, ist ein höchst interessanter und relevanter Bereich der Mathematikdidaktik. Die Autorin widmet sich dieser Thematik, indem sie einen durch philosophische und psychologische Einflüsse geprägten Theorierahmen nutzt, um individuelle Begriffsbildungsprozesse in ihrem Wechselspiel mit Lernsituationen zu verstehen. Dabei wird die Perspektive auf die Lernenden in ein konstruktives Verhältnis zur fachlichen Strukturierung gesetzt. Die empirische Studie zum Begriff der negativen Zahl zeigt die individuellen Begriffsnetze von Lernenden sowie deren Entwicklungen auf. Die Ergebnisse tragen zur Restrukturierung des mathematikdidaktischen Gegenstandsbereichs bei.

  • 9.
    Schindler, Maike
    Örebro University, School of Science and Technology.
    Stärken beim Begründen: Natürlich differenzierend2016In: Mathematik lehren: Die Zeitschrift für den Unterricht in allen Schulstufen, ISSN 0175-2235, no 195, p. 20-24Article in journal (Other academic)
  • 10.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Hussman, Stephan
    Technical university Dortmund, Dortmund, Germany.
    Ein Kontext für negative Zahlen ‒ auch für die Multiplikation: English: A context for negative numbers ‒ also for multiplication2014In: Mathematik lehren: Die Zeitschrift für den Unterricht in allen Schulstufen, ISSN 0175-2235, no 183, p. 28-32Article in journal (Other academic)
    Abstract [de]

    Der Beitrag stellt eine Konzept zur Einführung der negativen Zahlen sowie eine entsprechende Lernumgebung vor, das im Rahmen eines Unterrichtsprojekts erarbeitet wurde. Dazu wurde der tragfähige Kontext “Guthaben und Schulden" weiterentwickelt. Dieser kann beim Aufbau eines inhaltlichen Verstehens, das die Bedeutung von “Minus mal Minus" nicht auf eine Regel reduziert, hilfreich sein.          

  • 11.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Hussmann, Stephan
    IEEM, Technische Universität Dortmund, Dortmund, Germany.
    About students’ individual concepts of negative integers ‒ in terms of the order relation2013In: Proceedings of the eighth congress of the European Society of Research in Mathematics Education: Cerme 8 / [ed] Behiye Ubuz, Çiğdem Haser, Maria Alessandra Mariotti, Ankara: Middle East Technical University , 2013, p. 373-382Conference paper (Refereed)
    Abstract [en]

    We investigated sixth graders’ individual concepts of negative integers right before they were introduced to the “world" of the negatives. In order to investigate students’ first ideas of negative numbers, we initially investigated their ideas concerning the order relation of integers. With a qualitative data analysis utilizing a theoretical lens concerning individual concept formation, we gained insight into the students’ individual procedures and conceptions as well as into how the procedures are linked to the students’ previous knowledge.

  • 12.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Hußmann, Stephan
    International Conference on Industrial Engineering and Engineering Management (IEEM), Technische Universität Dortmund, Dortmund, Germany.
    Nilsson, Per
    Örebro University, School of Science and Technology.
    Bakker, Arthur
    Freudenthal Institute, Utrecht University, Utrecht, Netherlands.
    Sixth-grade students’ reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis2017In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 29, no 4, p. 471-492Article in journal (Refereed)
    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. 

  • 13.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Joklitschke, Julia
    Ruhr-Universität Bochum, Bochum, Germany.
    Designing tasks for mathematically talented students2015In: CERME 9: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer and Naďa Vondrová, Prague, Czech Republic: European Society for Research in Mathematics Education, 2015, p. 1066-1072Conference paper (Refereed)
    Abstract [en]

    For the Design Research project presented, a learning environment for mathematically talented and interested 7th-grade students was investigated. The results show that the subject matter of graph theory offers both opportunities and means for students to develop their abilities. The data analysis showed likewise how the tasks might be modified in order to impose on their potential and thereby foster students’ abilities of a formalized perception and pervasion of mathematical information and of generalization.

  • 14.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology. University of Cologne, Cologne, Germany.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Eye-Tracking and its Domain-Specific Interpretation: A Stimulated Recall Study on Eye Movements in Geometrical Tasks2017In: 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 (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.

  • 15.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology. University of Cologne, Cologne, Germany.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Eye-Tracking As A Tool For Investigating Mathematical Creativity2017In: The 10th Mathematical Creativity and Giftedness International Conference: Proceedings, Nicosia, Cyprus: Department of Education, University of Cyprus , 2017, p. 45-50Conference 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.

  • 16.
    Schindler, Maike
    et al.
    University of Cologne, Department of Special Education.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Eye-Tracking For Studying Mathematical Difficulties: Also In Inclusive Settings2018In: Proceedings of Annual Meeting of the International Group for the Psychology of Mathematics Education (PME-42), Umeå., Sweden: PME , 2018, Vol. 4, p. 115-122Conference paper (Refereed)
    Abstract [en]

    Eye-Tracking (ET) is a promising tool for mathematics education research. Interest is fue­led by recent theoretical and technical developments, and the potential to identify strategies students use in mathematical tasks. This makes ET in­teresting for studying students with mathematical difficulties (MD), also with a view on inclusive settings. We present a systematic analysis of the opportunities ET may hold for understanding strategies of students with MD. Based on an empirical study with 20 fifth graders (10 with MD), we illustrate that and why ET offers opportunities especially for students with MD and describe main advantages. We also identify limitations of think aloud protocols, using ET as validation method, and present characteristics of students’ strategies in tasks on quantity recognition in structured whole number representations.

  • 17.
    Schindler, Maike
    et al.
    University of Cologne, Department of Special Education.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Method and Theory in Their Interplay: Using Eye-Tracking for Investigating Mathematical Learning2018In: Dialogue between ontology and epistemology: New perspectives on theory and methodology in research on learning and education, 2018Conference paper (Refereed)
    Abstract [en]

    In this presentation, we discuss the interplay between theory and one particular method of data collection: eye-tracking. Eye-tracking promises various opportunities for research, in particular for studying students’ attention, strategies, and even collaboration in so-called dual eye-tracking (DUET), and has gained increased interest as a research method. Still, researchers acknowledge that eye-tracking data interpretation is difficult and ambiguous and often needs to be complemented with other sources. In this talk, we discuss two studies in which we aimed for a triangulation of eye-tracking with other research methods. In both studies, ontological and epistemological questions are intertwined.

  • 18.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Chadalavada, Ravi
    Örebro University, School of Science and Technology.
    Ögren, Magnus
    Örebro University, School of Science and Technology.
    Creativity in the eye of the student: Refining investigations of mathematical creativity using eye-tracking goggles2016In: Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (PME) / [ed] C. Csíkos, A. Rausch, & J. Szitányi, 2016Conference paper (Refereed)
    Abstract [en]

    Mathematical creativity is increasingly important for improved innovation and problem-solving. In this paper, we address the question of how to best investigate mathematical creativity and critically discuss dichotomous creativity scoring schemes. In order to gain deeper insights into creative problem-solving processes, we suggest the use of mobile, unobtrusive eye-trackers for evaluating students’ creativity in the context of Multiple Solution Tasks (MSTs). We present first results with inexpensive eye-tracking goggles that reveal the added value of evaluating students’ eye movements when investigating mathematical creativity—compared to an analysis of written/drawn solutions as well as compared to an analysis of simple videos.

  • 19.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology. Faculty of Human Sciences, University of Cologne, Cologne, Germany.
    Lilienthal, Achim J.
    Örebro University, School of Science and Technology.
    Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry2019In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 101, no 1, p. 123-139Article in journal (Refereed)
    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.

  • 20.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Rott, Benjamin
    University of Duisburg-Essen, Duisburg, Germany.
    Kreativität, Interesse und Talente: Mathematische Begabung vielfältig denken2016In: Mathematik lehren: Die Zeitschrift für den Unterricht in allen Schulstufen, ISSN 0175-2235, no 195, p. 2-7Article in journal (Other academic)
  • 21.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Rott, Benjamin
    Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany.
    Networking theories on giftedness: What we can learn from synthesizing Renzulli’s domain general and Krutetskii’s mathematics-specific theory2017In: Education Sciences, E-ISSN 2227-7102, Vol. 7, no 1Article in journal (Refereed)
    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.

  • 22.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology.
    Schauf, Eva-Maria
    Albert-Martmöller-Gymnasium, Witten, Germany.
    Hesse, Jörn Hagen
    Albert-Martmöller-Gymnasium, Witten, Germany.
    Mathematisch interessierte Köpfe anregen (MiKa!): Ein Konzept zur Begabtenförderung im Fach Mathematik für das Gymnasium2015In: Mathematische und Naturwissenschaftliche Unterricht, ISSN 0025-5866, Vol. 68, no 6, p. 331-337Article in journal (Other academic)
    Abstract [de]

    Im Projekt MiKa! wurde in der Praxis ein Konzept zur Förderung mathematisch interessierter und begabter Schüler für das Gymnasium entwickelt. Im Beitrag werden organisatorische, methodische und auch inhaltliche Gesichtspunkte dargestellt.

    Mithilfe zweier Themenbeispiele wird die inhaltliche Arbeit exemplarisch konkretisiert. Anhand der Praxiserfahrungen werden Chancen und potentielle Stolperstellen der Förderung mathematisch interessierter und begabter Lernender beleuchtet.

  • 23.
    Schindler, Maike
    et al.
    University of Cologne, Department of Special Education, Cologne, Germany.
    Schindler, Florian
    Dortmund University, Dortmund, Germany.
    Lilienthal, Achim
    Örebro University, School of Science and Technology.
    Bader, Eveline
    University of Cologne, Cologne, Germany.
    Vorgehensweisen bei der Anzahlerfassung am 100er Feld und 100er Rahmen: Eine Eye-Tracking Studie bei Kindern mit und ohne Rechenschwierigkeiten sowie sonderpädagogischem Unterstützungsbedarf2018In: Beiträge zum Mathematikunterricht 2018 / [ed] Fachgruppe Didaktik der Mathematik der Universität Paderborn, Münster, Germany: WTM Verlag, 2018, p. 1591-1594Conference paper (Refereed)
    Abstract [de]

    Arbeitsmittel werden im Mathematikunterricht zum Aufbau von Zahl- und Operationsvorstellungen genutzt. Gerade für Kinder mit Schwierigkeiten im strukturierten Erfassen von Anzahlen undunzureichenden Zahl- und Operationsvorstellungen ist die Nutzung von Darstellungen zentral. Wie gehenjedoch Kinder mit Rechenschwierigkeiten bei der Anzahlerfassung in unterschiedlichen Darstellungenvor und inwiefern erfolgt ein Transfer zwischen strukturell ähnlichen Darstellungen? Die vorgestellteStudie untersucht Vorgehensweisen bei der Anzahlerfassung am 100er Feld und 100er Rahmen bei 20Kindern (davon 11 mit Rechenschwierigkeiten und z.T. sonderpädagogischem Unterstützungsbedarf) zu Beginn der fünften Klasse. Eye-Tracking ermöglicht dabei neue Erkenntnisse gerade bei Kindern, die Schwierigkeiten haben, ihre Vorgehensweisen zu beschreiben. Die Ergebnisse liefern Einblicke in mathematische Kompetenzen und Schwierigkeiten der Kinder sowie die Unterschiede in der Nutzung derbeiden Darstellungen.

  • 24.
    Schindler, Maike
    et al.
    Örebro University, School of Science and Technology. Faculty of Human Sciences, University of Cologne, Cologne, Germany.
    Seidouvy, Abdel
    Örebro University, School of Science and Technology.
    Informal Inferential Reasoning and the Social: Understanding Students’ Informal Inferences Through an Inferentialist Epistemology2018In: 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.

  • 25.
    Seidouvy, Abdel
    et al.
    Örebro University, School of Science and Technology.
    Helenius, Ola
    Örebro University, School of Science and Technology. University of Gothenburg, Gothenburg, Sweden.
    Schindler, Maike
    Örebro University, School of Science and Technology. University of Cologne, Cologne, Germany.
    Authority in students’ peer collaboration in statistics: an empirical study based on inferentialism2019In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 24, no 2, p. 25-47Article in journal (Refereed)
    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.

  • 26.
    Seidouvy, Abdel
    et al.
    Örebro University, School of Science and Technology.
    Helenius, Ola
    Örebro University, School of Science and Technology. University of Gothenburg, Gothenburg, Sweden.
    Schindler, Maike
    Örebro University, School of Science and Technology. University of Cologne, Cologne, Germany.
    Data generation in statistics – both procedural and conceptual: An inferentialist analysis2018In: 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 (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.

  • 27.
    Seidouvy, Abdel
    et al.
    Örebro University, School of Science and Technology.
    Schindler, Maike
    Örebro University, School of Science and Technology. Faculty of Human Sciences, University of Cologne, Cologne, Germany.
    An inferentialist account of students’ collaboration in mathematics education2019In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050XArticle in journal (Refereed)
    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.

1 - 27 of 27
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