To Örebro University

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.

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.

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.

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).

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.

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.

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.

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.

Educators in mathematics have long been concerned about students' motivation, anxiety, and other affective characteristics. Typically, research into affect focuses on one theoretical construct (e.g., emotion, motivation, beliefs, or interest). However, we introduce the termaffective fieldto account for a person's various affective factors (emotions, attitudes, etc.) in their intraplay. In a case study, we use data from an extracurricular, inquiry-oriented collaborative problem posing and problem solving (PP&PS) program, which took place as a 1-year project with four upper secondary school students in Sweden (aged 16-18). We investigated the affective field of one student, Anna, in its social and dynamic nature. The question addressed in this context is:In what ways does an affective field of a student engaging in PP&PS evolve, and what may be explanations for this evolvement?Anna's affective field was dynamic over the course of the program. Her initial anxiety during the PP&PS program was rooted in her prior affective field about mathematics activities, but group collaboration, the feeling of safety and appreciation, together with an increased interest in within-solution PP and openness for trying new things went hand in hand with positive dynamics in her affective field.

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.          

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.

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. 

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.