To Örebro University

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.