To Örebro University

Eye tracking (ET) has shown great potential in mathematics education research (Schindler et al., 2020). Since high-quality ET (hqET) systems are expensive, cost-efficient alternatives are needed for practical applications, e.g., in schools. Webcam-based ET (wcET) provides an affordable alternative, yet comes with a lower data quality. Our research aims to make wcET usable for practical applications in mathematics education. To achieve this, we intend to enhance wcET data through, e.g., automatic offset calibration (Asgahri et al., 2023) and semantic remapping (using knowledge about the presented tasks), so that relevant information can be extracted from the students’ eye movement patterns as with hqET data. Here, we consider number line (NL) tasks and ask: To which degree can wcET data support math education in comparison to hqET data and how can we increase the degree?

Using our KI-ALF system (https://ki-alf.de), we collected gaze data from 136 fifth-grade students working on NL tasks using a Logitech BRIO webcam (wcET) and a Tobii Pro X3-120 eye tracker (hqET). We pre-processed the wcET data using AI for (1) correcting systematic wcET data inaccuracies using task information (automatic offset calibration); (2) grouping gaze points into areas of interest, e.g., specific numbers or landmarks, to improve data interpretation and reduce noise (semantic remapping). We evaluated the pre-processing pipeline using clustering algorithm to analyse strategy patterns in terms of cluster consistency compared the clusters to expert-labelled strategies based on hqET data. With our domain-specific post-processing, the consistency of strategy identification reached a level close to that of hqET data. Our findings show that wcET affords scalable and cost-effective solutions to identify students’ NL strategies. Based on our development, KI-ALF wcET systems are currently in use in a comprehensive school in Germany to support students’ mathematics learning utilizing eye-tracking-based identification of their strategies.

Early identification of mathematical difficulties of young learners is critical for their individual development, yet traditional assessments such as standardized tests or diagnostic interviews face challenges, e.g., in scalability and practicality. To address these challenges, we developed an AI-assisted, pedagogical domain-informed digital tool, DIDUNAS, to evaluate first graders’ individual skill profiles and identify their need for support. As our research question we ask, How accurately can AI identify first graders' need for support in mathematics?

Our study involved 290 students from 8 European schools (in Germany & Cyprus). The participants included multilingual students, students with disabilities, and diverse socioeconomic backgrounds. We used the ZAREKI-K standardized test (von Aster et al., 2009) as the ground truth of the students’ mathematical skill profiles. The test results indicated whether a student needed support or not. In our study, 71 students were identified as being in need of support in mathematics.

For developing the digital tool, we first let 55 students engage with 12 digitally presented mathematical activities (e.g., number line, quantity comparison, etc.) designed by pedagogical experts, and take individual standardized ZAREKI-K tests. We assessed both results with machine learning techniques to have an insight about which tasks contributed most to accurate identification of support needs based on students' errors in each task. The analysis allowed us to refine the assessment to just 10 tasks. The AI-assisted DIDUNAS app with the refined task set was validated with 235 students, and it was able to identify students in need of support with 85% accuracy with a much less time consumption compared to one-by-one diagnostic interviews.

Our results demonstrate that AI can enhance scalability for accurately identifying first graders’ need for support in mathematics. We use the results from the digital app DIDUNAS, which runs on typical tablet computers and PCs, to support teachers with overviews over their students’ skill profiles and needs for support. Future work will explore real-time adaptive feedback to improve user experience, longitudinal studies to assess long-term learning outcomes and applications across additional grade levels.

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.