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.

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 term affective field to 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.

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.

Interest in creativity in mathematics education research is increasing, and the field of research is growing. Yet, research on creativity and the notions (we use this wording to accumulate understandings, beliefs, and ideas about the construct) of creativity that are addressed in empirical research are diverse and difficult to organize in an overview, with different theoretical backgrounds and theoretical assumptions underlying them. The aim of this article is therefore to provide a systematic overview of notions of creativity addressed in recent empirical research on mathematical education. We conducted a systematic literature review, guided by the question, What notions of creativity are addressed in current mathematics education research and what theoretical foundations do they rely on? The article gives an overview of the five predominant notions of creativity that were identified in current empirical research in mathematics education from 2006 to 2019. We describe and evaluate these notions and identify trends that will help to structure this diverse field of research.

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).