Formulas are involved in most parts of the mathematical curriculum in upper secondary education and in everyday mathematics classrooms, but research shows that students have difficulties using formulas adequately. When students are presented with a task, the task activates a conceptual frame in the students, making them perceive formulas in a…

Teacher self-efficacy beliefs, epistemological beliefs, and beliefs about teaching with technology are regarded as crucial factors for teaching mathematics with technology. However, there is a lack of research that investigates these beliefs while taking into account the multidimensionality of the constructs. In this cross-sectional study with n =…

The important role of student agency in collaborative problem-solving has been acknowledged in previous mathematics education research. However, what remains unknown are the processes of agency in open-ended tasks that draw on real-life contexts and demand argumentation beyond "mathematical". In this study, we analyse a video recording…

Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N…

In this paper, we analyse a large, opportunistic dataset of responses (N = 219,826) to online, diagnostic multiple-choice mathematics questions, provided by 6-16-year-old UK school mathematics students (N = 7302). For each response, students were invited to indicate on a 5-point Likert-type scale how confident they were that their response was…

Drawing on Bourdieu's theory of social and cultural reproduction, this article utilizes the conceptual tools of habitus and cultural capital to examine intergenerational inequalities in attitudes towards mathematics and mathematics learning in three secondary schools in England. Data from 1079 students aged 14-16 included mathematics achievement,…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

This study investigates the relationship between children's subitizing activity and their construction of arithmetic units. In particular, the study hypothesizes a positive association between children's construction of subitized units and their construction of arithmetic units, and hypothesizes that children who can subitize larger units, such as…

When it comes to choosing tasks, values can have a significant impact. This study explores teachers' values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants' analyses of each task, as well as their reasons for choosing one task as most…

Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…

Teaching mathematical modeling is a demanding task. Thus, fostering teachers' competencies in this regard is an essential component of teacher education. Recent conceptualizations of teachers' competencies include situation-specific skills based on the concept of noticing, which is of particular interest for the spontaneous reactions needed when…

Designers in out-of-school spaces often negotiate the meaning of mathematics as part of the design process, determining what to include in classes and exhibits both implicitly and explicitly. This analysis suggests that instead of keeping these conversations behind the scenes, we should foreground them for participants. In doing so, we may…

This study examined how expert and novice (preservice) teachers solved mathematical modelling tasks as well as how they noticed written artifacts of student thinking that were in response to the mathematical modelling tasks. Some teachers in both groups were aware of the openness and underdetermination of the modelling tasks and that these…

Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling…

Models-and-modeling perspective (MMP) is a problem-solving and learning perspective in mathematics education. Although modeling processes have been addressed widely in the international discussion on mathematical modeling, a homogeneous understanding has not been established yet. Hence, the field needs studies addressing the epistemological…