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…

This study concerns the cognitive process of mathematical problem posing, conceptualized in three stages: understanding the task, constructing the problem, and expressing the problem. We used the eye tracker and think-aloud methods to deeply explore students' behavior in these three stages of problem posing, especially focusing on investigating…

Fermi problems are real-context estimation tasks that are suitable for introducing open-ended problems in primary school education. To ensure their effective introduction in the classroom, teachers must have adequate proficiency to deal with them. One of the key aspects of problem-solving proficiency is flexibility, but there are few studies on…

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f…

In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior…

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models.…

Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students' creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with…

An essential task for mathematics teachers is posing problems. Selecting mathematics problems that develop mathematical proficiency and engage students in desirable mathematical practices is a critical decision-making process. We present the Framework for Posing Elementary Mathematics Problems (F-PosE) developed to focus prospective teacher…

In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

Affects are intuitively accepted as having a role in the key stages that determine success in problem-solving (PS) and problem-posing (PP). Two disjoint groups of prospective mathematics teachers with similar background and competences have been exposed to PS and PP activities, respectively, and they had to describe their affective states during…

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…

Decades of research have documented young students' misinterpretations of the equal sign and the impediments these present for children's mathematical development. Much less is known about individual differences in adults' knowledge of the equal sign. We assessed 182 college students from developmental math courses and present analyses from a…

Mathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years, there has been increased attention to teaching prospective teachers to lead discussions with students. This paper examines the possibilities of designing a formative assessment that gathers…