A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

Mathematics proficiency in the Philippines is a persistent concern, seen by many as a sign of an educational crisis. Teachers are responsible for improving learning outcomes in any discipline, including math. Thus, the study intended to conduct an error analysis of verbal problems among pre-service mathematics teachers. The researcher employed…

Mathematical word problem-solving skills are crucial for students across their lives, yet solving such tasks poses challenges for many. Therefore, understanding the characteristics of mathematical word problems that are associated with students' performance is important. The objective of this systematic review and meta-analysis was to evaluate the…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems,…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

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…

Algebraic thinking is the ability to generalize about numbers and calculations, find concepts from patterns and functions and form ideas using symbols. It is important to know the student's algebraic thinking process, by knowing the student's thinking process one can find out the location of student difficulties and the causes of these…

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers' ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences…

Successful adoption of proven effective practice strategies such as distributed practice may contribute to much-needed improvement in mathematics performance. However, it is not yet fully understood if distributed practice is beneficial for long-term retention of complex procedural knowledge and, if so, for which initial practice performance level…

This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as…

A quantitative literacy course titled "Computational Geology" has been taught at the University of South Florida for over 20 years at the undergraduate level, largely by the same professor. Due to the extended course tenure, a unique opportunity presented itself to qualitatively study what the perceived broader impacts of the course were…

Studies have demonstrated that task-evoked pupillary responses (TEPRs) can be adopted to measure the examinee's cognitive load. This study compared three approaches for the measurement of TEPRs, mean pupil diameter, mean pupil dilation, and mean percentage of pupil dilation, to determine the best-fit measuring method. The valid participants of…

Although previous research has demonstrated that the acquisition of mathematical skills requires support from multiple cognitive abilities, the associations between cognitive precursors in different domains and mathematics at different hierarchical levels among primary school children are not well understood. This study explores the cognitive…

Mathematical proficiency is essential to supporting students' success in learning mathematics. It is the ability to use conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition in problem-solving. Cognitive independence shows students' ability to process information. Meanwhile, motivation…