This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

Previous studies suggest that parental involvement in children's mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data…

Research under the key word 'secondary-tertiary transition problem' in mathematics education points to a range of difficulties students face when passing from learning mathematics at school to attending undergraduate mathematics courses. One of these problems concerns the change in criteria for what counts as a legitimate mathematical activity.…

The Interactive Whiteboard (IWB) is now a common technological artefact in Swedish preschools and schools. This study examines preschool teachers' thinking behind the embedding of IWB in the early years' mathematics classroom and how preschool teachers structure their mathematical activities when using IWB. Two complementary empirical studies,…

This article is the result of research aims to describe the patterns and characteristics of the process of metacognition student of mathematics in solving calculus problems. Description was done by looking at changes in "awareness," "evaluation," and "regulation" as components of metacognition. The changes in…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

This study examined pre-service primary school teachers' performance in posing problems that require knowledge of problem-solving strategies. Quantitative and qualitative methods were combined. The 120 participants were asked to pose a problem that could be solved by using the find-a-pattern a particular problem-solving strategy. After that,…

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…

Although creativity plays a critical role in mathematics, it remains underestimated in the context of a mathematics classroom. This study aims to explore the views and differences creativity displays in prospective teachers and one of their lecturers with respect to the characteristics and practices of creative teachers and the characteristics of…

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

The complementary use of the theories of instrumental genesis and shifts of attention enabled me to obtain insights into students' understandings of the concepts of eigenvector and eigenvalue. My analysis suggests that the use of different dragging modalities can provide evidence of shifts in structure of a student's attention and consequently can…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

The relationship between adolescent extra-curricular activities and choice of graduate-education field was examined among students from three fields of study, science (n = 12), art (n = 12), and education (n = 14), using qualitative and quantitative methods. Results of profile analysis indicated that the different majors participated in…