This study investigated students' procedural and conceptual knowledge of the definite integral. Twenty-five students enrolled in one section of an undergraduate Calculus II class participated in this study. Data were collected from a test that was conducted during the fourth week of the semester. The test aimed at collecting information about the…

The aim of this study was to determine how successful elementary school teacher candidates are in forming and mathematically defining the surfaces of spheres, cones, cylinders and circular objects with the aid of various geometric elements. The study group consisted of a total of 40 teacher candidates in their fourth year attending a public…

In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We used Epistemic Network Analysis to consider the teachers' knowledge organization and connections between knowledge resources as a way to make sense of his understanding. Then, we examined how his understanding was reflected…

Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students in a ten-session teaching experiment. The students successfully reinvented four basic counting…

Children (n = 747; 6.5 years) were assessed on domain-general processes and mathematics and reading-related competencies (start of first grade), addition retrieval (end of second grade), and calculations and word reading (end of third grade). Attentive behavior, reasoning, visuospatial memory, and rapid automatized naming (RAN) indirectly…

This paper presents the outcomes of the work of the ICME 13 Survey Team on "Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research". It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as…

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…

In chemistry, lack of academic preparation and math ability have been offered as explanations as to why women seem to enroll, perform, and graduate at lower levels than men. In this paper, we explore the alternative possibility that the gender gap in chemistry instead originates from differential gender effects of academic factors on students'…

This study was carried out to determine whether there is a relationship between the preschool teachers' attitudes towards mathematics and mathematical development in 6-year-old preschool children. The sampling of the study was consisted of 30 teachers working with 6 years old children and their 120 students in public kindergartens and independent…

This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…

Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

This study investigates error sources and the effects of each error source to determine optimal weights of the composite score of teacher recommendation letters and self-introduction letters using multivariate generalizability theory. Data were collected from the science education institute for the gifted attached to the university located within…

Although an understanding of time is crucial in our society, curriculum documents have an undue emphasis on reading time and little emphasis on core underlying ideas. Given this context, a one-to-one assessment interview, based on a new framework, was developed and administered to investigate students' understanding of core ideas undergirding the…

The Calculus Concept Readiness (CCR) instrument assesses foundational understandings and reasoning abilities that have been documented to be essential for learning calculus. The CCR Taxonomy describes the understandings and reasoning abilities assessed by CCR. The CCR is a 25-item multiple-choice instrument that can be used as a placement test for…

Children's worrying about their academic performance has profound implications for their learning and wellbeing in school. Understanding the contextual and psychological antecedents of students' worry thus represents an important area of research. Drawing on Eccles and colleagues' expectancy-value theory and Pekrun's control-value theory and using…