This study aims to examine pre-service elementary mathematics teachers' knowledge of quadrilaterals and evaluate their understanding within the framework of Van Hiele's Geometric Thinking Levels. In particular, the study investigates how pre-service teachers define quadrilaterals and establish relationships between different types of…

The study examines the impact of APOS theory on students' achievement in Elementary Linear Algebra (ELA) in accordance with their adequate prior knowledge (APK) and inadequate prior knowledge (IAPK). The mixed methods were used to determine the problem-solving test in ELA. Data were obtained from 65 industrial engineering students at Andalas…

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

A transcribed conversation between a mathematics educator and a disability studies educator is presented to highlight cross-disciplinary dialog as a fruitful space for recursive and reflexive engagement from which may emerge concepts to further both mathematics and disability education. The opening question, "How can I know what's possible in…

The purpose of this paper is to account for the advancement of questioning in mathematics education. Four sections focus on: (1) Importance of Questioning in Education (a historical perspective of questioning from the 1960s through the 1990s); (2) Cognitive Classification of Questions (Costa's Levels of Thinking, Webb's Depth of Knowledge, and…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

The aim of this article is to discuss key elements of a constructivist-based elementary mathematics methods course and the role of each component in enhancing elementary school teacher candidates' mathematical understanding, interest in, and confidence with learning and teaching mathematics while decreasing their math-related anxiety and fear. The…

The aim of this study was to evaluate the implementation of the cooperative learning model supported with dynamic mathematics software (DMS), that is a reflection of constructivist learning theory in the classroom environment, in the teaching of mathematics. For this purpose, a workshop was conducted with the volunteer teachers on the…

This paper reports on a portion of a research study that examined the development of 43 preservice elementary school teachers' conceptual understanding of place value, and highlights the experiences of one middle-performing preservice teacher. After participating in a research-based constructivist unit of instruction in place value, the findings…

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…

This research study examined the development of 43 preservice elementary school teachers' conceptual understanding of place value after participating in a research-based constructivist unit of instruction in place value. The preservice teachers were enrolled in one of three terms of an elementary mathematics methods course in a private midwestern…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

This study explored support for engagement in 2 settings: a high school basketball team and high school mathematics classrooms. Specifically, the study examined 3 aspects of these practices: (a) access to the domain, (b) opportunities to take on integral roles, and (c) opportunities for self-expression in the practice. Drawing on videotape and…

This study explores the mathematical problem-solving process of trainee teachers in a teachers' training institute. This research adopts a constructivist perspective that views learning mathematics as a process of constructing meaningful representation and knowledge as being constructed by the individual. The research methodology employs the case…