Conventions play an important communicative role in mathematics. Likely due to the complex relationship between conventions and school mathematics, few education researchers have questioned or investigated the consequences of instruction and curricula that primarily, if not unquestionably, maintain conventions. Drawing on Piagetian notions of…

Writing in mathematics provides students with the opportunity to think critically about and reflect on their experiences while solving problems. While many studies have documented the benefit of writing in math, it is not clear which instructional methods should be used to help students learn how to use writing to support learning. In this study,…

This mixed-method, qualitative/quantitative study examined (a) how a constructivist-based intervention (CBI) effected adults' learning of unit fractions and performance on whole-number (WN) or unit fraction (FR) comparisons and (b) brain circuitry implicated (fMRI) when processing these comparisons. The CBI used unit-iteration based activities to…

Foundation phase teachers in South African schools follow a socio-constructivist approach to the teaching and learning of mathematics, which entails that learners experiment freely with concepts and are encouraged to communicate and share their thoughts and ideas. In an effort to understand the impact that the physical learning environment, such…

The objective of this paper is to present attitudinal and cognitive beliefs of two preservice secondary mathematics teachers about teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised ten task-based interviews, a series of five each with two participants, senior undergraduate preservice mathematics…

The paper proposes a new interdisciplinary approach to helping low attaining learners in basic mathematics. It reports on the research-informed design and user testing of an adaptive digital game based on constructionist tasks with intrinsic feedback. The approach uses findings from the neuroscience of dyscalculia, cognitive science research on…

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…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

This study examined the mathematics teaching efficacy of traditional and non-traditional elementary pre-service teachers enrolled in a three-course, three-semester mathematics sequence. Self-efficacy scales were administered at the beginning of the three-course sequence and at the end. The three-course mathematics sequence was taught from a…

Little is known about how students learn the basic ideas of ring theory. While the literature addressing student learning of group theory is certainly relevant, the concepts of zero-divisor and, more generally, elements with no multiplicative inverse are among those for which group theory has no analogue. In order to better understand how students…

Acquaintance with various ways of inculcating concepts in any studied area of knowledge is one of teachers' duties, particularly mathematics teachers. Studies indicate errors and difficulties when inculcating concepts in mathematics and learning them. Many concepts have different meanings in different contexts. Hence, teachers should deal with the…

We investigated perceptions about learning strategy use and instructional roles among a sample of high needs adolescents (n = 230) who acted as near-peer instructional facilitators. The sample was drawn from science and mathematics classes in nonselective public secondary schools in New York City. Students participated in an inschool intervention…

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a "real-world" scenario. Even though the school values students' ideas, the reaction of the teacher to one student's alternative modelling of the problem suggests that he was expecting a particular answer to be…

Eastern philosophies of education such as Confucianism and Taosim advocate the use of silence in the teacher-pupil tradition of pedagogy. We investigate contemporary classrooms in Korea, and study whether teachers in Korea today incorporate this method implicitly or explicitly in their classrooms. Empirical data in the form of video-taped…