The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

Mathematical conventions -- which account for the choices of mathematics community regarding definitions of concepts, their names and symbols -- are the focus of this paper. We introduce the task of unpacking, that is, offering plausible explanations and arguments for the choice of conventions. Using responses of four prospective teachers to the…

In this article, I investigate the influence of the dominant culture characterizing mathematics education--which I term the "culture of exclusion"--on efforts to teach for equity. Analyzing a year of observations in an urban high school mathematics department, I found that this culture structured everyday instruction even for teachers…

The purpose of the study is to identify the classroom mathematical practices developed within a learning environment designed by Realistic Mathematics Education for teaching cone and pyramid to preservice teachers. A teaching experiment including five-week instructional sequence by a hypothetical learning trajectory about the solids of cone and…

Preparing children to be successful in mathematics begins with what they learn before they reach 1st grade. Math knowledge in prekindergarten and kindergarten predicts school achievement in math and in other topics, such as reading. Indeed, early math knowledge is one of the strongest predictors of math grades in high school, high school…

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories--the preferred form of narrative assessment--currently downplay domain knowledge. In this paper,…

Quek, Tay, Toh, Leong, and Dindyal (2011) proposed that a design-theory-practice troika should always be considered for a designed package to be acceptable to the research users who, in this case, are teachers and schools. This paper describes the fine-tuning to the MProSE problem-solving design made by the teachers in the school after first round…

As current mathematics standards, such as the Common Core, are being implemented throughout the United States, it has become evident that teachers need support to enact the tenets of those standards. To help in this endeavor, this article was published as a guideline to emphasize to mathematics education stakeholders that "effective teaching…

This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing…

Aspects of the Math for America organization's actions, aims and affiliations are analyzed for their effects on urban schools and society at large. These aspects are argued as evidence to consider MfA as an agent working against democratic practice and in favor of furthering profit and its resultant inequitable resource distribution. The…

In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of…

Research has shown that students should be given the opportunity to explore mathematical concepts by building on their knowledge and focusing on mathematical reasoning. When students represent ideas, make conjectures, collaborate with others, and give explanations and arguments, they are using mathematical reasoning (NCTM 2000). Certain teaching…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

In this paper we report on the process, outcomes, and impact of a weekly homework assignment for which students write about the mathematics they do in their everyday lives. Data from 17 fifth-grade students suggest that after doing the assignment for a full school year, students clearly communicated their beliefs about the assignment having…