According to two studies of middle school and high school mathematics classrooms, 15 to 20 percent of class time tends to be spent reviewing homework (Grouws et al. 2010; Otten, Herbel-Eisenmann, and Cirillo 2012). So how can class time spent going over homework (GOHW) provide students with rich opportunities to learn from their homework? What are…

An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…

In this paper we report the interview questions used in a study of middle school students' mathematical problem solving behaviors which were chosen based on Vygotsky's concept formation theory and Berger's appropriation theory. We discuss the task design/selection process along with the findings associated with the use of these tasks so to provide…

In Calculus, students are often both presented problems with and taught to use three interconnected types of representations: symbolic, graphic, and numeric. However, students often fail to notice the relationship between mathematical objects (and even the same object) that are presented using different types of representations. Using the APOS…

The contribution of algebra to a shared understanding of the world and the society is vital to the development of science, technology and engineering. Thus, the teaching of algebra in schools must be maximised. This study examined the effects of blended learning (BL) and problem-based learning (PBL) instructional strategies on senior secondary…

The authors report on three students' argumentative knowledge construction in an asynchronous online graduate level geometry course designed for in-service secondary mathematics (ISM) teachers. Using Weinberger and Fischer's framework, they analyzed the ISM teachers' (a) geometry autobiography and (b) discussion board posts (both comments and…

The availability of technological resources for designing animations opens new possibilities for teacher education. However, there are limited examples illustrating the process of designing and writing stories that can be shown with animations or staged video in relation to specific teacher education goals. We use the case of a professional…

The 2015-16 Civil Rights Data Collection (CRDC) is a survey of all public schools and school districts in the United States. The CRDC measures student access to courses, programs, staff, and resources that impact education equity and opportunity for students. The CRDC has long provided critical information used by the Department of Education's…

Mathematics is central in school curricula around the world, yet outcomes are mixed at best. This is true both in relation to attitudes expressed towards mathematics, and in relation to observed assessment outcomes, showing how poorly individuals are prepared to use mathematics in a world in which the ability to do so is of increasing importance.…

Success and failure in formal mathematics education has been used to legitimize stratification. We describe participatory design research as a methodology for systemic repair. The analysis describes epistemic authority--exercising the right or the power to know--as a form of agency in processes of mathematical problem solving and learning. We…

Mathematics and science are natural partners. One of many examples of this partnership occurs when scientific observations are made, thus providing data that can be used for mathematical modeling. Developing mathematical relationships elucidates such scientific principles. This activity describes a data-collection activity in which students employ…

Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their…

The mean can be interpreted as a fair-share value and as a balance point. Standards documents, including Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), suggest focusing on both interpretations. In this article, the authors propose a sequence of five activities to help students develop these understandings of the mean, and they…

Given the increasing number of English Language Learners (ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers (SMTs) understand and respond instructionally to these students. This paper reports on the initial development and…

This paper discusses the importance of considering bilingual learners' non-linguistic forms of communication for understanding their mathematical thinking. In particular, I provide a detailed analysis of communication involving a pair of high school bilingual learners during an exploratory activity where a touchscreen-based dynamic geometry…