This study examines the research on middle school students' understanding of variables and explores preservice elementary and middle school teachers' knowledge of variables. According to research studies, middle school students have limited understanding of variables. Many studies have examined the performance of middle school students and offered…

How can the use of the Standards for Mathematical Practice in the classroom be supported? Professional developers and teacher educators strive to support teachers as they seek to answer this question. When teachers personally and intentionally experience the practices and reflect on how the practices support and promote mathematical understanding,…

The game of Plinko offers students an exciting real-world example of the applications of probability and data analysis. The Common Core State Standards for Mathematics (CCSSI 2010) and the Guidelines for Assessment in Statistics Education (GAISE) (Franklin et al. 2007) suggest that students in grades 6-8 be given ample opportunities to engage in…

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this study,…

Equivalence relations and partitions are two interconnected ideas that play important roles in advanced mathematics. While students encounter the informal notion of equivalence in many courses, the formal definition of an equivalence relation is typically introduced in a junior level transition-to-proof course. This paper reports the results of a…

The study investigated teachers' pedagogical content knowledge of common students' errors and misconceptions in sets. Five mathematics teachers from one Lesotho secondary school were the sample of the study. Questionnaires and interviews were used for data collection. The results show that teachers were able to identify the following students'…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…

The difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

This paper examines correspondences and disjunctions within a national curriculum and between various aspects of its delivery, and how these align with the mathematical needs of the workplace. This is investigated in the context of the New Zealand school mathematics curriculum; the Numeracy Development Project; the senior school assessment regime,…

A review of the research literature indicated that there were probable orders in which students develop understandings and skills for calculating with percentages. Such calculations might include using models to represent percentages, knowing fraction equivalents, selection of strategies to solve problems and determination of percentage change. To…

This multipart study looked at pre-service teachers' (PSTs') understandings of the equal sign using an experimental measure, the EQ score. The data were analyzed for PSTs as a group and cross-sectionally at three key points during their elementary teacher education program. Relationships between equal sign understandings and other variables (e.g.,…

The Building Math Readiness in Young Deaf/Hard-of-Hearing Children: Parents as Partners (MRPP) Project works with parents to increase the understanding of foundational mathematics concepts in their preschool deaf/hard-of-hearing (d/hh) children in preparation for formal mathematics education. A multiple-case/single-unit case study incorporating…

As part of a larger project focused on decolonising mathematics education for Aboriginal students in Atlantic Canada, this article reports on the role of the Mi'kmaw language in mathematics teaching. By exploring how mathematical concepts are talked about (or not talked about) in the Mi'kmaw language, teachers and researchers can gain insight into…