This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

This study investigates how 20 prospective elementary teachers make connections among children's multiple mathematical knowledge bases in their thinking about assessing children's understanding of fractions. The researcher facilitated concept-mapping tasks to examine the ways the prospective teachers linked concepts related to children's lives and…

In this report, we will consider in-service elementary school teachers' noticing of the mathematical practice: justification. This study is part of a larger project evaluating the efficacy of a three year professional development built around attending to student thinking and promoting mathematical habits of justifying, generalizing and making…

The Long-Term Trend (LTT) mathematics assessment of the National Assessment of Educational Progress (NAEP) used the same set of items from 1982 through 2004, including 20 items that were administered to 9-and 13-year-olds, 29 items that were administered to 13-and 17-year-olds, and 4 items that were administered at all three ages. This study used…

Instruction that meaningfully incorporates students' mathematical thinking is widely valued within the mathematics education community (NCTM 2000; Sherin, Louis, and Mendez 2000; Stein et al. 2008). Although being responsive to student thinking is important, not all student thinking has the same potential to support mathematical learning.…

The aim of the paper is to provide a process model to evaluate mathematical problem solving by analogy, in order to better determine at which point and under what conditions a learner is prompted to use analogies. The model is a theoretical construct. Qualitative results of an empirical study are used to underline and illustrate core aspects of…

In this paper we examine deficit perspectives that prospective elementary school teachers (PTs) noticed their mentor teachers held with regards to classifying students by their achievement or behavior. Using a sociopolitical framework, we explored the following research question: What labels and forms of labeling of students have elementary school…

In this research, we examined how 200 students in seventh grade (around 12 years old) solved simple addition problems. A cluster approach revealed that less than half of the cohort displayed proficiency with simple addition: 35% predominantly used min-counting and were accurate, and 16% frequently made min-counting errors. Students who frequently…

In recent years there has been an increased focus on the need for teachers to develop learning communities where all students have opportunities to engage in interactive discourse. However, there are few studies that focus on student perceptions and accounts of mathematical reasoning in classrooms with interactive mathematical talk as a focus of…

Empirical work that connects content knowledge to teaching practice has become increasingly important in discussions around a professional knowledge base for teaching. This paper aims to continue that work, reporting a single exploratory case study of one elementary mathematics teacher. The purpose of the study was to investigate how introducing…

Student evaluations of quantitative methods courses in political science often reveal they are characterised by aversion, alienation and anxiety. As a solution to this problem, this paper describes a pedagogic research project with the aim of embedding quantitative methods by stealth into the first-year undergraduate curriculum. This paper…

Background: Spatial skills have been linked to better performance in mathematics. Aim The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Sample:…

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

Many teachers try to engage their students in meaningful mathematical discussions in which one or more students share their thinking about a problem while the other students are expected to listen and learn from the sharing. Indeed, such discussions can help students learn from one another and promote high levels of mathematical proficiency.…

This study investigated the relationship between motivation and self-regulated learning (SRL) in a nationally representative sample of 5245, 15-year-old students in the USA. A multivariate multilevel analysis was conducted to examine the role of three motivational variables (self-efficacy, intrinsic value & instrumental value) in predicting…