This article focuses on the career paths in higher education taken by 351 doctoral graduates in mathematics education and provides insight into their career path and their resulting workload. Because some of the sample is drawn from graduates of programs with NSF funding related to doctoral preparation, it represents a best-case scenario of…

This study explores secondary in-service mathematics teachers' professional noticing of student work on a statistical task involving informally placing a line of best fit. The manuscript describes how teachers interpreted student work on the line of best fit task, how teachers responded to the student work, and associations between their…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear…

This study focuses on proportional division, a specific problem type of proportions and proportional relationships, which embeds a part-part-whole relationship. We investigated how students in grades 6 to 9 solved and perceived three proportional division problems. Analysis of the students' performance on the tasks revealed three types of…

Teacher noticing and the related construct of professional noticing of children's mathematical thinking have proven to be fertile ground for education researchers. Professional noticing is a framework for a teaching practice consisting of three component parts: attending, interpreting, and deciding. The current study investigates the conceptions…

This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students' abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal…

Teachers' perceptions of written curriculum influence the way in which they use the curriculum. As multiple states begin to implement state specific standards, understanding the perceptions teachers may have of these standards is critical. This study used quantitative and qualitative methods to investigate the perceptions teachers had of one…

Teacher self-efficacy and teaching practices are both related to effective teaching and learning of mathematics. Given the theoretical and empirical basis for the importance of teacher self-efficacy, we hypothesized that teacher reported self-efficacy would be positively related to teacher self-reported effective teaching practices. This study…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Using a national sample of students' writing from the National Study of Writing Instruction, this study examines the current state of writing in the mathematics classroom and the extent to which enactments align with the intentions established in the research base and curricula articulated by NCTM and the CCSS-M. Over 3,000 writing assignments…

This article reports proof schemes used by pre-service mathematics teachers enrolled in third- and fourth-year mathematics education courses at a Midwestern university. Six pre-service teachers constructed proofs for mathematical conjectures and were subsequently interviewed. Using Harel and Sowder's (1998) proof schemes theoretical framework, the…

An executive report to the President of the United States titled "Engaging to Excel: Producing One Million Additional College Graduates with Degrees in Science," predicted that over the next decade, the United States will lack college graduates in the fields of science, technology, engineering, and mathematics (STEM). One contributing…