Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.
Jennifer Noll and J. Michael Shaughnessy
Robert E. Reys
Institutions of higher education are having a difficult time filling positions requiring a doctorate in mathematics education. This study reports that about one half of the 83 national searches by institutions for mathematics educators for the 2005–06 academic year were unsuccessful. Salaries for assistant professors were slightly higher in departments/colleges of education than in mathematics departments.
Helen J. Forgasz, Gilah C. Leder and Paul L. Gardner
The Fennema-Sherman Mathematics Attitude Scales (MAS) have been used extensively in research on gender differences in mathematics learning outcomes. The MAS comprise 9 scales measuring attitudes related to mathematics learning, including Mathematics as a Male Domain. The construct “mathematics as a male domain” remains a critical variable in explorations of the continued disadvantage experienced by females in the field of mathematics. We present recent research evidence that indicates that several items in the Mathematics as a Male Domain scale of the MAS may no longer be valid. In light of this evidence, it is appropriate to consider revisions to the scale to ensure that it continues to measure accurately its originally operationalized construct.
Creso Franco, Paola Sztajn and Maria Isabel Ramalho Ortigão
In this article, we use data from a large-scale Brazilian national assessment to discuss the relation between reform teaching and equity in mathematics education. We study the dimensionality of teaching style to better qualify what reform teaching means. We then use hierarchical linear models to explore whether reform teaching is associated with student achievement in mathematics and with student socioeconomic status (SES). Our results indicate that reform and traditional teaching are not opposite sides of a one-dimensional axis. They also emphasize both that reform teaching is related to higher school average achievement in mathematics and that the dissemination of reform teaching contributes to minimize the achievement gap between students who attend schools with low average SES and students who attend schools with high average SES. However, our results also show that reform is associated with an increase in within-school inequality in the social distribution of achievement.
John A. Ross, Douglas McDougall, Anne Hogaboam-Gray and Ann LeSage
Intensive case study is an expensive tool for measuring teachers' instructional practice. Previous research suggests that teacher self-report surveys provide a low-cost and relatively accurate picture of classroom practice. To examine the extent to which teachers implement mathematics education reform, we developed a 20-item survey based on nine dimensions of standards-based teaching. In this article, we provide evidence of the reliability (i.e., internal consistency) and validity of the instrument. The evidence consists of correlations of survey scores with a mandated performance assessment in Grade 6 mathematics, congruence with classroom observations of a small sample of teachers, and demonstrations that teachers who are similar in their claims about using a standards-based text series differ in how they use the text in ways predicted by the survey.
Heather C. Hill
This article explores elementary school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625) and at the same time collected information on teacher and student characteristics. Performance did not vary according to mathematical topic (e.g., whole numbers or rational numbers), and items categorized as requiring specialized knowledge of mathematics proved more difficult for this sample of teachers. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.
Anne Quinn and Karen Larson
The free Web-based app Census at School allows random sampling of survey data for students' use in projects and statistical analysis.
Denise T. Johnson
And the survey says … Whether listening to the news, reading a newspaper article, or watching reruns of such television game shows as Family Feud, we are frequently bombarded with surveys and survey results. But what do these numbers really tell us? This month your students explore that very question as they analyze survey data.
Kathleen Melhuish, Eva Thanheiser and Joshua Fagan
In classrooms, students engage in argumentation through justifying and generalizing. However, these activities can be difficult for teachers to conceptualize and therefore promote in their classrooms. In this article, we present the Student Discourse Observation Tool (SDOT) developed to support teachers in noticing and promoting student justifying and generalizing. The SDOT serves the purpose of (a) focusing teacher noticing on student argumentation during classroom observations, and (b) promoting focused discussion of student discourse in teacher professional learning communities. We provide survey data illustrating that elementary-level teachers who participated in professional development leveraging the SDOT had richer conceptions of justifying and generalizing and greater ability to characterize students' justifying and generalizing when compared with a set of control teachers. We argue that the SDOT provides both an important focusing lens for teachers and a means to concretize the abstract mathematical activities of justifying and generalizing.
Bilge Yurekli, Mary Kay Stein, Richard Correnti and Zahid Kisa
–2015 academic year. As part of a study to understand mathematics teaching on a large scale, we collected survey data from 403 fourth- through eighth-grade teachers. Our final analytical models included 248 teachers without missing data 1 on any of the teacher