Mathematics

In this study we investigated eighth grade students’ informal justification for the circle area formula to expand accounts of the measurement knowledge for middle-school age students. Data were collected during three paired interviews of a three-year teaching experiment. Here we describe schemes students exhibited as they operated on measurement tasks at a level we have described as “conceptual area measurer”; the tasks prompted the use of square units to quantify a figure that is not rectilinear.

We analyzed 37 PSTs’ written solutions to four figural pattern generalization tasks, video recordings of class discussions, and audio-recordings of problem-based interviews during which the PSTs were asked to solve one pattern generalization task, to answer the following research questions: (1) What relationships and structural aspects of a figural pattern do PSTs build upon to formulate pattern generalization? (2) How do they utilize uncovered relationships and structural aspects of a figural pattern to justify their general rules? 

Learning from video is a theoretically grounded and popular professional development activity. In online professional development communities, however, responses to video are often shallow and lack meaningful commentary about issues that surround teaching and learning mathematics. By altering the framing conditions that accompany video clips posted to the Everyday Mathematics Virtual Learning Community, this study examined whether more deeply analytical comments could be elicited from pre-service teachers.

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making).

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making).

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making).

Background Inclusive STEM (traditionally known to stand for “Science, Technology, Engineering, and Math”) high schools are emerging across the country as a mechanism for improving STEM education and getting more and diverse students into STEM majors and careers. However, there is no consensus on what these schools are or should be, making it difficult to both evaluate their effectiveness and scale successful models. We addressed this problem by working with inclusive STEM high school leaders and stakeholders to articulate and understand their intended school models.

Recently, there has been an increase in the number of cluster randomized trials (CRTs) to evaluate the impact of educational programs and interventions. These studies are often powered for the main effect of treatment to address the ‘‘what works’’ question. However, program effects may vary by individual characteristics or by context, making it important to also consider power to detect moderator effects. This article presents a framework for calculating statistical power for moderator effects at all levels for two- and three-level CRTs.

Mathematics professional development is widely offered, typically with the goal of improving teachers’ content knowledge, the quality of teaching, and ultimately students’ achievement. Recently, new assessments focused on mathematical knowledge for teaching (MKT) have been developed to assist in the evaluation and improvement of mathematics professional development. This study presents empirical estimates of average program change in MKT and its variation with the goal of supporting the design of experimental trials that are adequately powered to detect a specified program effect.

We develop a theoretical and empirical basis for the design of teacher professional development studies. We build on previous work by (a) developing estimates of intraclass correlation coefficients for teacher outcomes using two- and three-level data structures, (b) developing estimates of the variance explained by covariates, and (c) modifying the conventional optimal design framework to include differential covariate costs  so as to capture the point at which the cost of collecting a covariate overtakes the reduction in variance it supplies.