In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during…

The U.S. storyline of emergent bilinguals has historically failed to highlight the mathematical and linguistic assets of this group; instead, it has primarily focused on providing support. To disrupt this narrative, a case study of one elementary teacher, Ms. Bristow, is presented. Ms. Bristow's discursive practices and pedagogy illustrate how she…

Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in…

As numerous research studies suggest, teachers who desire increased student learning should adopt active learning. This article explores the research, defines active learning, discusses its value, offers suggestions for implementing it, and provides six concrete examples of active learning approaches: Thinking-Aloud Pair Problem-Solving;…

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

The everyday use of "proficient" carries connotations of having reached a level of expertise. One would not describe someone stumbling through a rendition of "Chopsticks" as a proficient piano player; but novice pianists work on musical proficiencies--practicing scales or playing a polka--in parallel. They do not put off…

Mike Rose, author of "The Mind at Work," extols both the wholesome, pragmatic qualities of handcraft and the implicit intellectual skills required of its practitioners. His recent article, "Rethinking Remedial Education and the Academic-Vocational Divide," is titled with a call to action; in these few words alone, Rose problematizes the polar…

This article presents engaging interactive hypothesis tests which can be conducted with students very efficiently.

Over the past decade, the National Institute for Learning Outcomes Assessment (NILOA) has been documenting what colleges and universities are doing to gather evidence about student learning and helping institutions to productively use assessment data to strengthen undergraduate education. NILOA also has been monitoring how institutions communicate…

Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in…

This article is based on a pedagogical action research initiative comprising two research cycles. The study explores what constitutes meaningful experiences in the classroom from the pupils' perspectives and how understanding pupils' perspectives can foster the development of teachers' practical theory and classroom actions. Photography and group…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

The use of collaborative problem solving within mathematics education is imperative in this day and age of integrative science. The formation of interdisciplinary teams of mathematicians and scientists to investigate crucial problems is on the rise, as greater insight can be gained from an interdisciplinary perspective. Mathematical modelling, in…

Against the backdrop of mentor teachers' reasoning about practice, we seek to understand shifts in intern teachers' reasoning about practice during a year in which they take their final methods course in the fall and then do intern teaching in the spring. The data we analyze consist of intern and mentor teacher study group discussions of repeated…

Teachers who participated in a recent summer institute focused on implementing the Common Core State Standards for Mathematics (CCSSM). Throughout the summer institute, teachers had many in-depth discussions about the meanings they attributed to the Standards for Mathematical Practice (SMPs). In this article, the authors share some of the…