In "School Rethink 2.0," editors Frederick M. Hess, Michael B. Horn, and Juliet Squire gather leaders immersed in the nuts-and-bolts work of educational reinvention to present ten promising education improvements and ways to implement them. Contributors, including acclaimed education pioneers Sal Khan, Beth Rabbitt, and Larry Berger,…

One major obstacle for integrating the history of mathematics in teaching (hereafter referred to as IHT) is how to help teachers, particularly those who lack experience in IHT, use historical materials in their teaching. Based on many IHT practices in Shanghai, this paper proposes an IHT framework including two parts: one is a triangular pyramid…

In this Forum article, Curry focuses on a few ways math and numeracy instructors can assure their students are ready for college and/or a career. For example, when considering the math levels of so many adult learners, teachers might focus on teaching their students how to reason mathematically, and ensure that they have a solid conceptual…

We theorize about ambiguity in mathematical communication and define a certain subset of ambiguous language usage as imprecise. For us, imprecision in classroom mathematics discourse hinders in-the-moment communication because the instance of imprecision is likely to create inconsistent interpretations of the same statement among individuals. We…

The mathematics education field, including prospective teacher education program, has seen a continuous effort to change teaching practices to be more cognitively demanding, conceptually oriented and student centred. Our goal in this study was to examine how certain underlying assumptions about mathematical learning, as reflected in a skilled…

Supporting students' mathematical reasoning is an important goal of mathematics instruction, but can be challenging for many teachers .We report the results of a study aimed at better understanding and identifying the ways in which teachers support student reasoning when provided with conceptually rich tasks. This study resulted in the Teacher…

Accumulating research has established explicit mathematics instruction as an evidence-based teaching practice. This study utilized observation data from a multi-year efficacy trial to examine the longitudinal effects of a core kindergarten mathematics program on the use of explicit mathematics instruction among two distinct groups of teachers: one…

Accumulating research has established explicit mathematics instruction as an evidence-based teaching practice. This study utilized observation data from a multi-year efficacy trial to examine the longitudinal effect of a core kindergarten mathematics program on the use of explicit mathematics instruction among two distinct groups of teachers: one…

In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…

In this paper we consider how mathematics instruction that values, attends to, and builds on students' mathematical ideas is realized through discourse. We describe interactions that build on students' thinking and in which students help to determine the direction of mathematics lessons as responsive. Using a framework we developed to characterize…

The goal of the authors' ongoing research is to better understand how student mathematical thinking that becomes public in a classroom can be used to support the learning of mathematics content and practices (e.g., Stockero & Van Zoest, 2011). Although there are often instances of student thinking that the teacher has intentionally cultivated…

Sometimes a student's unexpected solution turns a routine classroom task into a real problem, one that the teacher cannot resolve right away. Although not knowing the answer can be uncomfortable for a teacher, these moments of uncertainty are also an opportunity to model authentic problem solving. This article describes such a moment in Zahner's…

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts.…