•Levels of decomposition of practice is useful for retrospective analysis of professional development design.•The organization, technique, domain sequence may be useful for supporting professional development design.•Retrospective analysis of the design of successful professional development using specific theoretical lenses should occur.

Computational thinking is identified as one of the "essential skills for 21st-Century students." [1] Studies of CT in school programs are being funded by many organizations, including the United States National Science Foundation. In this paper, we describe "lessons learned" over the first two years of a research program (PREDICTS: Principles and Resources for Educators to Infuse Computational Thinking in the Sciences) with the goal of developing knowledge of how to integrate CT into introductory high school biology and chemistry classes for all students. Using curricular modules developed by program staff, two in biology and two in chemistry, teachers piloting the program engaged students in CT with computational evidence from authentic tools in order to develop understanding of science concepts. Each module, representing about a week of instruction, addresses science ideas in the prescribed course of study for high school programs. Project researchers have collected survey data on teachers': (1) beliefs about effective science teaching; (2) beliefs about their effectiveness as a science teacher and their students' ability to learn science, and; (3) content preparedness. In addition, we observed module implementation, collected and analyzed student artifacts, and interviewed teachers at the conclusion of module implementation. Preliminary results indicated some challenges (access to technology, varying levels of experience among students) and cause for optimism (student and teacher engagement in CT and the computational tools used in the modules). Continuing research efforts are described in this paper, along with descriptions of the curricular modules and the use of observations and "CT check-ins" to assess student engagement in, application of, and learning of CT.

Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner. We compared the impact of three PLE formats on the early algebra knowledge and teaching practices of elementary mathematics teachers: (1) a facilitated summer workshop, (2) a multimedia course completed on teachers’ own time, and (3) learning resources provided in the algebra curriculum unit that teachers used individually. Our findings suggest that all three formats can be mapped against a set of principles for quality professional learning. Analysis of pre- and post-treatment measures indicate that participating teachers’ knowledge of algebra content and best practices significantly increased, regardless of the PLE format with which they engaged. Interviews with a subset of the teachers from the three groups point to the key features of each of the formats that can be capitalized on by designers of PLEs.

Three seventh graders, working as a small group in their math class, had a conversation about adding and subtracting integers. The students discussed the challenges they faced in the assigned task.

•Sociopedagogical norms are participation patterns when talking about instruction.•Sociopedagogical norms are as important as social or sociomathematical norms.•Sociopedagogical norms should be considered when designing professional development.•Sociopedagogical norms can differ for discussions of own versus others' instruction.

This discourse strategy helps students understand story problems by revealing the task in stages and having learners adjust their predictions.

Adapted from literacy instruction for use in mathematics, the think-aloud strategy models mathematical thinking.

This article explores the following question: What does it mean to enact curriculum? In order to do so, it offers a conceptualization of the enacted curriculum and situates it within a curriculum policy, design, and enactment system. The system depicts the formal and operational domains in which curricular aims and objectives are developed and curriculum plans formulated and enacted. The authors situate the enacted mathematics curriculum in the operational part of the system and define it as the interactions between teachers and students around mathematical tasks of a lesson and collection of lessons, but argue that understanding what it means to enact curriculum involves examining the many places within the system that curricular elements are translated and transformed. The authors describe each of the articles in this special issue with respect to the framework.

This chapter documents how a seventh-grade mathematics teacher enacted the same Math Thematics lesson with two different classes. A brief overview of this textbook series is provided, followed by contextual information about the teacher and detailed information about the specific lesson that was enacted. Vignettes illustrate differences in how students engaged with the mathematical content of the lesson during the two classes. This investigation of enactment serves as a springboard to examine opportunities students are provided to make sense of the mathematical content of a lesson, provides an impetus to develop a conceptual framework to guide research, and suggests ways in which chaos theory might be applied to further research on the enacted mathematics curriculum.

The main goal of the Learning and Teaching Geometry project is to build professional development materials that provide opportunities for teachers to learn about mathematical similarity through the use of videocases, in which specific and increasingly complex mathematical ideas are presented within the dynamics of classroom practice. The central component of the Learning and Teaching Geometry materials is the Foundation Module, which is intended to provide teachers with a thorough grounding in key mathematical and pedagogical issues related to similarity. Field test data indicate that the Foundation Module can promote gains in both teachers' and students' knowledge of similarity. By highlighting the design elements behind this successful professional development effort and documenting the urgent need for further supports in this content domain, the paper has important implications for mathematics educators.

The National Council of Teachers of Mathematics (NCTM) espouses priorities to foster stronger linkages between mathematics education research and teaching practice. Of the five foundational priorities, one is directly focused on research, indicating NCTM's commitment to “ensure that sound research is integrated into all activities of the Council” (NCTM, n.d.). Another priority specifically references the relationship between research and mathematics teaching; the priority on curriculum, instruction, and assessment states that NCTM pledges to “Provide guidance and resources for developing and implementing mathematics curriculum, instruction, and assessment that are coherent, focused, well-articulated, and consistent with research in the field [emphasis added], and focused on increasing student learning” (NCTM, n.d.).