This conceptual article explores teaching as design work, arguing that a critical thing teachers do is design systems that enable their students to learn. Designing occurs when teachers generate new learning activities or modify curricular programs to create coherence for themselves and their students. Nonetheless, few teacher education programs…

The purpose of this article was to describe a group coaching model and present preliminary evidence of its impact on teachers' implementation of Pyramid Model practices. In particular, we described coaching strategies used to support teachers in reflecting and problem solving on the implementation of the evidence-based strategies. Preliminary…

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…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

This article focuses on how technology educators can challenge students to "think" about technical problems. A key aspect of success in quality problem solving is understanding learning preferences and problem-solving approaches. The Learning Style Inventory (LSI) can be used to assess an individual's ideal way to learn, in essence, a…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

The research article in this article is part of a larger study that examines an initiative to expand teacher expertise in facilitating mathematical problem solving within the framework of developing and field-testing pedagogical resources. We focus on one year of the study and report on the complex process of professional development as teachers…

A need has emerged in the curriculum for more teamwork experience, for the development of better communication and critical thinking skills, and for the acquisition of specialized knowledge. A focus on the processes by which problems are solved has served our discipline well and can continue to serve us if in the classroom we make appropriate…

School subjects are analogous to medieval alchemy. There is a magical change as mathematics, science, and social sciences move from their disciplinary spaces into the classroom. The educational and social psychologies have little or nothing to do with understanding disciplinary practices. They are intellectual inventions for normalizing and…