Research has shown that the ways in which teachers engage in professional development activities vary widely. identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

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…

With the introduction of the Common Core State Standards (CCSS), teachers must now teach math with an eye on simultaneously meeting the Standards for Mathematical Practice (CCSSI 2010). These Standards "describe varieties of expertise that math educators at all levels should seek to develop in their students" (p. 6). The first Standard, that…

It has been well-documented that many students do not understand the meaning of the equal sign. Thus, researchers have called for instruction that specifically addresses misconceptions about the equal sign, and have indicated that such work must start at the elementary level. In response to these recommendations, some state curriculums require…

"The World Is Flat" (Friedman 2005) describes the globalization that advances in technology have imposed on the world economy in recent decades. For the U.S. to maintain its stature in the world, future citizens must be prepared to problem solve and apply their skills to new situations. These future citizens are sitting in elementary school…

Mathematics educators promote student engagement in the Process Standards and create problem-solving tasks and facilitate discussions to help their students develop strengths in explaining their methods, using and interpreting multiple representations, and making connections between topics. They are excited and encouraged when they see students…