Teachers' questions shape the instructional environment and the direction of mathematics discussions in critical ways. This article is the product of a research study on the relationship between teachers' questions and student engagement in the Standards for Mathematical Practice (SMP) during whole-class discussions. Using classroom video gathered…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

A team of teachers from the same New York City public school met to discuss and compare the Common Core State Standards for Mathematics (CCSSM) to their current math curriculum. The group consisted of four kindergarten teachers, a representative from the first-grade teaching team, and the school's math coach. During the first meeting, the…

The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

The best Science, Technology, Engineering, and Mathematics (STEM) design challenges are student centered, with students themselves making the key decisions. But with young children who are still learning basic academic and social skills, implementing projects where they truly take the lead can be quite challenging. To give students at one…

Technology has the potential to make complex and abstract mathematical ideas more accessible to students, especially to those who have difficulties with challenging curricular concepts (NCTM 2000, NCTM 2008). What one sometimes forgets is that technology is a tool and, like any tool, can be used productively only in the hands of a skilled…

Telling children that they can learn from their mistakes is common practice. Yet research indicates that many teachers in the United States limit public attention to errors during mathematics lessons (Bray 2011; Santagata 2005). Some believe that drawing attention to errors publicly may embarrass error makers or may be confusing to struggling…

The old adage goes, "Parents are their children's first and most important teachers." Yet when it comes to mathematics, parents often feel inadequate to help their children with homework tasks, let alone teach them important content. Compounding the problem of low parental knowledge of mathematics, parents' "perceived" inadequacies or indifference…

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

The concepts of angle and angle measure have been acknowledged as difficult for elementary school students to grasp (Strutchens, Martin, and Kenney 2003). The Wedge activity (Browning and Garza-Kling 2009; Van de Walle 2004; Wilson 1990) can provide an opportunity for students to examine their understanding of angle measurement and to rethink what…

The Common Core State Standards for Mathematics (CCSSM) were "designed to be robust and relevant to the real world, reflecting the knowledge and skills that young people need for success in college and careers" (CCSSI 2010). For the first time in U.S. history, a set of standards is established that will be taught in nearly every state. Forty-four…

Given the recent release and widespread state adoption of the Common Core State Standards for Mathematics (CCSSM), teachers across the country now have common goals related to what their students should understand about particular mathematical topics. The authors of CCSSM explain, "Asking a student to understand something means asking a teacher to…