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…

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,…

The concrete, pictorial, and abstract methods of this lesson give students access to investigate, isolate, define, and use prime numbers. In this article, the authors describe an enrichment lesson that offers opportunities to investigate prime numbers in concrete, pictorial, and abstract ways. Originally introduced by Jerome Bruner in 1960, the…

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…

The results of the cognitive research on numbers' representations can provide a sound theoretical framework to develop educational activities on representing numbers. A program of such activities for a nursery school was designed in order to enable the children to externalize and strengthen their internal representations about numerosity and link…