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Susan Jo Russell

To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics launched a series of articles beginning in the February 2012 issue. In this concluding installment, we concentrate on the implementation of the eight Standards of Mathematical Practice and the constellations of Practices and Standards. In the September issue, Matthew Larson follows up the series with a feature article that looks at CCSSM through the lens of mathematics education reform history and asks the provocative question, Will CCSSM Matter in Ten Years?

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Susan Jo Russell

Principles and Standards for School Mathematics (NCTM 2000) emphasizes the goal of computational fluency for all students. It articulates expectations regarding fluency with basic number combinations and the importance of computational facility grounded in understanding (see a summary of key messages regarding computation in Principles and Standards in the sidebar on page 156). Building on the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) and benefiting from a decade of research and practice, Principles and Standards articulates the need for students to develop procedural competence within a school mathematics program that emphasizes mathematical reasoning and problem solving. In fact, learning about whole-number computation is a key context for learning to reason about the baseten number system and the operations of addition, subtraction, multiplication, and division.

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Deborah Schifter, Susan Jo Russell, and Virginia Bastable

Experience with explicitly stating generalizations and finding examples, counterexamples, and proofs—algebraic reasoning—lets young students think more about the principles that underlie their work and can support those who struggle as well as those who excel.

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Susan Jo Russell and Jan Mokros

The statistical idea we come across most frequently is the idea of average. Children in fourth grade and beyond fairly easily learn to apply the algorithm for finding the mean, but what do they understand about the mean as a statistical idea?

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Jan Mokros and Susan Jo Russell

Whenever the need arises to describe a set of data in a succinct way, the issue of mathematical representativeness arises. The goal of this research is to understand the characteristics of fourth through eighth graders' constructions of “average” as a representative number summarizing a data set. Twenty-one students were interviewed, using a series of open-ended problems that called on children to construct their own notion of representativeness. Five basic constructions of representativeness are identified and analyzed. These approaches illustrate the ways in which students are (or are not) developing useful, general definitions for the statistical concept of average.