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• Future Basics: Developing Numerical Power

FUTURE BASICS: DEVELOPING NUMERICAL POWER

By Randall Charles and Joanne Lobato

The following is only the Table of Contents and Introduction for this monograph. The monograph itself is NOT available online. (NOTE: NCSM members may purchase copies of Future Basics at a cost of $10 each. Order Form) Join NCSM

Table of Contents

Introduction

Section 1: What Does It Mean to Be Numerically Powerful?

Section 2: What Are Some Issues Related to Developing Numerical Power?

Section 3: What Are Reasonable Computational Skill Expectations?

Section 4: What Activities Can Be Used to Develop and Assess Numerical Power?

Section 5: What Instructional Practices Promote Numerical Power?

References

Introduction

Many reports have documented the reasons and need for de-emphasizing the development of paper and pencil computational skills (see, e.g., National Council of Teachers of Mathematics, 1989). Despite calls for change, the standard for success in too many classrooms remains the flawless and speedy implementation of paper and pencil computational algorithms. One reason change has been slow is that no national statement exists identifying specific ways in which curriculum and instruction can change to accommodate a new vision for computational competence. Thus, teachers, administrators, curriculum developers, test developers, and leaders in mathematics education have had nowhere to turn for help in answering the specific questions that arise when articulating curriculum and assessment goals throughout the number and operations strands.

The purpose of this monograph is to initiate a shift in the standard for success in K-7 mathematics classrooms relative to number and operations, from the mastery of paper and pencil algorithms to the development of numerical power. Section 1 discusses the competencies and characteristics of a numerically powerful child. This section argues that numerical power includes but goes far beyond the ability to compute accurately and efficiently. Section 2 provides answers to key questions and concerns that arise when numerical power becomes the focus of the number and operations strands. Section 3 makes specific recommendations about skills for which mastery should be delayed until a later grade, making way for more instruction on understandings that contribute to numerical power. This section also includes recommendations for skills that no longer deserve to be emphasized in curriculum and assessment, as well as recommendations for concepts that deserve increased attention when striving for the development of numerical power. Section 4 gives examples of mathematical activities that promote the development of numerical power, and Section 5 identifies characteristics of instructional practices that encourage the development of numerical power.

The recommendations in this paper are a start toward a total rethinking of the K-7 mathematics curriculum, shifting the standard from the flawless, speedy, and too often meaningless mastery of paper and pencil computational skills to the development of numerical power.

Errata

There were two corrections to the first edition of the Future Basics monograph (March 1998). They are available in the form of an errata sheet. If you are in need of a copy of the errata sheet, contact NCSM. (Note: Necessary corrections were made before the July 1998 second printing of Future Basics and no errata sheet is needed for that edition.)

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