The First Four Standards deal with mathematical processes that apply to every topic in the mathematics curriculum. Students should always be improving their ability to solve problems, to communicate about mathematics, to make connections within mathematics and between mathematics and other subjects, and to reason mathematically.

Although the First Four Standards are conceptually separate, in practice they are interwoven. For example, when students are working in groups to solve a mathematics problem that may have arisen in another area, they use communication to explain their solution strategies and reasoning to justify their conclusions. The inter-relation of the First Four Standards is reflected in the graphic that appears above and elsewhere in this chapter.

This Framework therefore discusses the First Four Standards in a single chapter. It begins with a separate K-12 Overview for each of the First Four Standards. Following that, as with other standards, there is a grade-level section for each of the grade levels K-2, 3-4, 5-6, 7-8, and 9-12. In the grade-level sections, the First Four Standards are discussed together in a grade-level overview, vignettes are used to illustrate how the First Four Standards can be achieved at that grade-level, and the vignettes are then related to the cumulative progress indicators for each of the First Four Standards at that grade-level.

In the Curriculum and Evaluation Standards for School Mathematics of the National Council of Teachers of Mathematics, these four standards are referred to as "process standards." In the Mathematics Standards of the New Jersey State Department of Education's Core Curriculum Content Standards, they are enumerated among the core curriculum content standards because, like the other content standards, the First Four Standards involve concepts and skills that students must master, and explicit focus on them is necessary in order for that mastery to be achieved.

Table of Contents

Problem Solving

Communicating Mathematics

Mathematical Connections

Reasoning

The First Four Standards - Grades K-2

The First Four Standards - Grades 3-4

The First Four Standards - Grades 5-6

The First Four Standards - Grades 7-8

The First Four Standards - Grades 9-12