### Standards Update: The 2000 Principles and Standards for School Mathematics

In April 2000, the National Council of Teachers of Mathematics released its Principles and Standards for School Mathematics. This document updates the 1989 Curriculum and Evaluation Standards and includes some components of both Professional Standards for Teaching Mathematics and Assessment Standards for Teaching Mathematics as well.

With such far-reaching significant goals (see the standards box below), the 2000 Principals and Standards will certainly serve as a major influence in changes and trends in mathematics education and reform in the years to come. However, the focus of this document remains on curriculum, and so Professional Standards for Teaching Mathematics and Assessment Standards for Teaching Mathematics will both also continue to play major roles in math education and reform.

The 2000 Principles and Standards identifies six principles of high-quality mathematics education.

#### Content Standards

The 2000 Principles and Standards document describes in detail standards and expectations for grade levels Pre-K–2, 3–5, 6–8, and 9–12 for each of the five content strands:

- Number and Operations
- Algebra
- Geometry
- Measurement
- Data Analysis and Probability

Each of the content strands will be covered within the material of this textbook. Number and Operations is especially important in the early childhood curriculum. The Algebra strand includes patterns, relations, functions, and mathematical models. You may be surprised to see the various types of algebra that are included in today’s early childhood curriculum.

#### Process Standards

Process standards differ from content standards in that the process standards are not subject matter that can be learned but are the methods by which content knowledge can be acquired. The 2000 Principles and Standards document describes in detail the five process standards:

- Problem Solving
- Reasoning and Proof
- Communication
- Connections
- Representation

Problem solving is the heart of any solid mathematics curriculum. Reasoning is also important. Students who are exposed to the logic behind mathematical procedures are more likely to be able to learn and correctly apply those procedures than students who attempt to apply rules without regard to their reasonableness (Carpenter, Franke, Jacobs, Fenemma, & Empson, 1998; Hiebert & Wearne, 1996; NCTM, 2003).

Communication is especially important for assessment. Students must learn to explain, write, draw, or otherwise show what they have learned. A variety of nonverbal forms of communication must be used in the early childhood classroom. Teachers must often devise alternate means of assessment and communication when dealing with students with disabilities or students who have limited-English abilities.

Connections refers to connections among mathematics topics as well as connections to other subject areas and to real-life situations. By stressing connections, one can show the relevance and importance of mathematics. Students must also be able to make connections among mathematical representations (Coxford, 1995).

There are often a variety of representations for a single mathematical concept. For example, to represent the amount twenty-five cents, one can use a word phrase such as “twenty-five cents” or “a quarter,” use actual coins (or representations of coins) to show the amount in a variety of ways (one quarter, two dimes and a nickel, etc.), draw a pictorial representation, or use a symbolic expression such as 25¢ or $0.25. By learning several representations for a single concept, teachers can adapt their teaching methods to the needs and abilities of their students. Students should learn a variety of representations to best express and use their mathematical knowledge.

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