1 / 27

Principles and Standards for School

Mathematics

- National Council of Teachers of Mathematics

- Principles and Standards supplies guidance and

vision while leaving specific curriculum

decisions to the local level. This document is

intended to - set forth a comprehensive and coherent set of

goals for mathematics for all students from

prekindergarten through grade 12 that will orient

curricular, teaching, and assessment efforts

during the next decades - serve as a resource for teachers, education

leaders, and policymakers to use in examining and

improving the quality of mathematics

instructional programs

- guide the development of curriculum frameworks,

assessments, and instructional materials - stimulate ideas and ongoing conversations at the

national, provincial or state, and local levels

about how best to help students gain a deep

understanding of important mathematics.

Chapter 1A Vision for School Mathematics

- those who understand and can do mathematics

will have significantly enhanced opportunities

and options for shaping the future. Mathematical

competence opens doors to productive futures. A

lack of mathematical competence keeps those doors

closed.

Chapter 1 contd

- everyone needs to understand mathematics. All

students should have the opportunity and the

support necessary to learn significant

mathematics with depth and understanding. There

is no conflict between equity and excellence.

Chapter 2Principles for School Mathematics

- They (the six principles) describe crucial

issues that, although not unique to school

mathematics, are deeply intertwined with school

mathematics programs.

The Six Principles Can Influence

- the development of curriculum frameworks
- the selection of curriculum materials
- the planning of instructional units or lessons
- the design of assessments
- the assignment of teachers and students to

classes - instructional decisions in the classroom
- the establishment of supportive professional

development programs for teachers.

The Equity Principle

- Expectations must be raisedmathematics can and

must be learned by all students. - All students should have access to an excellent

and equitable mathematics program

The Curriculum Principle

- A school mathematics curriculum is a strong

determinant of what students have an opportunity

to learn and what they do learn.

The Teaching Principle

- Students' understanding of mathematics, their

ability to use it to solve problems, and their

confidence in, and disposition toward,

mathematics are all shaped by the teaching they

encounter in school.

The Learning Principle

- In the twenty-first century, all students should

be expected to understand and be able to apply

mathematics. - conceptual understanding is an important

component of proficiency, along with factual

knowledge and procedural facility.

The Assessment Principle

- Assessment should be
- not merely done to students, but for students, to

guide and enhance their learning. - an integral part of instruction that informs and

guides teachers as they make instructional

decisions.

The Technology Principle

- Technology
- enhances mathematics learning.
- supports effective mathematics teaching.
- influences what mathematics is taught.

Chapter 3

- Overview
- of
- Standards for Mathematics Education
- in
- Prekindergarten through Grade 12

Chapters 4-7

- Four Grade Bands
- Prekindergarten-grade 2
- Grades 3-5
- Grades 6-8
- Grades 9-12

- Content
- and
- Process
- Standards

Chapter 8

- Steps Needed to Move
- Toward the Vision
- in
- Principles and Standards

(No Transcript)

Process Standards

Communication StandardInstructional programs

from prekindergarten through grade 12 should

enable all students to

- Organize and consolidate their mathematical

thinking through communication - Communicate their mathematical thinking

coherently and clearly to peers, teachers, and

others - Analyze and evaluate the mathematical thinking

and strategies of others - Use the language of mathematics to express

mathematical ideas precisely

Communication Task Grades 3 - 5 Pretend you are

a jeweler. Sometimes people come in to get rings

resized. When you cut down a ring to make it

smaller, you keep the small portion of gold in

exchange for the work you have done. Recently you

have collected these amounts Now you have a

repair job to do for which you need some gold.

You are wondering if you have enough. Work

together with your group to figure out how much

gold you have collected. Be prepared to show the

class your solution.

1.14 g .089 g .3 g

Communication Task Grades 6-8A certain

rectangle has length and width that are whole

numbers of inches, and the ratio of its length to

its width is 4 to 3. Its area is 300 square

inches. What are its length and width?

Communication Task Grades 9 - 12Imagine

you are talking to a student in your class on the

telephone and want the student to draw some

figures. The other student cannot see the

figures. Write a set of directions so that the

other student can draw the figures exactly as

shown in the figure below.

Connections StandardInstructional programs

from prekindergarten through grade 12 should

enable all students to

- Recognize and use connections among mathematical

ideas - Understand how mathematical ideas interconnect

and build on one another to produce a coherent

whole - Recognize and apply mathematics in contexts

outside of mathematics

Connections Task Grades 3 - 5Estimate

the cost of 12 notebooks.

Problem Solving StandardInstructional programs

from prekindergarten through grade 12 should

enable all students to

- Build new mathematical knowledge through problem

solving - Solve problems that arise in mathematics and in

other contexts - Apply and adapt a variety of appropriate

strategies to solve problems - Monitor and reflect on the process of

mathematical problem solving

Representation StandardInstructional programs

from prekindergarten through grade 12 should

enable all students to

- Create and use representations to organize,

record, and communicate mathematical ideas - Select, apply, and translate among mathematical

representations to solve problems - Use representations to model and interpret

physical, social, and mathematical phenomena

Reasoning and Proof StandardInstructional

programs from prekindergarten through grade 12

should enable all students to

- Recognize reasoning and proof as fundamental

aspects of mathematics - Make and investigate mathematical conjectures
- Develop and evaluate mathematical arguments and

proofs - Select and use various types of reasoning and

methods of proof