Principles and Standards for School Mathematics

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Principles and Standards for School
Mathematics

• National Council of Teachers of Mathematics

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• 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

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• 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.

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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.

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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.

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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.

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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.

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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

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The Curriculum Principle

• A school mathematics curriculum is a strong
  determinant of what students have an opportunity
  to learn and what they do learn.

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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.

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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.

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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.

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The Technology Principle

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

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Chapter 3

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

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Chapters 4-7

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

• Content
• and
• Process
• Standards

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Chapter 8

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

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Process Standards
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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

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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
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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?
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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.
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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

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Connections Task Grades 3 - 5Estimate
the cost of 12 notebooks.
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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

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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

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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