1. an overview of the standards for school mathematics? 2

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“Higher Standards for Our Students...

NCTM Presents

Higher Standards for Ourselves”

An Overview of the Standards for School Mathematics?

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The Standards

The ten Standards describe a connected body of mathematical understandings and competencies. It is a comprehensive foundation recommended for all students. Standards are descriptions of what mathematics instruction should enable students to know and do.

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The Standards

The standards are in two sets. The content standards and the processing standards.

The standards are in two sets. The content standards and the processing standards.

For purposes of curriculum development and teaching the two sets are inseparable.

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The Content Standards

• Number and Operations

These standards span all grade bands and describe the content that students should learn.

• Number and Operations

• Algebra

• Number and Operations

• Algebra

• Geometry

• Number and Operations

• Algebra

• Geometry

• Measurement

• Number and Operations

• Algebra

• Geometry

• Measurement

• Data Analysis and Probability

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The Processing Standards

• Problem Solving

These standards span all grade bands and highlight ways of acquiring and using content knowledge.

• Problem Solving

• Reasoning and Proof

• Problem Solving

• Reasoning and Proof

• Communication

• Problem Solving

• Reasoning and Proof

• Communication

• Connections

• Problem Solving

• Reasoning and Proof

• Communication

• Connections

• Representation

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Emphasis Across the Grades

Number

Algebra

Geometry

Measurement

Data Analysis and Probability

Pre-K–2 3–5 6–8 9–12

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Each standard comprises a small number of goals that apply across all grades.

Each of the content Standards offer an additional set of expectations specific to each grade band.

The appendix contains a summary of the Standards.

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Although the ten Standards apply to all grades, emphasis will vary both within and between grade bands.

Because mathematics as a discipline is highly interconnected, the standards overlap and are integrated.

Those who design curriculum frameworks will need to make their own decisions about emphasis and order.

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Standards for Grades 6 – 8.

Middle-grades students are

drawn toward mathematics

if they find both challenge

and support in the

mathematics classroom.

Grades 6–8

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Characteristics of Students

• Major physical, emotional and intellectual changes in adolescence.

Grades 6–8

• These factors make it especially important for teachers to create classroom environments in which clearly established norms support the learning of mathematics.

continued

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Characteristics of Students

• Are drawn toward mathematics with challenge and support in the classroom

• Are drawn toward mathematics with challenge and support in the classroom

• Should see mathematics as an exciting, useful, and creative field

• Are drawn toward mathematics with challenge and support in the classroom.

• Should see mathematics as an exciting, useful, and creative field.

• Will benefit from rich and integrated mathematics instruction.

Grades 6–8

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More and Better Mathematics

• More understanding and flexibility with rational numbers.

• More understanding and flexibility with rational numbers

• More algebra and geometry.

• More understanding and flexibility with rational numbers

• More algebra and geometry

• More integration across topics.

Grades 6–8

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Stronger Basics

• rational numbers

Increasing students’ ability to understand and use—

• rational numbers

• linear functions

• rational numbers

• linear functions

• proportionality

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• Builds on and helps build “more and better mathematics”

In Grades 6–8Developing Flexible Problem Solvers

• Builds on and helps strengthen “stronger/bolder basics”

• Builds on and helps strengthen “stronger/bolder basics”

• Builds on and enhances flexible use of representations

• Builds on and helps strengthen “stronger/bolder basics”

• Builds on and enhances flexible use of representations

• Builds on and deepens UNDERSTANDING of mathematical ideas

• Builds on and helps strengthen “stronger/bolder basics”

• Builds on and enhances flexible use of representations

• Builds on and deepens UNDERSTANDING of mathematical ideas

• Develops through regular experience with interesting, challenging problems

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Middle school teachers need to know much more mathematics than is required in most elementary school teacher-certification program.

Middle school teachers need to know much more about adolescent development, pedagogical alternatives, and interdisciplinary approaches than most secondary school teachers.

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Standards for Grades 9 – 12.

To ensure that students will

have a wide range of career

and educational choices,

the secondary school

mathematics program must

be both broad and deep.

Grades 9–12

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Characteristics of Students

• Face decisions that will determine the course of their lives

Grades 9–12

• Face decisions that will determine the course of their lives

• Are more autonomous, also more able to work with others

• Face decisions that will determine the course of their lives

• Are more autonomous, also more able to work with others

• Are more reflective

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More and Better Mathematics

• Should study mathematics all four years

• Should experience a common foundation of mathematics

• Should experience a common foundation of mathematics

• Can study mathematics beyond what is expected for all, via:

– Increased depth within foundational courses

– Supplementary courses

– Options in the fourth year

Grades 9–12

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More and Better Mathematics

• Use of algebra to model interesting situations

• Use of algebra to model interesting situations

• Increased attention to data analysis

• Use of algebra to model interesting situations

• Increased attention to data analysis

• Connections between algebra, geometry, and data analysis

• Use of algebra to model interesting situations

• Increased attention to data analysis

• Connections between algebra, geometry, and data analysis

• Discrete mathematics

Grades 9–12

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Stronger Basics

• Transforming algebraic expressions

• Transforming algebraic expressions

• Families of functions

• Transforming algebraic expressions

• Families of functions

• Conjecture and proof

Grades 9–12

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In Grades 9–12

• Builds and deepens UNDERSTANDING of mathematical concepts

Developing Flexible Problem Solvers—

• Builds and deepens UNDERSTANDING of mathematical concepts

• Builds and promotes “more and better mathematics”

• Builds and deepens UNDERSTANDING of mathematical concepts

• Builds and promotes “more and better mathematics”

• Builds and strengthens “stronger basics”

• Builds and deepens UNDERSTANDING of mathematical concepts

• Builds and promotes “more and better mathematics”

• Builds and strengthens “stronger basics”• Builds and enhances flexible use of

representations

• Builds and deepens UNDERSTANDING of mathematical concepts

• Builds and promotes “more and better mathematics”

• Builds and strengthens “stronger basics”• Builds and enhances flexible use of

representations• Develops through regular experiences with

interesting, challenging problems

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The content and curricula aligned with these Standards will require extensive and sustained professional development for teachers and a large degree of administrative support.

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Assignment

Read:

• NCTM Principles and Standards p 41-43, 232-39, and 308-18.