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“Higher Standards for Our Students...

NCTM Presents

Higher Standards for Ourselves”

Principles• Equity

• Curriculum

• Teaching

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• Teaching

• Assessment

• Technology

Principles

The principles describe particular features of high-quality mathematics programsThe principles describe particular features of high-quality mathematics programs

• Equity

• Curriculum

• Learning

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Using Principles to Prepare Students

Equity

Curriculum

Technology

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Statement of Principles

The Equity PrincipleExcellence in mathematics education requires equity– high expectations and strong support for all students.

The Curriculum Principle

A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.

The Teaching Principle

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

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Equity

• High expectations and worthwhile opportunities for all.

• Accommodating differences to help everyone learn mathematics.

• Resources and support for all classrooms and all students.

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Equity requires high expectations and worthwhile opportunities for all.

• Expectations must be raised — mathematics can and must be learned by all students.

• Schools have an obligation to ensure that all students participate in a strong instructional program that supports their mathematics learning.

• Schools have an obligation to ensure that all students participate in a strong instructional program that supports their mathematics learning.

• High expectations can be achieved in part with instructional programs that are interesting for students and help them see the importance and utility of continued mathematical study.

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Equity requires accommodating differences to help all learn math.

• Some students may need further assistance and different assessments to meet high expectations.

• Some students may need further assistance and different assessments to meet high expectations.

• Some students may need enrichment programs or additional resources to challenge and engage them.

• Some students may need further assistance and different assessments to meet high expectations.

• Some students may need enrichment programs or additional resources to challenge and engage them.

• Technology can help achieve equity in the classroom.

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Equity requires resources and support for all classrooms and all students.

• Achieving equity requires a significant allocation of human and material resources in schools and classrooms.

• Instructional tools, curriculum materials, special supplemental programs, and the skillful use of community resources undoubtedly play important roles.

• Instructional tools, curriculum materials, special supplemental programs, and the skillful use of community resources undoubtedly play important roles.

• Teachers need to understand and confront their own beliefs and biases.

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Curriculum

• Should be coherent

• Focus on important mathematics

• Well articulated across the grades

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A curriculum should be coherent.

• A coherent curriculum effectively organizes and integrates important mathematical ideas .

• A coherent curriculum effectively organizes and integrates important mathematical ideas .

• Typical lessons should have topics that are closely related and well developed.

• A coherent curriculum effectively organizes and integrates important mathematical ideas.

• Typical lessons should have topics that are closely related and well developed.

• Lessons should be organized so that the fundamental ideas form an integrated whole.

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A curriculum should focus on important mathematics.

• School mathematics curricula should focus on mathematics content and processes that are worth the time and attention of students.

• Foundational ideas, mathematical thinking and reasoning skills, real-world phenomena are examples of important mathematics.

• Foundational ideas, mathematical thinking and reasoning skills, real-world phenomena are examples of important mathematics.

• The relative importance of particular mathematics topics is likely to change over time.

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A curriculum should be well articulated across the grades.

• Curriculum should help teachers guide students to increasing levels of sophistication and depths of knowledge.

• As they reach higher levels, students should engage more deeply with mathematical ideas and their understanding and ability to use the knowledge is expected to grow.

• As they reach higher levels, students should engage more deeply with mathematical ideas and their understanding and ability to use the knowledge is expected to grow.

• The curriculum should give guidance on the depth of study warranted at particular times and when closure is expected for particular skills or concepts.

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Teaching

• Understanding mathematics, students and strategies

• Changing and supportive classroom environment

• Continual improvement

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Effective teaching requires knowledge and understanding of

math, students and strategies. • Teachers need a profound understanding of

fundamental mathematics. • Teachers need a profound understanding of

fundamental mathematics.

• Teachers also need to understand the different representations of an idea.

• Teachers need a profound understanding of fundamental mathematics.

• Teachers also need to understand the different representations of an idea.

• Because students learn by connecting teachers need to know how mathematics is connected to other disciplines and the real-world.

Continued

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Effective teaching requires knowledge and understanding of

math, students and strategies. • Pedagogical knowledge helps teachers understand

how students learn mathematics.

• Engaging in reflective practice and continuous self-improvement are actions good teachers take every day.

• Engaging in reflective practice and continuous self-improvement are actions good teachers take every day.

• One of the complexities of mathematics teaching is that it must balance purposeful, planned classroom lessons with the ongoing decision making that inevitably occurs as teachers and students encounter unanticipated discoveries or difficulties that lead them into uncharted territory.

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Effective teaching requires a challenging and supportive environment.

• The teacher is responsible for creating an intellectual environment where serious mathematical thinking is the norm.

• The teacher is responsible for creating an intellectual environment where serious mathematical thinking is the norm.

• Worthwhile mathematical tasks are used to pique students' curiosity and draw them into mathematics.

• The teacher is responsible for creating an intellectual environment where serious mathematical thinking is the norm.

• Worthwhile mathematical tasks are used to pique students' curiosity and draw them into mathematics.

• The teacher should support students without taking over the process of thinking for them.

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Effective teaching requires continually seeking improvement.

• Effective teaching involves observing students, listening carefully to their ideas and explanations, and using this information to make instructional decisions.

• Effective teaching involves observing students, listening carefully to their ideas and explanations, and using this information to make instructional decisions.

• Teachers must be able to analyze what they and their students are doing and consider how those actions are affecting students' learning.

Continued

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Effective teaching requires continually seeking improvement.

• Reflection and analysis are important tool for teachers to use in improving student learning.

• Reflection and analysis are important tool for teachers to use in improving student learning.

• The work and time of teachers must be structured to allow and support professional development that will benefit them and their students.

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Summary

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Statement of Principles

The Equity PrincipleExcellence in mathematics education requires equity– high expectations and strong support for all students.

The Curriculum Principle

A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.

The Teaching Principle

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

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Assignment Read:

• Principles and Standards, pages 20-27.