NCTM Principles: The Character of School Mathematics

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NCTM Principles The Character of School
Mathematics

• Cynthia Lanius
• Technology Integration Specialist
• Sinton ISD

June 2003
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a comprehensive and fundamental law, doctrine, or
assumption Example The Uncertainty Principle
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• The principles are statements reflecting basic
  precepts that are fundamental to a high-quality
  mathematics education.
• -NCTM Principles and Standards

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Content and Character

• Decisions made by teachers, school
  administrators, and other education professionals
  about the content and character of school
  mathematics have important consequences both for
  students and for society.
• -NCTM Principles and Standards

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• Content and Character
• The Standards describe the mathematical content
  and processes that students should learn.

Content and Processes
The Principles describe particular features of
high-quality mathematics education.
Character
-NCTM Principles and Standards
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main or essential nature especially as strongly
marked and serving to distinguish
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Character

• Equity
• Curriculum
• Teaching
• Learning
• Assessment
• Technology

Distinguish
High Quality Mathematics
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Learning
Students must learn mathematics with
understanding, actively building new knowledge
from experience and prior knowledge.
Understanding
Remembering
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• Equity
• Excellence in mathematics education requires
  equityhigh expectations and strong support for
  all students.

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What Does All Students Mean?
It does NOT mean that all students are the same.
Students have different abilities, needs, and
interests. Yet all students deserve an
opportunity to understand the power and beauty of
mathematics, and they need to be able to use
mathematics in their personal lives, in the
workplace, and in further study. -NCTM
Principles and Standards

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TX ACC. promotes the Equity Principle

• At-risk students could no longer be ignored
• No ethnic group could be ignored

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• Teaching
• Effective mathematics teaching requires
  understanding what students know and need to
  learn and then challenging and supporting them to
  learn it well.
• -NCTM Principles and Standards

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• Technology
• is essential in teaching and learning
  mathematics it influences the mathematics that
  is taught and enhances students' learning.
• -NCTM Principles and Standards

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• Technology vs. Teaching
• Would you choose the worlds greatest technology
  or the worlds greatest teacher for a child you
  love?

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What we really want

Worlds Greatest Technologies
in the hands of the
Worlds Greatest Teachers
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Technologies can build understanding
In a right triangle, c2 a2 b2
Pythagorean Theorem
c
a
b
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Converse of the Pythagorean Theorem
If c2 a2 b2 right triangle
If c2 gt a2 b2 obtuse triangle
acute triangle
If c2 lt a2 b2
Remembering
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Converse of the Pythagorean Theorem
If c2 a2 b2 right triangle
obtuse triangle
c
a
b
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Converse of the Pythagorean Theorem
If c2 a2 b2 right triangle
If c2 gt a2 b2 obtuse triangle

acute triangle
c
a
b
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Converse of the Pythagorean Theorem
If c2 a2 b2 right triangle
obtuse triangle
c
a
b
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And if c gets even bigger
If c gt a b
c
a
b
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Great technology

arcytech.org/java/population
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Curriculum

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

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Assessment
should support the learning of important
mathematics and furnish useful information to
both teachers and students. -NCTM Principles and
Standards
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Assessment

• TAKS Higher Expectations a good thing.
• It will be tough on all of us to rise to the
  challenge.
• But we SHOULD and we CAN

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In closing
Equity Curriculum Teaching Learning Assessment Tec
hnology
Learning is our motive for all that we do.
Learning
Everything we do is designed to support that.
And thats all about Character
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