nctm principles: the “character” of school mathematics cynthia lanius technology integration...
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NCTM Principles: The “Character” of School Mathematics
Cynthia LaniusTechnology 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 CharacterThe Standards describe the mathematical content and processes that students should learn. Content and Processes
Character
The Principles describe particular features of high-quality mathematics education.
-NCTM Principles and Standards
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main or essential nature especially as strongly marked and serving to distinguish
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• Equity• Curriculum• Teaching• Learning• Assessment• Technology
DistinguishDistinguish
High
Quality
Mathematic
s
High
Quality
Mathematic
s
Character
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Learning
Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.
RememberingUnderstanding
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EquityExcellence in mathematics education requires equity—high 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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Technologyis 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 world’s greatest technology or the world’s greatest teacher for a child you love?
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What we really want…
in the hands of the
World’s Greatest Teachers
World’s Greatest Technologies
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a
b
c
In a right triangle, c2 = a2 + b2
Pythagorean Theorem
Technologies can build understanding
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If c2 = a2 + b2 right triangle
If c2 > a2 + b2 obtuse triangle
acute triangle
Converse of the Pythagorean Theorem
If c2 < a2 + b2
Remembering
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a
b
c
If c2 = a2 + b2 right triangle
If c2 > a2 + b2 obtuse triangle
Converse of the Pythagorean Theorem
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a
b
c
If c2 = a2 + b2 right triangle
If c2 > a2 + b2 obtuse triangle
If c2 < a2 + b2 acute triangle
Converse of the Pythagorean Theorem
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a
b
c
If c2 = a2 + b2 right triangle
If c2 > a2 + b2 obtuse triangle
Converse of the Pythagorean Theorem
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a
b
c
If c > a + b no triangle
And if c gets even bigger…
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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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• 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…
Assessment
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Learning is our motive for all that we do.
In closing…
EquityCurriculumTeachingLearningAssessmentTechnology
Learning
Everything we do is designed tosupport that.
And that’s all about Character
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