Transcript Success for all: Its contradictions and challenges

NCTM
Principles: The
“Character” of
School
Mathematics
Cynthia Lanius
Technology Integration Specialist
Sinton ISD
June 2003
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
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Equity
Curriculum
Teaching
Learning
Assessment
Technology
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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 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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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 world’s greatest
technology or the world’s greatest teacher
for a child you love?
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What we really want…
World’s Greatest Technologies
in the hands of the
World’s 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
If c2 > a2 + b2
right triangle
obtuse triangle
If c2 < a2 + b2
acute triangle
Remembering
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Converse of the Pythagorean Theorem
If c2 = a2 + b2
If c2 > a2 + b2
right triangle
obtuse triangle
c
a
b
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Converse of the Pythagorean Theorem
If c2 = a2 + b2
If c2 > a2 + b2
If c2 < a2 + b2
right triangle
obtuse triangle
acute triangle
c
a
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b
Converse of the Pythagorean Theorem
If c2 = a2 + b2
If c2 > a2 + b2
right triangle
obtuse triangle
c
a
b
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And if c gets even bigger…
If c > a + b
no triangle
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
Technology
Learning is our motive
for all that we do.
Everything we do is designed to
support that.
And that’s all about Character
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