2. A Little History
1989: NCTM’s Curriculum and Evaluation Standards
2000: NCTM’s Principles and Standards for School
Mathematics
2006: NCTM’s Curriculum Focal Points –
Standards Clarification Document (NJ)
2008: National Math Advisory Panel Report
2010: Common Core State Standards
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3. What We Have Learned about
Mathematics Education
Students must learn basics, but knowing the
basics alone is not enough.
Learning mathematics with understanding is
essential to enable students to solve new
problems.
Students learn mathematics primarily by doing
mathematics rather than just listening and
memorizing.
4. Intro to Common Core
https://www.teachingchannel.org/videos/common-
core-state-standards-elementary-school
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5. Goals of Common Core
Provide a consistent, clear understanding of what
students are expected to learn, so teachers and
parents know what they need to do to help them.
Be robust and relevant to the real world,
reflecting the knowledge and skills that our young
people need for success in college and careers.
Prepare students for the future, our communities
will be best positioned to compete successfully in
the global economy.
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8. 8
Grade-Level Standards (Content)
K-8 grade-by-grade standards organized by
domain
9-12 high school standards organized by
conceptual categories
Common Core State Standards
for Mathematics
Standards for Mathematical Practice
Describe mathematical “habits of mind”
What good mathematicians do
Connect with content standards in each grade
9. CCSS Domain Progression
K 1 2 3 4 5 6 7 8 HS
Counting &
Cardinality
Number and Operations in Base Ten
Ratios and Proportional
Relationships Number &
QuantityNumber and Operations –
Fractions
The Number System
Operations and Algebraic Thinking
Expressions and Equations Algebra
Functions Functions
Geometry Geometry
Measurement and Data Statistics and Probability
Statistics &
Probability
10. 10
Format of K-8
Mathematics Standards
Domains: overarching ideas that connect topics across
the grades
Clusters: illustrate progression of increasing
complexity from grade to grade
Standards: define what students should know and be
able to do at each grade level
12. CCSS Mathematical Practices
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
14. What’s the Bottom Line?
Less likely to retain
information
More likely to retain
information
Isolated Basic
Skills
Connected Facts
Contextual
Setting
Use Technology
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PURPOSE: To share what research and classroom practice over the last decade or more has shown
RESOURCE: Principles and Standards, Chapter 1
“For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards must address the problem of a curriculum that is ‘a mile wide and an inch deep.’ These Standards are a substantial answer to that challenge. It is important to recognize that ‘fewer standards’ are no substitute for focused standards. Achieving ‘fewer standards’ would be easy to do by resorting to broad, general statements. Instead, these Standards aim for clarity and specificity.”
Focus
Coherence
Clarity
Specificity
What do these words mean? We will begin by examining the structure of the high school standards. By the end of this and subsequent sessions, we will be able to elaborate on the meaning of these words as they relate to high school mathematics.
This diagram illustrates how the domains are distributed across the Common Core State Standards.
What is not easily seen is how a domain may impact multiple domains in future grades.
An example is K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in grade 6.
Likewise, Operations and Algebraic Thinking in K-5 provides foundation Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions in grades 6-8.
