Transcript Perspective… - JKDixonMath

Empowering Learners
through the Common
Core State Standards
Juli K. Dixon, Ph.D.
University of Central Florida
[email protected]
Solve this…
3 ÷ 1/7
Solve this…
3 ÷ 1/7
Tell someone near you how you solved it.
Perspective…
When asked to justify the solution to 3 ÷ 1/7
A student said this…
Perspective…
When asked to justify the solution to 3 ÷ 1/7
A student said this…
“Just change the division sign to
multiplication and flip the fraction after the
sign. 3 ÷ 1/7 becomes 3 x 7/1. So I find
3/1 x 7/1 which is 21/1 or 21.”
Perspective…
When asked to justify the solution to 3 ÷ 1/7
A student said this…
“Just change the division sign to
multiplication and flip the fraction after the
sign. 3 ÷ 1/7 becomes 3 x 7/1. So I find
3/1 x 7/1 which is 21/1 or 21.”
Is this an acceptable justification?
Perspective…
When asked to justify the solution to 3 ÷ 1/7
Another student said this…
“I know there are 7 groups of 1/7 in one
whole. Since there are three wholes, I
have 3 x 7 or 21 groups of 1/7 in 3
wholes so 3 ÷ 1/7 = 21.”
Perspective…
When asked to justify the solution to 3 ÷ 1/7
Another student said this…
“I know there are 7 groups of 1/7 in one
whole. Since there are three wholes, I
have 3 x 7 or 21 groups of 1/7 in 3
wholes so 3 ÷ 1/7 = 21.”
How is this justification different and
what does it have to do with the CCSSM?
Background of the CCSSM
• Published by the National Governor’s
Association and the Council of Chief State
School Officers in June 2010
• Result of collaboration from 48 states
• Provides a focused curriculum with an
emphasis on teaching for depth
Background of the CCSSM
45 States + DC have adopted the Common Core State Standards
Minnesota adopted the CCSS in ELA/literacy only
Background of the CCSSM
“… 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” (CCSS, 2010, p. 3).
Background of the CCSSM
“… 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” (CCSS, 2010, p. 3).
We began this process in 2007 with the Next
Generation Sunshine State Standards… they
are similar to the CCSS but with important
distinctions.
NGSSS Content Standards
Wordle
CCSSM Content Standards
Wordle
Content Standards
• Define expectations for students at each grade
level
• Use concepts from earlier grades
• Emphasize need to justify mathematical moves
• Indicate understanding and skill are equally
important
• Include expectations that students demonstrate
understanding of procedures
Content Standards
(CCSS)
• Critical Areas – major areas of focus for grade
• Domains – group related clusters
• Clusters – group related standards
• Standards – define what students should know
and be able to do
Content Standards
(NGSSS)
• Big Ideas– major areas of focus for grade
• Supporting Ideas – connect to and between big
ideas and address gaps in big ideas
Content Standards
Number & Operations in Base Ten
4.NBT
Use place value understanding and properties of operations to
perform multi-digit arithmetic
5.
Multiply multi-digit numbers using strategies based on place value
and the properties of operations. Illustrate and explain the calculations by
using equations, rectangular arrays, and/or area models.
Content Standards
Domain
Number & Operations in Base Ten
4.NBT
Cluster
Use place value understanding and properties of operations to
perform multi-digit arithmetic
Standard
5.
Multiply multi-digit numbers using strategies based on place value
and the properties of operations. Illustrate and explain the calculations by
using equations, rectangular arrays, and/or area models.
Background of the CCSSM
The CCSSM consist of Content Standards and
Standards for Mathematical Practice.
“The Standards for Mathematical Practice
describe varieties of expertise that
mathematics educators at all levels should
seek to develop in their students” (CCSS),
2010, p. 6).
Making Sense of the
Mathematical Practices
The Standards for Mathematical Practice
are based on:
• The National Council of Teachers of
Mathematics’ (NCTM) Principles and
Standards for School Mathematics
(NCTM, 2000), and
• The National Research Council’s (NRC)
Adding It Up (NRC, 2001).
Making Sense of the
Mathematical Practices
NCTM Process Standards:
• Problem Solving
• Reasoning and Proof
• Communication
• Representation
• Connections
Making Sense of the
Mathematical Practices
NRC Strands of Mathematical Proficiency:
• Adaptive Reasoning
• Strategic Competence
• Conceptual Understanding
• Procedural Fluency
• Productive Disposition
Making Sense of the
Mathematical Practices
NRC Strands of Mathematical Proficiency:
• Adaptive Reasoning
• Strategic Competence
• Conceptual Understanding
• Procedural Fluency
• Productive Disposition
Standards for Mathematical
Practice Wordle
Perspective…
According to a recommendation from
the Center for the Study of
Mathematics Curriculum (CSMC,
2010), we should lead with the
Mathematical Practices.
Perspective…
Lead with Mathematical Practices
1Implement CCSS beginning with mathematical
practices,
2Revise current materials and assessments to
connect to practices, and
3Develop an observational scheme for principals
that supports developing mathematical practices.
(CSMC, 2010)
Making Sense of the
Mathematical Practices
The 8 Standards for Mathematical Practice:
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
Content Standards
Domain
Number & Operations in Base Ten
4.NBT
Cluster
Use place value understanding and properties of operations to
perform multi-digit arithmetic
Standard
5.
Multiply multi-digit numbers using strategies based on place value
and the properties of operations. Illustrate and explain the calculations by
using equations, rectangular arrays, and/or area models.
Solve this…
Solve this…
What did you do?
Perspective…
What do you think fourth grade
students would do?
How might they solve 4 x 7 x 25?
Perspective…
Are you observing this sort of
mathematics talk in classrooms?
Is this sort of math talk important?
Perspective…
What does this have to do with the
Common Core State Standards for
Mathematics (CCSSM)?
With which practices were the
fourth grade students engaged?
The 8 Standards for Mathematical Practice:
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
With which practices were the
fourth grade students engaged?
The 8 Standards for Mathematical Practice:
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
Perspective…
In an effort to simplify student’s learning
pathways and minimize barriers (stigler, et. al.,
1999), teachers often provide students with
efficient procedures too early.
When we do this – we minimize students’
opportunities to engage in these practices.
Impact on Depth…
What does it mean to use
strategies to multiply?
When do students begin to
develop these strategies?
Content Standards
Operations & Algebraic Thinking
3.OA
Understand properties of multiplication and the relationship
between multiplication and division.
5.
Apply properties as strategies to multiply and divide…
Multiply and divide within 100.
7.
Fluently multiply within 100, using strategies such as the
relationship between multiplication and division or properties of
operations...
What does it mean to use
strategies to multiply?
Consider 6 x 7
What does it mean to use
strategies to multiply?
Consider 6 x 7
What strategies can we use?
With which practice were the
third grade students engaged?
The 8 Standards for Mathematical Practice:
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
With which practice were the
third grade students engaged?
The 8 Standards for Mathematical Practice:
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
The Standards for Mathematical
Practice help us to focus on
processes, not just products.
We will continue to focus on
them throughout the semester you need to get to know them
within the broader context of
the CCSS. Knowing both will
serve you well.