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Empowering Learners through the Common Core State Standards in Grades 3-5

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Title: Empowering Learners through the Common Core State Standards in Grades 3-5


1
Empowering Learners through the Common Core State
Standards in Grades 3-5
  • Juli K. Dixon, Ph.D.
  • University of Central Florida
  • juli.dixon_at_ucf.edu

2
Solve this
3 1/7
3
Solve this
3 1/7
Tell someone near you how you solved it.
4
Perspective
When asked to justify the solution to 3 1/7
A student said this
5
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.
6
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?
7
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.
8
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?
9
Background of the CCSSM
  • Published by the National Governors 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

10
Background of the CCSSM
45 States DC have adopted the Common Core State
Standards
Minnesota adopted the CCSS in ELA/literacy only
11
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).

12
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).
  • So what do these standards look like anyway?

13
CCSSM Content Standards Wordle for Grades 3-5
14
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

15
Content Standards
  • 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

16
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.
17
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.
Domain
Cluster
Standard
18
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).
19
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 Councils (NRC) Adding It
    Up (NRC, 2001).

20
Making Sense of the Mathematical Practices
NCTM Process Standards
  • Problem Solving
  • Reasoning and Proof
  • Communication
  • Representation
  • Connections

21
Making Sense of the Mathematical Practices
NRC Strands of Mathematical Proficiency
  • Adaptive Reasoning
  • Strategic Competence
  • Conceptual Understanding
  • Procedural Fluency
  • Productive Disposition

22
Making Sense of the Mathematical Practices
NRC Strands of Mathematical Proficiency
  • Adaptive Reasoning
  • Strategic Competence
  • Conceptual Understanding
  • Procedural Fluency
  • Productive Disposition

23
Standards for Mathematical Practice Wordle
24
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

25
Perspective
According to a recommendation from the Center for
the Study of Mathematics Curriculum (CSMC, 2010),
we should lead with the Mathematical Practices.
26
Perspective
  • Lead with Mathematical Practices
  • Implement CCSS beginning with mathematical
    practices,
  • Revise current materials and assessments to
    connect to practices, and
  • Develop an observational scheme for principals
    that supports developing mathematical practices.
  • (CSMC, 2010)

27
SMARTER Balanced Assessment Consortium
Draft Assessment Claims for Mathematics
  • Concepts and Procedures
  • Problem Solving
  • Communicating Reasoning
  • Data Analysis and Modeling
  • See Draft Item Spec released January 26, 2012

28
Content Standards
Number Operations in Base Ten 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.
Domain
Cluster
Standard
29
Solve this
30
Solve this
31
What did you do?
32
Perspective
What do you think fourth grade students would
do? How might they solve 4 x 7 x 25?
33
(No Transcript)
34
Perspective
Are you observing this sort of mathematics talk
in classrooms? Is this sort of math talk
important?
35
Perspective
What does this have to do with the Common Core
State Standards for Mathematics (CCSSM)?
36
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

37
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

38
Perspective
In an effort to simplify students 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.
39
Impact on Depth
What does it mean to use strategies to
multiply? When do students begin to develop
these strategies?
40
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...
41
What does it mean to use strategies to multiply?
  • Consider 6 x 7

42
What does it mean to use strategies to multiply?
  • Consider 6 x 7
  • What strategies can we use?

43
What does it mean to use strategies to multiply?
  • Consider 6 x 7
  • What strategies can we use?
  • How can using strategies to multiply these
    factors help students look for and make use of
    structure? (SMP7)

44
(No Transcript)
45
The Standards for Mathematical Practice help us
to focus on processes, not just products.
46
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

47
Reason abstractly and quantitatively
2
  • Reasoning abstractly and quantitatively often
    involves making sense of mathematics in
    real-world contexts.
  • Word problems can provide examples of mathematics
    in real-world contexts.
  • This is especially useful when the contexts are
    meaningful to the students.

48
Reason abstractly and quantitatively
2
  • Consider the following problems
  • Jessica has 8 key chains. Calvin has 9 key
    chains. How many key chains do they have all
    together?
  • Jessica has 8 key chains. Alex has 15 key chains.
    How many more key chains does Alex have than
    Jessica?

49
Reason abstractly and quantitatively
2
  • Consider the following problems
  • Jessica has 8 key chains. Calvin has 9 key
    chains. How many key chains do they have all
    together?
  • Jessica has 8 key chains. Alex has 15 key chains.
    How many more key chains does Alex have than
    Jessica?
  • Key words seem helpful

50
Reason abstractly and quantitatively
2
  • Consider the following problems
  • Jessica has 8 key chains. Calvin has 9 key
    chains. How many key chains do they have all
    together?
  • Jessica has 8 key chains. Alex has 15 key chains.
    How many more key chains does Alex have than
    Jessica?
  • Key words seem helpful, or are they.

51
Reason abstractly and quantitatively
2
  • Now consider this problem
  • Jessica has 8 key chains. How many more key
    chains does she need to have 13 key chains all
    together?

52
Reason abstractly and quantitatively
2
  • Now consider this problem
  • Jessica has 8 key chains. How many more key
    chains does she need to have 13 key chains all
    together?
  • How would a child who has been conditioned to use
    key words solve it?

53
Reason abstractly and quantitatively
2
  • Now consider this problem
  • Jessica has 8 key chains. How many more key
    chains does she need to have 13 key chains all
    together?
  • How would a child who has been conditioned to use
    key words solve it?
  • How might a child reason abstractly and
    quantitatively to solve these problems?

54
Which Practices Have We Addressed?
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

55
Which Practices Have We Addressed?
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

56
The exploration of fractions provide excellent
opportunities for student engagement with the
Standards for Mathematical Practice.
57
How do we support this empowerment?
  • a lack of understanding of mathematical
    content effectively prevents a student from
    engaging in the mathematical practices
  • (CCSS, 2010, p. 8).

58
How do we support this empowerment?
  • a lack of understanding of mathematical
    content effectively prevents a student from
    engaging in the mathematical practices
  • (CCSS, 2010, p. 8).
  • When and how do we develop this understanding?

59
We must anticipate student misconceptions and use
them as spring boards to learning.
60
Consider this 5th grade class.
61
(No Transcript)
62
What was the misconception?
63
What was the misconception? With which practice
were the students engaged?
64
With which practice were the fifth 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

65
With which practice were the fifth 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

66
How might you change your practice to address
these now?
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

67
Where do we start?
  • There are at least three ways to think about
    this
  • Where do we start as teachers and administrators?
  • Where do we start as users of mathematics?
    Thinking mathematically.
  • Where do we start with respect to grade level?

68
Describing the Standards
a lack of understanding of mathematical
content effectively prevents a student from
engaging in the mathematical practices (CCSS,
2010, p. 8).
69
Engaging Students in Reasoning and Sense Making
  • We need to question students when they are wrong
    and when they are right.
  • We need to create an environment where students
    are expected to share their thinking.
  • We need to look for opportunities for students to
    reason about and make sense of mathematics.

70
Advice to help parents support their children
  • Teach procedures only after they are introduced
    in school. Ask your child to explain his or her
    thinking to you. Discuss this with your teacher.
  • Drill addition/multiplication facts only after
    your child explores strategies.
  • Help your child become more proficient in using
    mathematics at home.

71
How do we support this empowerment?
  • What we know best might be the most difficult to
    change.

72
How do we support this empowerment?
  • Teachers need content knowledge for teaching
    mathematics to know the tasks to provide, the
    questions to ask, and how to assess for
    understanding.
  • Math Talk needs to be supported in the classroom.
  • Social norms need to be established in classroom
    and professional development settings to address
    misconceptions in respectful ways.

73
Empowering Learners through the Common Core State
Standards in Grades 3-5
  • Juli K. Dixon, Ph.D.
  • University of Central Florida
  • juli.dixon_at_ucf.edu
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