1. Common Core State Standards: An Overview
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2. Goals for Our Session
• Help to calm fears concerning Common Core State Standards (CCSS)
• Common Core Instructional Shifts in Education
• Implementation of CCSS (what, why, how and when)
• Analyzing a Performance Based Assessment
• Mathematical Content vs. Mathematical Practices
• The Structure of a Lesson
• How the Implementation of a Task Impacts Learning
• Assessing and Advancing Questions
• How CCSS Ties to TEAM Evaluation
1

3. State Adoption of Common Core
2

4. Transitional Plan for 2012-2013
Six Key Instructional Shifts
MATH:
1.
Focus strongly where the Standards focus
2.
Coherence: think across grades, and link to major topics within grades
3.
Rigor: require conceptual understanding, procedural skill and fluency, and application
with intensity.
ELA:
1.
Building knowledge through content-rich nonfiction and informational texts
2.
Reading and writing grounded in evidence from text
3.
Regular practice with complex text and its academic vocabulary
3

5. Shift One: Focus
Strongly where the Standards focus
•Significantly narrow the scope of content and deepen how time and
energy is spent in the math classroom
•Focus deeply only on what is emphasized in the standards, so that
students gain strong foundations
4

6. It starts with Focus
• The current U.S. curriculum is “a mile wide and an inch deep.”
• Focus is necessary in order to achieve the rigor set forth in the
standards.
• Hong Kong example: more in-depth mastery of a smaller set of
things pays off
5

7. The shape of math in A+ countries
Mathematics topics intended at
each grade by at least
two-thirds of A+ countries
Mathematics topics intended
at each grade by at least twothirds of 21 U.S. states
1 Schmidt,
Houang, & Cogan, “A Coherent Curriculum: The
Case of Mathematics.” (2002).
6

8. Shift Two: Coherence
Think across grades, and link to major topics
within grades
• Carefully connect the learning within and across grades so that
students can build new understanding onto foundations built in
previous years.
• Begin to count on solid conceptual understanding of core
content and build on it. Each standard is not a new event, but
an extension of previous learning.
7

9. Shift Three: Rigor
In the major work, equal intensity in conceptual
understanding, procedural skill/fluency, and
application
•The CCSSM require a balance of:
– Solid conceptual understanding
– Procedural skill and fluency
– Application of skills in problem solving situations
•This requires equal intensity in time, activities, and resources in
pursuit of all three
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10. Implementation of Common Core State Standards
Compliments other Work Underway
Student readiness for
postsecondary education
and the workforce
(WHY we teach)
Common Core State
Standards provide a
vision of excellence
for WHAT we teach
TEAM provides a
vision of excellence
for HOW we teach
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11. Our Transition to Common Core Standards is Central
to Strengthening Tennessee’s Competitiveness
Only 21% of adults in
TN have a college
degree
TN ranks 46th in 4th
grade math and 41st in
4th grade reading
nationally
Tennessee’s
Competitiveness
54% of new jobs will
require postsecondary education
Only 15% of high
school seniors in TN
are college ready
Source: “Projections of Jobs and Education Requirements Through 2018” (The Georgetown University Center on Education and the
Workforce), 2011 NCES NAEP data, ACT
10

12. What are the Common Core State Standards?
The Standards . . .
• are aligned with college and work expectations;
• are clear, understandable and consistent;
• include rigorous content and application of knowledge through high-order skills;
• build upon strengths and lessons of current state standards;
• are informed by other top performing countries, so that all students are
prepared to succeed in our global economy and society; and
• are evidence-based.
http://corestandards.org/about-the-standards
11

13. Common Core State Standards are narrower…
# of TN Standards for 3rd Grade Math:
# of Common Core Standards for 3rd Grade Math:
25
113
There are 1,119 Tennessee ELA standards not covered in the Common Core
CLE
CU
GLE
SPI
Grand Total
45
501
109
464
1119
12

14. …and deeper.
3rd Grade Math
3OA.3 (Operations and Algebraic thinking): Use multiplication and division within 100 to solve word problems in
situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with
a symbol for the unknown number to represent the problems.
There were 28 cookies on a plate.
Five children each ate 1 cookie.
Two children each ate 3 cookies.
One child ate 5 cookies.
The rest of the children each ate 2 cookies.
Then the plate was empty
How many children ate 2 cookies? Use multiplication equations
and other operations, if needed, to show how you found your
answer.
Jane thinks this question can be solved by dividing 28 by 2. She
is wrong. Explain using equations and operations why this is not
possible.
Source: University of Pittsburgh, Copyrighted
13

15. How to Read the Grade Level Standards
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16. How will the Common Core State Standards affect
Teaching in Tennessee?
• Creativity and Flexibility
• Deeper Engagement
• Smaller Number of Standards
• Critical Thinking and Problem Solving
15

17. Forms of Assessment
Assessment as Learning
Assessment of Learning
Assessment for Learning
1
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18. 2012-2013 Assessment Plan, Math 3-8
Student performance on the Constructed Response
Assessments will not affect teacher, school, or district
accountability for the next two years.
October
• CRA 1
(paper and online
option, scored by
teachers in Field
Service Center
region, reported by
school team)
February
• CRA 2
(paper and online
option, scored by
teachers in Field
Service Center
region, reported
by school team)
May
• Official Constructed
Response Assessment
(paper-based
only, scored by
state, results reported
in July)
17

19. We will narrow the focus of the TCAP and
expand use of Constructed Response Assessments
2011-2012
2012-2013
2013-2014
2014-2015
TCAP
Constructed Response
PARCC
We will remove 15-25% of SPIs that are not reflected in
Common Core State Standards from the TCAP NEXT year.
The specific list of SPI’s will be shared on May 1.
We will expand the constructed response assessment for all
grades 3-8, focused on the TNCore focus standards for math.
NAEP
NAEP
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20. The Common Core State Standards
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The standards consist of:
 The CCSS for Mathematical Content
 The CCSS for Mathematical Practice
19

21. Overview of Activity
• Analyze and discuss the CCSS for mathematical content and
mathematical practices.
• Analyze the PBA in order to determine the way the assessment is
assessing the CCSSM.
• Discuss the CCSS related to the tasks and the implications for
instruction and learning.
• Discuss what it means to develop and assess conceptual
understanding.
2
20

22. Analyzing a
Performance-Based Assessment
2
21

23. 2012 – 2013 Tennessee Focus Clusters Grade 5
• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending
previous understanding of operations of whole numbers.
2
22

24. Analyzing Assessment Items (Private Think Time)
One assessment item has been provided:
 48 Gumdrops Task
• Solve the assessment item.
• Make connections between the standard(s) and the
assessment item.
2
23

25. 1. 48 Gumdrops Task
Two children are sharing 48 gumdrops.
Jessica says, “I want 2/4 of the set of 48 gumdrops.”
Samuel says, “I want 2/3 of the set of 48 gumdrops.”
a.
Is it possible for Jessica and Samuel to each have a fraction of the
gumdrops that they want?
Answer: ____________________
b.
If you respond yes, use diagrams and equations to explain how you know
they can each receive the share of gumdrops they want. If you respond
no, use diagrams and equations to explain why the children cannot receive
the number of gumdrops they each want.
24

26. Discussing Content Standards (Small-Group Time)
With your small group, discuss the connections
between the content standard(s) and the
assessment item.
2
25

27. The CCSS for Mathematical Content: Grade 5
Number and Operations – Fractions
5.NF
Apply and extend previous understandings of multiplication and division to
multiply and divide fractions.
Apply and extend previous understandings of multiplication to
5.NF.4
multiply a fraction or whole number by a fraction.
Interpret multiplication as scaling (resizing), by:
5.NF.5
Explaining why multiplying a given number by a fraction greater than
5.NF.5b
1 results in a product greater than the given number (recognizing
multiplication by whole numbers greater than 1 as a familiar case);
explaining why multiplying a given number by a fraction less than 1
results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of
multiplying a/b by 1.
Solve real-world problems involving multiplication of fractions and
5.NF.6
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem.
Apply and extend previous understandings of division to divide unit
5.NF.7
fractions by whole numbers and whole numbers by unit fractions.
Common Core State Standards, NGA Center/CCSSO, 2010
26

28. The CCSS for Mathematical Content: Grade 5
Number and Operations – Fractions
5.NF
Apply and extend previous understandings of multiplication and division to multiply
and divide fractions.
Interpret division of a unit fraction by a non-zero whole number, and
5.NF.7a
compute such quotients. For example, create a story context for (1/3) ÷ 4,
and use a visual fraction model to show the quotient. Use the relationship
between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because
(1/12) × 4 = 1/3.
Interpret division of a whole number by a unit fraction, and compute such
5.NF.7b
quotients. For example, create a story context for 4 ÷ (1/5), and use a visual
fraction model to show the quotient. Use the relationship between
multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5)
= 4.
Solve real-world problems involving division of unit fractions by non-zero
5.NF.7c
whole numbers and division of whole numbers by unit fractions, e.g., by
using visual fraction models and equations to represent the problem. For
example, how much chocolate will each person get if 3 people share 1/2 lb
of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Common Core State Standards, NGA Center/CCSSO, 2010
27

29. 1. 48 Gumdrops Task
Two children are sharing 48 gumdrops.
Jessica says, “I want 2/4 of the set of 48 gumdrops.”
Samuel says, “I want 2/3 of the set of 48 gumdrops.”
a.
Is it possible for Jessica and Samuel to each have a fraction of the
gumdrops that they want?
Answer: ____________________
b.
If you respond yes, use diagrams and equations to explain how you know
they can each receive the share of gumdrops they want. If you respond
no, use diagrams and equations to explain why the children cannot receive
the number of gumdrops they each want.
28

30. Determining the Mathematical Practices
Associated with the
Performance-Based Assessment
29

31. The CCSS for 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.
Common Core State Standards for Mathematics, 2010, NGA Center/CCSSO
30

32. Discussing Practice Standards (Small-Group Time)
With your small group, discuss the connections between
the practice standards and the assessment item.
3
31

33. 1. 48 Gumdrops Task
Two children are sharing 48 gumdrops.
Jessica says, “I want 2/4 of the set of 48 gumdrops.”
Samuel says, “I want 2/3 of the set of 48 gumdrops.”
a.
Is it possible for Jessica and Samuel to each have a fraction of the
gumdrops that they want?
Answer: ____________________
b.
If you respond yes, use diagrams and equations to explain how you know
they can each receive the share of gumdrops they want. If you respond
no, use diagrams and equations to explain why the children cannot receive
the number of gumdrops they each want.
3
32

34. Mathematical Tasks:
A Critical Starting Point for Instruction
33

35. The Structures and Routines of a Lesson
Set Up the Task
Set-Up of the Task
The Explore Phase/Private Work Time
Generate Solutions
The Explore Phase/
Small-Group Problem Solving
1. Generate and Compare Solutions
2. Assess and Advance Student Learning
MONITOR: Teacher selects
examples for the Share Discuss
based on:
• Different solution paths to
the same task
• Different representations
• Errors
• Misconceptions
SHARE: Students explain
their methods, repeat others’
ideas, put ideas into their own
words, add on to ideas and
ask for clarification.
REPEAT THE CYCLE FOR EACH
SOLUTION PATH
COMPARE: Students discuss
Share Discuss and Analyze Phase
1. Share and Model
2. Compare Solutions
3. Focus the Discussion on Key
Mathematical Ideas
4. Engage in a Quick Write
similarities and differences
between solution paths.
FOCUS: Discuss the
meaning of mathematical
ideas in each representation.
REFLECT: Engage students
in a Quick Write or a
discussion of the process.
34

36. Mathematical Tasks:
A Critical Starting Point for Instruction
There is no decision that teachers make that has a greater
impact on students’ opportunities to learn and on their
perceptions about what mathematics is than the selection
or creation of the tasks with which the teacher engages
students in studying mathematics.
Lappan & Briars, 1995
35

37. Linking to Research/Literature:
The QUASAR Project
The Mathematical Tasks Framework
TASKS
TASKS
TASKS
as they
appear in
curricular/
instructiona
l materials
as set up by
the teachers
as
implemented
by students
Student
Learning
Stein M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics
instruction: A casebook for professional development, p. 16. New York: Teachers College Press.
36

38. The Enactment of the Task (Private Think Time)
• Read the Vignettes
• Consider the following question:
What are students learning in each classroom?
37
37

39. The Enactment of the Task (Small-Group Discussion)
Discuss the following question and cite evidence from
the cases:
What are students learning in each classroom?
38
38

40. The Enactment of the Task (Whole-Group Discussion)
What opportunities did students have to
think and reason in each of the classes?
39
39

41. Linking to Research/Literature:
The QUASAR Project
How High-Level Tasks Can Evolve During a Lesson
•
Maintenance of high-level demands
•
Decline into procedures without connection to meaning
•
Decline into unsystematic and nonproductive exploration
•
Decline into no mathematical activity
40

42. Factors Associated with the Decline and Maintenance
of High-Level Cognitive Demands
Decline
Maintenance
• Problematic aspects of the task
become routinized
• Scaffolds of student thinking and
reasoning provided
• Understanding shifts to
correctness, completeness
• A means by which students can
monitor their own progress is
provided
• Insufficient time to wrestle with the
demanding aspects of the task
• Classroom management problems
• Inappropriate task for a given group
of students
• Accountability for high-level
products or processes not expected
• High-level performance is modeled
• A press for
justifications, explanations through
questioning and feedback
• Tasks build on students’ prior
knowledge
• Frequent conceptual connections
are made
• Sufficient time to explore
41

43. Linking to Research/Literature:
The QUASAR Project
Task Set-Up
Task Implementation
A.
High
High
B.
Low
Low
C.
High
Low
Student Learning
High
Low
Moderate
Stein & Lane, 1996
42

44. Assessing and Advancing Questions
43

45. Using Questioning During the Exploration Phase
Imagine that you are walking around the room as your groups of students
work on 48 Gumdrops Task – if it were a lesson, not an assessment.
Consider what you would say to the groups who produced responses in
order to assess and advance their thinking about key mathematical ideas,
problem-solving strategies, or use of and connection between
representations.
Specifically, for each response, indicate what questions you would ask:
– to determine what the student knows and understands
(ASSESSING QUESTIONS)
– to move the student towards the target mathematical goals
(ADVANCING QUESTIONS)
44

46. Characteristics of Questions that Support
Students’ Exploration
Assessing Questions
• Based closely on the work
the student has produced.
• Clarify what the student has
done and what the student
understands about what
s/he has done.
• Provide information to the
teacher about what the
student understands.
Advancing Questions
• Use what students have
produced as a basis for
making progress toward the
target goal.
• Move students beyond their
current thinking by pressing
students to extend what they
know to a new situation.
• Press students to think about
something they are not
currently thinking about.
45

47. 48 Gumdrops Task: Amanda's Work
46

48. Gumdrops Task
•Assessing Questions:
•Advancing Questions:
• Tell me what you did.
• Can you write an explanation for how
you used the values to draw a
diagram?
• What does ___ represent?
• Why did you … ?
• How does you diagram represent the
equation (or vice versa)?
• How did you know how to draw your
diagram?
• If Amanda had 1/5 of the gumdrops
and Samuel had 2/3 of the gumdrops,
how many would be leftover?
• Your neighbor says that they have do
enough to share. How could you help
them understand that this conclusion
is incorrect?
47

49. Supporting Student Thinking and Learning
In planning a lesson, what do you think can be gained by
considering how students are likely to respond to a task and
by developing questions in advance that can assess and
advance their learning, depending on the solution path they
choose?
48

50. Reflection
What have you learned about assessing and advancing
questions that you can use in your classroom?
Turn and Talk
49

51. Tennessee Education Rubric
Which of the indicators on the Teacher Education
Rubric are related to the use of
Assessing and Advancing questions?
50

52. Using the Assessment to Think About Instruction
In order for students to perform well on the PBA, what are
the implications for instruction?
• What kinds of instructional tasks will need to be used in
the classroom?
• What will teaching and learning look like and sound like
in the classroom?
51

53. Common Core and the TN Core 4 –
Linking to the TEAM Evaluation Model
This year the TEAM Evaluation will focus on the following four
areas:
1.
Questioning
2.
Academic Feedback
3.
Thinking
4.
Problem Solving
52

54. Questioning
53

55. Academic Feedback
54

56. Thinking
55

57. Problem Solving
56