1

Common Core State Standards: An Overview

2

• 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

Goals for Our Session

3

State Adoption of Common Core

4

Transitional Plan for 2012-2013

Six Key Instructional ShiftsMATH:

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:

4. Building knowledge through content-rich nonfiction and informational texts

5. Reading and writing grounded in evidence from text

6. Regular practice with complex text and its academic vocabulary

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

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

7

Mathematics topics intended at each grade by at least

two-thirds of A+ countries

Mathematics topics intended at each grade by at least two-

thirds of 21 U.S. states

The shape of math in A+ countries

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

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.

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

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

11

Our Transition to Common Core Standards is Central to Strengthening Tennessee’s Competitiveness

Source: “Projections of Jobs and Education Requirements Through 2018” (The Georgetown University Center on Education and the Workforce), 2011 NCES NAEP data, ACT

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

54% of new jobs will require post-secondary education

Only 15% of high school seniors in TN are college ready

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

13

Common Core State Standards are narrower…

11325

# of TN Standards for 3rd Grade Math: # of Common Core Standards for 3rd Grade Math:

There are 1,119 Tennessee ELA standards not covered in the Common Core

CLE CU GLE SPI Grand Total

45 501 109 464 1119

14

…and deeper.

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.

3rd Grade Math3OA.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.

Source: University of Pittsburgh, Copyrighted

15

How to Read the Grade Level Standards

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

17

Forms of Assessment

17

Assessment for Learning

Assessment of Learning

Assessment as Learning

18

2012-2013 Assessment Plan, Math 3-8

• Official Constructed Response Assessment

• (paper-based only, scored by state, results reported in July)

May

• CRA 2 • (paper and online

option, scored by teachers in Field Service Center region, reported by school team)

February

• CRA 1• (paper and online

option, scored by teachers in Field Service Center region, reported by school team)

October

Student performance on the Constructed Response Assessments will not affect teacher, school, or district accountability for the next two years.

19

We will narrow the focus of the TCAP and expand use of Constructed Response Assessments

NAEP

PA

RC

C

NAEP

2011-2012 2012-2013 2013-2014 2014-2015

TCAP

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.

Constructed Response

We will expand the constructed response assessment for all grades 3-8, focused on the TNCore focus standards for math.

20

The Common Core State Standards

The standards consist of:

The CCSS for Mathematical Content

The CCSS for Mathematical Practice

20

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.

21

22

Analyzing a

Performance-Based Assessment

22

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.

23

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.

24

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.

26

Discussing Content Standards (Small-Group Time)

With your small group, discuss the connections between the content standard(s) and the

assessment item.

26

27

Number and Operations – Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NF.5 Interpret multiplication as scaling (resizing), by:

5.NF.5b Explaining why multiplying a given number by a fraction greater than 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.

5.NF.6 Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

The CCSS for Mathematical Content: Grade 5

Common Core State Standards, NGA Center/CCSSO, 2010

28

Number and Operations – Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NF.7a Interpret division of a unit fraction by a non-zero whole number, and 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.

5.NF.7b Interpret division of a whole number by a unit fraction, and compute such 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.

5.NF.7c Solve real-world problems involving division of unit fractions by non-zero 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?

The CCSS for Mathematical Content: Grade 5

Common Core State Standards, NGA Center/CCSSO, 2010

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.

30

Determining the Mathematical Practices

Associated with the

Performance-Based Assessment

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

32

Discussing Practice Standards (Small-Group Time)

With your small group, discuss the connections between the practice standards and the assessment item.

32

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.

33

34

Mathematical Tasks:A Critical Starting Point for Instruction

35

The Structures and Routines of a Lesson

The Explore Phase/Private Work TimeGenerate Solutions

The Explore Phase/ Small-Group Problem Solving

1. Generate and Compare Solutions2. Assess and Advance Student Learning

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

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 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.

Set Up the TaskSet-Up of the Task

36

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

Mathematical Tasks:A Critical Starting Point for Instruction

37

Linking to Research/Literature: The QUASAR Project

The Mathematical Tasks Framework

TASKS

as they appear in curricular/ instructional materials

TASKS

as set up by the teachers

TASKS

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.

38

The Enactment of the Task (Private Think Time)

• Read the Vignettes

• Consider the following question:

What are students learning in each classroom?

38

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?

39

40

The Enactment of the Task (Whole-Group Discussion)

What opportunities did students have to

think and reason in each of the classes?

40

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

42

Factors Associated with the Decline and Maintenance of High-Level Cognitive Demands

Decline• Problematic aspects of the task

become routinized• Understanding shifts to correctness,

completeness• 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

Maintenance• Scaffolds of student thinking and

reasoning provided• A means by which students can

monitor their own progress is provided

• 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

43

Stein & Lane, 1996

A.

B.

C.

High High

Low Low

High LowModerate

Low

High

Task Set-Up

Task Implementation

Student Learning

Linking to Research/Literature: The QUASAR Project

44

Assessing and Advancing Questions

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)

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.

47

48 Gumdrops Task: Amanda's Work

48

Gumdrops Task

•Assessing Questions:

• Tell me what you did.

• 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?

•Advancing Questions:

• Can you write an explanation for how you used the values to draw a 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?

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?

50

Reflection

What have you learned about assessing and advancing questions that you can use in your classroom?

Turn and Talk

51

Tennessee Education Rubric

Which of the indicators on the Teacher Education Rubric are related to the use of

Assessing and Advancing questions?

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?

53

Common Core and the TN Core 4 – Linking to the TEAM Evaluation Model

1. Questioning

2. Academic Feedback

3. Thinking

4. Problem Solving

This year the TEAM Evaluation will focus on the following four areas:

54

Questioning

55

Academic Feedback

56

Thinking

57

Problem Solving