achievethecore.org 1 implementing standards and incorporating mathematical practices sandra m....

achievethecore.org 1

Implementing Standards and Incorporating Mathematical Practices

Sandra M. AlbertiAMTNJOctober 24, 2013


achievethecore.org

Student Achievement Partners – Who We Are

2

• SAP is a nonprofit organization founded by three of the contributing authors of the Common Core State Standards

• Currently a team of approximately 30; office in NY and team members located throughout the country

• Funded by foundations: GE Foundation, Hewlett Foundation, Bill & Melinda Gates Foundation and The Helmsley Charitable Trust

Our mission:

• Student Achievement Partners is devoted to accelerating student achievement by supporting effective and innovative implementation of the CCSS.


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Our Principles – How we approach the work

WE HOLD NO INTELLECTUAL PROPERTYOur goal is to create and disseminate high quality materials as widely as possible. All resources that we create are open source and available at no cost. We encourage states, districts, schools, and teachers to take our resources and make them their own.

WE DO NOT COMPETE FOR STATE, DISTRICT OR FEDERAL CONTRACTS

Ensuring that states and districts have excellent materials for teachers and students is a top priority. We do not compete for these contracts because we work with our partners to develop high quality RFPs that support the Core Standards.

WE DO NOT ACCEPT MONEY FROM PUBLISHERSWe work with states and districts to obtain the best materials for teachers and students. We are able to independently advise our partners because we have no financial interests with any publisher of education materials. Our independence is essential to our work.



Why are we doing this? We have had standards.

• Before Common Core State Standards we had standards, but rarely did we have standards-based instruction.

Long lists of broad, vague statementsMysterious assessmentsCoverage mentalityFocused on teacher behaviors – “the

inputs”


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Results of Previous Standards, and Hard Work

Previous state standards did not improve student achievement.

Gaps in achievement, gaps in expectationsNAEP resultsHigh school drop out issueCollege remediation issue

This is about more than just working

hard!

5


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Principles of the CCSS

Fewer - Clearer - Higher

• Aligned to requirements for college and career readiness

• Based on evidence

• Honest about time



Implications

• What implications do the CCSS have on what we teach?

• What implications do the CCSS have on how we teach?

This effort is about much more than implementing the next version of the standards: It is about preparing all students for success in college and careers.


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Mathematics: 3 shifts

1. Focus: Focus strongly where the standards focus.



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).



K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach


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Focusing attention within Number and Operations

Operations and Algebraic Thinking

Expressions and Equations

Algebra

Number and Operations—Base Ten

The Number System

Number and Operations—Fractions

K 1 2 3 4 5 6 7 8 High School


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Grade Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2 Addition and subtraction - concepts, skills, and problem solving and place value

3–5 Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6 Ratios and proportional reasoning; early expressions and equations

7 Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra, linear functions

Priorities in Mathematics



Where to focus in mathematics – K example


14achievethecore.org 14


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2. Coherence: Think across grades, and link to major topics


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Coherence: Link to major topics within grades

Example: data representation

Standard 3.MD.3


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2. Coherence: Think across grades, and link to major topics

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application


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Conceptual understanding of place value…?



Conceptual understanding of place value…?


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Conceptual Understanding of Fractions

Resource/Tool:http://www.illustrativemathematics.org/standards/k8

http://www.illustrativemathematics.org/standards/k8



Required Fluencies in K-6Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations


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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.

Don’t Bureaucratize



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2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Overarching habits of mind of a productive mathematical thinker.

Reasoning and explaining

Modeling and using tools

Seeing structure and generalizing


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AM I DOING THE CORE?



Standards for Mathematical Practice

•

There is not a one-to-one correspondence between the indicators for Core Action 3 and the Standards for Mathematical Practice. These indicators and the associated illustrative student behavior collectively represent the Standards for Mathematical Practice that are most easily observable during instruction.



Core Action 3: Provide all students with opportunities to exhibit mathematical practices in connection with the content of the lesson.

4 Some or most of the indicators and student behaviors should be observable in every lesson, though not all will be evident in all lessons.


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Evidence Observed or Gathered

1 = The teacher does not provide students opportunity and very few students demonstrate this behavior.

2 = The teacher provides students opportunity inconsistently and very few students demonstrate this behavior.

3 = The teacher provides students opportunity consistently and some students demonstrate this behavior.

4 = The teacher provides students opportunity consistently and some students demonstrate this behavior.


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Am I doing the Core?Indicators Illustrative Student BehaviorA. The teacher uses strategies to keep

all students persevering with challenging problems.

Even after reaching a point of frustration, students persist in efforts to solve challenging problems.

B. The teacher establishes a classroom culture in which students explain their thinking.

Students elaborate with a second sentence (spontaneously or prompted by the teacher or another student) to explain their thinking and connect it to their first sentence.

C. The teacher orchestrates conversations in which students talk about each other’s thinking.

Students talk about and ask questions about each other’s thinking, in order to clarify or improve their own mathematical understanding.


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Am I doing the Core?Indicators Illustrative Student BehaviorD. The teacher connects students’

informal language to precise mathematical language appropriate to their grade.

Students use precise mathematical language in their explanations and discussions.

E. The teacher has established a classroom culture in which students choose and use appropriate tools when solving a problem.

Students use appropriate tools strategically when solving a problem.

F. The teacher asks students to explain and justify work and provides feedback that helps students revise initial work.

Student work includes revisions, especially revised explanations and justifications.


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Evidence-Centered Design (ECD)

Claims

Design begins with the inferences (claims) we want to make about students

Evidence

In order to support claims, we must gather evidence

Tasks

Tasks are designed to elicit specific evidence from students in support of claims

ECD is a deliberate and systematic approach to assessment development that will help to establish the validity of the assessments, increase the comparability of year-to year results, and increase efficiencies/reduce costs.

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Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready (or “on-track” to being ready) in mathematics. The student solves grade-level /course-level problems in mathematics as set forth in

the Standards for Mathematical Content with connections to the Standards for Mathematical Practice.

Sub-Claim A: Major Content1 with Connections to Practices

The student solves problems involving the Major Content1 for her

grade/course with connections to the Standards for Mathematical

Practice.

Sub-Claim B: Additional & Supporting Content2 with Connections to

PracticesThe student solves problems involving

the Additional and Supporting Content2 for her grade/course with connections to the Standards for

Mathematical Practice.

Sub-Claim E: Fluency in applicable grades (3-6)

The student demonstrates fluency as set forth in the Standards for Mathematical

Content in her grade.

Claims Structure: Mathematics

Sub-Claim C: Highlighted Practices MP.3,6 with Connections to Content3

(expressing mathematical reasoning)The student expresses grade/course-

level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others, and/or attending to precision

when making mathematical statements.

Sub-Claim D: Highlighted Practice MP.4 with Connections to Content (modeling/application)

The student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills articulated in the standards for the

current grade/course (or for more complex problems, knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them (MP. 1),reasoning abstractly and quantitatively (MP. 2), using appropriate

tools strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for and expressing regularity in repeated reasoning (MP.8).

Total Exam Score Points: 82 (Grades 3-8), 97 or 107(HS)

12 pts (3-8),18 pts (HS)

6 pts (Alg II/Math 3 CCR)

~37 pts (3-8),~42 pts (HS) ~14 pts (3-8),

~23 pts (HS)

14 pts (3-8),14 pts (HS)

4 pts (Alg II/Math 3 CCR)

7-9 pts (3-6)

1 For the purposes of the PARCC Mathematics assessments, the Major Content in a grade/course is determined by that grade level’s Major Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. Note that tasks on PARCC assessments providing evidence for this claim will sometimes require the student to apply the knowledge, skills, and understandings from across several Major Clusters.2 The Additional and Supporting Content in a grade/course is determined by that grade level’s Additional and Supporting Clusters as identified in the PARCC Model Content Frameworks v.3.0 for Mathematics. 3 For 3 – 8, Sub-Claim C includes only Major Content. For High School, Sub-Claim C includes Major, Additional and Supporting Content.


achievethecore.org


Implementing Standards and Incorporating Mathematical Practices

Sandra M. AlbertiAMTNJOctober 24, 2013

achievethecore.org 1 implementing standards and incorporating mathematical practices sandra m....

Documents

core standards

systemic standards

list of standards

typical state standards

standardsbased instruction

round of standards revision

previous versions of

student achievement