The 8 Standards for Mathematical Practice in the Common Core State Standards

Sherry GettemyMarcia Torgrude

Content Created by June Apaza and Vicki Kapust

Outcomes Participants will:• Develop a better understanding of the 8

Standards for Mathematical Practice

• Develop an understanding of how the 8 Practices will be integrated into instruction at each grade band.

• Develop an understanding of how the 8 Standards for Mathematical Practice will be assessed along with the Content Standards.

Grade Level Overview Page

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. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.”

(CCSS, 2010)

Background Information:Standards for Mathematical

Practice• “These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.”

(Massachusetts Curriculum Frameworks for Mathematics, 2011, p. 15)

• The NCTM process standards (2000)

• The National Research Council’s report Adding It Up (2001)

Underlying Frameworks

NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Underlying Frameworks

Strands of Mathematical Proficiency• Conceptual Understanding – comprehension of mathematical

concepts, operations, and relations• Procedural Fluency – skill in carrying out procedures flexibly,

accurately, efficiently, and appropriately• Strategic Competence – ability to formulate, represent, and

solve mathematical problems• Adaptive Reasoning – capacity for logical thought, reflection,

explanation, and justification• Productive Disposition – habitual inclination to see

mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

What’s different about CCSS?

These Standards are not intended to be new names for old ways of doing business. They are a call to take the

next step. It is time for states to work together to build on lessons learned from two decades of

standards based reforms. It is time to recognize that standards are not just promises to our children, but

promises we intend to keep.

- CCSS (2010, p.5)

Standards for Mathematical Practice

Integration of Standards for Mathematical

Practice• Not “Problem Solving Fridays”• Not “enrichment” for advanced students• Most lie in the process of arriving at an

answer, not necessarily in the answer itself• Every lesson should seek to build student

expertise in Content and Practice standards

Integration of Standards for Mathematical

Practice• Each group will have a standard• Rewrite the standard in your own words• Respond to “How will incorporating this

standard impact your teaching?”• Share on poster with the large group

Grouping the Standards for Mathematical Practice

(McCallum, 2011)

Integration of Standards for Mathematical

Practice• If we do things well, the teaching and learning will look different!

• Return to your standard and respond to the questions:• What will the student be doing?• What will the teacher be doing?• What kinds of tasks will foster proficiency

for this Practice Standard?

What Kind of Mathematical Tasks Contribute to Proficiency

in the CCSSM Practice Standards ?

Why Instructional Tasks are Important

Comparing Two Mathematical Tasks

• Martha’s Carpeting Task

• The Fencing Task

Martha’s Carpeting Tasks

Martha was re-carpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

The Fencing Task

Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. • If Ms. Brown’s students want their rabbits to have

as much room as possible, how long would each of the sides of the pen be?

• How long would each of the sides of the pen be if they had only 16 feet of fencing?

• How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

Comparing Two Mathematical Tasks

Grouping the Standards for Mathematical Practice

(McCallum, 2011)

The Brownie Problem – Elementary Task

Basic Student Budget Task – Secondary Task

Assessment and the Common Core Content & Practice Standards

What types of evidence will students have to demonstrate to show they’ve mastered both the content and practice standards?

What types of test questions will be developed to gather this evidence?

The SMARTER Balanced Assessment Consortium (SBAC)

SBAC is one of two federally funded groups of states that are designing assessments for the Common Core State Standards in Mathematics.

A National Consortium of States South Dakota is a member of The Smarter Balanced Assessment Consortium.

29 states representing 48% of K-12 students

21 governing, 8 advisory states

Washington state is fiscal agent

The SMARTER Balanced Assessment Consortium (SBAC)

SMARTER Balanced released a draft document outlining the content specifications that are intended to ensure that the assessment system accurately assesses the full range of the standards (including the Practice Standards).

Assessments are scheduled for full implementation in 2014.

(Field test questions are scheduled for 2013, however)

The SMARTER Balanced Assessment Consortium (SBAC)

Include a variety of question types: • selected response, • short constructed response,• extended constructed response, • technology enhanced, and • performance tasks

Assessing Levels of Expertise

Level 1: Demonstrating basic procedural skills AND conceptual understanding.

Level 2: Assessing knowledge in a context where their work on complex tasks is scaffolded.

Level 3: Unscaffolded situations that call on substantial chains of reasoning.

Claims & Evidence for CCSS Mathematics Assessments

Claim #1—Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Claim #2—Students can frame and solve a range of complex problems in pure and applied mathematics.

Claim #3—Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

Claim #4—Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

Claims & Evidence for CCSS Mathematics Assessments

Claim #1—Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.Claim #2—Students can frame and solve a range of complex problems in pure and applied mathematics.Claim #3—Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.Claim #4—Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

These 4 claims were developed based on the CCSSM Content and Practice Standards.

Quotes from CCSSM, page 8:

“The Standards for Mathematical Practice describe ways in which [students] ought to engage with the subject matter…”

“Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content…”

Sample Task--Grade 8from Smarter Balanced Assessment

Consortium

A Claim #1, Level 1 example Claim #1—Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.

Level 1—Demonstrating basic procedural skills AND conceptual understanding.

Water Tank Problem: A water tank has shape and dimensions as shown in the diagram below. At the beginning the tank is empty. Then it is filled with water at the rate of one liter per second.

Water Tank

Sample Tasks—Elementary, MS, HSConstructed Response, Level 2

Choose one task and work on the problem by yourself for about 10-15 minutes. Elementary: T-Shirts MS: Taxi Cabs HS: Shadows

Discuss your solutions AND explanations with others who worked on the same problem as you did.

Analyze the instructional tasks in terms ofopportunities for students to regularlyengage in the Practice Standards.

Standards for Mathematical Practice

Web site for Smarter Balanced Assessment Consortium:

http://www.k12.wa.us/smarter/

• Q & A

• Fill out End of Day Reflection form.

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Thank You!