# The Standards for Mathematical Practice

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The Standards for

Mathematical Practice

2010

Alabama Course of Study: Mathematics

College- and Career-Ready Standards

Slide2Standards 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)

Slide3Underlying Frameworks

National Council of Teachers of Mathematics

NCTM (2000M

). Principles and Standards for School Mathematics

. Reston, VA: Author.

5

PROCESS

Standards

Problem Solving

Reasoning and Proof

Communication

Connections

Representations

Slide4Underlying Frameworks

Strands of

Mathematical Proficiency

NRC (2001).

Adding It Up.

Washington, D.C.: National Academies Press.

Conceptual Understanding

Procedural Fluency

Strategic Competence

Adaptive Reasoning

Productive Disposition

National Research Council

Slide5Standard 1

: Make sense of problems and persevere in

solving them.

Standard 2

: Reason abstractly and quantitatively.

Standard 3

: Construct viable arguments and critique

the reasoning of others.

Standard 4

: Model with mathematics.

Standard 5

: Use appropriate tools strategically.

Standard 6

: Attend to precision.

Standard 7

: Look for and make use of structure.

Standard 8

: Look for and express regularity in repeated

reasoning.

The Standards for Mathematical Practice

Mathematically proficient students:

Slide6What does this standard look like in the classroom?

What will students need in order to do this?What will teachers need in order to do this?Adapted from Kathy Berry, Monroe County ISD, Michigan

Questions to consider…

Slide7Analyze givens, constraints, relationshipsMake conjectures Plan solution pathways

Make meaning of the solutionMonitor and evaluate their progressChange course if necessaryAsk themselves if what they are doing makes sense

Standard 1: Make sense of problems and persevere in solving them.

What do mathematically proficient students do?

Slide8Make sense of quantities and relationshipsAble to decontextualize

Abstract a given situationRepresent it symbolicallyManipulate the representing symbolsAble to contextualize

Pause during manipulation processProbe the referents for symbols involved

Standard 2

: Reason abstractly and quantitatively.

What do mathematically proficient students do?

Slide9Construct argumentsAnalyze situationsJustify conclusions

Communicate conclusionsReason inductivelyDistinguish correct logic from flawed logicListen to/Read/Respond to other’s arguments and ask useful questions to clarify/improve arguments

Standard 3: Construct viable arguments and critique the reasoning of others.

What do mathematically proficient students do

?

Slide10Apply mathematics to solve problems from everyday life situationsApply what they know

Simplify a complicated situationIdentify important quantitiesMap math relationships using toolsAnalyze mathematical relationships to draw conclusionsReflect on improving the model

Standard 4: Model with mathematics.

What do mathematically proficient students do?

Slide11Consider and use available toolsMake sound decisions about when different tools might be helpfulIdentify relevant external mathematical resources

Use technological tools to explore and deepen conceptual understandings

Standard 5: Use appropriate tools strategically. What do mathematically proficient students do?

Slide12Communicate precisely to othersUse clear definitions in discussionsState meaning of symbols consistently and appropriately

Specify units of measurementsCalculate accurately & efficiently

Standard 6: Attend to precision.

What do mathematically proficient students do?

Slide13Discern patterns and structuresUse strategies to solve problemsStep back for an overview and can shift perspective

Standard 7

: Look for and make use of structure. What do mathematically proficient students do?

Slide14Notice if calculations are repeatedLook for general methods and shortcutsMaintain oversight of the processes

Attend to detailsContinually evaluates the reasonableness of their results

Standard 8: Look for and express regularity in repeated reasoning. What do mathematically proficient students do?

Slide15The Standards for [Student] Mathematical Practice

SMP1:

Explain and make conjectures…SMP2: Make sense of…SMP3:

Understand and use…

SMP4:

Apply and interpret…

SMP5:

Consider and detect…

SMP6:

Communicate precisely to others…

SMP7:

Discern and recognize…

SMP8:

Note and pay attention to…

Slide16CONNECTION and BALANCE

Slide17Slide18

Slide19

Draw Pattern 4 next to Pattern 3

.

See answer above.How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 15 buttons and 18 buttons

How many buttons in all does

Gita

need to make Pattern 11? Explain how you figured this out.

34 buttons

Gita

thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is NOT correct? How many buttons does she need to make Pattern 24?

73 buttons

Slide20Slide21

Slide22

Slide23

Analyzing the Button Task

The Button Task was:

Scaffolded

Foreshadows linear relationships

Requires critical thinking skills

Did not suggest specific strategy

Slide24www.insidemathematics.org

Slide25The Standards for [Student] Mathematical Practice

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein

, Smith,

Henningtsen

& Silver, 2000

“The level and kind of thinking in which students engage determines what they will learn.”

Herbert, Carpenter,

Fennema

,

Fuson

, Wearne, Murray, Oliver, & Human, 1997

Slide26But, WHAT TEACHERS DO with the tasks matters too!

The Mathematical Tasks Framework

Tasks as they appear in curricular materials

Tasks are set up by teachers

Tasks are enacted by teachers and students

Student Learning

Stein, Grover, &

Henningsen

(1996)

Smith & Stein (1998)

Stein, Smith,

Henningsen

, & Silver (2000)

Slide27Standards for [Student] Mathematical Practice

The Standards for Mathematical Practice place an emphasis on student demonstrations of learning…

Equity begins with an understanding of how the selection of tasks, the assessment of tasks, and how the student learning environment create inequity in our schools…

Slide28Leading with theMathematical Practice Standards

You can

begin

by implementing the 8 Standards for Mathematical Practice

now

Think about the relationships among the practices and how you can

move forward

to implement BEST PRACTICES

Analyze instructional tasks so students

engage

in these practices repeatedly

Slide29?? Questions ??

Slide30ALSDE Office of Student Learning

Curriculum and Instruction SectionCindy Freeman, Mathematics Specialist Phone: 334.353.5321

E-mail: cfreeman@alsde.eduContact Information

## The Standards for Mathematical Practice

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