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## The Standards for Mathematical Practice

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Slide1

The Standards for

Mathematical Practice

2010

Alabama Course of Study: Mathematics

Slide2

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)

Slide3

Underlying 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

Slide4

Underlying Frameworks

Strands of

Mathematical Proficiency

NRC (2001).

Conceptual Understanding

Procedural Fluency

Strategic Competence

Productive Disposition

National Research Council

Slide5

Standard 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:

Slide6

1. What student behaviors are included in this standard?

2. What type of activities could help my students develop this behavior?

Adapted from Kathy Berry, Monroe County ISD, Michigan

Questions to consider…

Slide7

What 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…

Slide8

Analyze 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?

Slide9

Make 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?

Slide10

Construct 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

?

Slide11

Apply 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?

Slide12

Consider 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?

Slide13

Communicate 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?

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Discern 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?

Slide15

Notice 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?

Slide16

The 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…

Slide17

CONNECTION and BALANCE

Slide18

www.insidemathematics.org

This task gives students the chance to: Find relationships between graphs,

equations, tables, and rules. Explain reasoning for answers.

Slide19

Sorting Functions

Slide20

Sorting Functions

Slide21

www.insidemathematics.org

Slide22

Algebra – 2008

Slide23

Making connections between different algebraic representations: graphs, equations, verbal rules, and tablesUnderstanding how the equation determines the shape of the graphDeveloping a convincing argument using a variety of algebraic conceptsBeing able to move from specific solutions to thinking about generalizations

Slide24

Standard 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:

Slide25

Student B

Student A

Slide26

The 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,

Henningsen

, & 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

Slide27

But, WHAT TEACHERS DO with the tasks matters too!

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)

Slide28

Standards 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 the student learning environment create inequity in our schools…

Slide29

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

engage

in these practices repeatedly

Slide30

?? Questions ??

Slide31

Contact Information

ALSDE Office of Student LearningCurriculum and Instruction Cindy Freeman, Mathematics Specialist

Phone: 334.353.5321 E-mail: cfreeman@alsde.edu

Slide32