SOUTH DAKOTA SOUTH DAKOTA COUNTSCOUNTS

LEADERSHIP LEADERSHIP INSTITUTEINSTITUTE

Brookings, SD - 2012Brookings, SD - 2012

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ADDING IT UPStrands of Mathematical ProficiencyPresented by: Karen Taylor

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TODAY’S OBJECTIVESTODAY’S OBJECTIVES::Participants will:Participants will:•Have an increased understanding of Have an increased understanding of the five strands of mathematical the five strands of mathematical proficiency.proficiency.•Have an introduction to classroom Have an introduction to classroom applications of the five strands of applications of the five strands of mathematical proficiency.mathematical proficiency.•Have an increased understanding of Have an increased understanding of the research supporting inquiry-the research supporting inquiry-based mathematics in teaching and based mathematics in teaching and learninglearning

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““Adding It Up”Adding It Up”4

Connections to Common Core Connections to Common Core MathematicsMathematics

8 Standards of Mathematical 8 Standards of Mathematical PracticePractice

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

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

• The NCTM process standards The NCTM process standards (2000)(2000)

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

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Connections to Common Connections to Common CoreCore

CCSS – MathematicsTwo Types of StandardsTwo Types of Standards

Mathematical PracticeMathematical Practice (recurring throughout the grades)(recurring throughout the grades)

Mathematical ContentMathematical Content (this will be different at each (this will be different at each grade level)grade level)

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1.1. Make sense of problems and persevere in Make sense of problems and persevere in solving them.solving them.

2.2. Reason abstractly and quantitatively.Reason abstractly and quantitatively.3.3. Construct viable arguments and critique Construct viable arguments and critique

the reasoning of others.the reasoning of others.4.4. Model with mathematics.Model with mathematics.5.5. Use appropriate tools strategically.Use appropriate tools strategically.6.6. Attend to precision.Attend to precision.7.7. Look for and make use of structure.Look for and make use of structure.8.8. Look for and express regularity in repeated Look for and express regularity in repeated

reasoning.reasoning.

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8 Standards of 8 Standards of Mathematical PracticeMathematical Practice

Five Stands of Five Stands of Mathematical Mathematical

ProficiencyProficiency8

Making ConnectionsMaking Connections8 Standards of Mathematical

Practice5 Strands of Mathematical

Proficiency

Make sense of problems and Make sense of problems and persevere in solving thempersevere in solving them

Adaptive ReasoningAdaptive Reasoning

Reason abstractly and Reason abstractly and quantitativelyquantitatively

Strategic CompetenceStrategic Competence

Construct viable arguments Construct viable arguments and critique the reasoning of and critique the reasoning of othersothers

Conceptual UnderstandingConceptual Understanding

Model with mathematicsModel with mathematics Productive DispositionProductive Disposition

Use appropriate tools Use appropriate tools strategicallystrategically

Procedural FluencyProcedural Fluency

Attend to precisionAttend to precision

Look for and make use of Look for and make use of structurestructure

Look for and express Look for and express regularity in repeated regularity in repeated reasoningreasoning

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“ADDING IT UP” - GOALS1.1. Represent a synthesis of Represent a synthesis of

the research of the research of mathematical learning.mathematical learning.

2.2. Provide research-based Provide research-based recommendations for recommendations for improving student learning.improving student learning.

3.3. Provide advice and Provide advice and guidance guidance

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Group NormsGroup Norms

Private Think Time:Private Think Time:Locate the group norms in your Locate the group norms in your participant packet.participant packet.•Put a star by the norms that will be Put a star by the norms that will be easy for you to followeasy for you to follow•Circle the norms you may have Circle the norms you may have difficulty remembering to follow.difficulty remembering to follow.

Discussion:Discussion:•Turn and talk to a shoulder partner Turn and talk to a shoulder partner about the norms you circled. Discuss about the norms you circled. Discuss how you might support each other in how you might support each other in following the norms you circled.following the norms you circled.

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Agenda8:30Welcome and IntroductionsStrands of Mathematical ProficiencyMath Task – Cancelling Zeros

LunchMaking the CaseMath Task – Analyzing Student WorkMeaningful Practice

4:00 Closure

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UNDERSTANDING STRANDS UNDERSTANDING STRANDS OF MATHEMATICAL OF MATHEMATICAL

PROFICIENCYPROFICIENCYAssigned ReadingAssigned Reading• All Groups – Pgs. 115 – 118All Groups – Pgs. 115 – 118• Group 1: Group 1: Conceptual Understanding Conceptual Understanding – Pgs. 118 – 120– Pgs. 118 – 120• Group 2: Group 2: Procedural Fluency – Pgs. Procedural Fluency – Pgs. 121 – 124121 – 124• Group 3: Group 3: Strategic Competence – Strategic Competence – Pgs. 124 – 129Pgs. 124 – 129•Group 4: Group 4: Adaptive Reasoning – Pgs. Adaptive Reasoning – Pgs. 129 – 131129 – 131• Group 5: Group 5: Productive Disposition – Productive Disposition – Pgs. 131 - 133Pgs. 131 - 133

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GROUP WORK•Read assigned pages Read assigned pages individually.individually.

•Create a Frayer Model that will Create a Frayer Model that will describe your strand to the describe your strand to the large group.large group.

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REFLECTION REFLECTION QUESTIONSQUESTIONS

•What questions do you still What questions do you still have about the five strands of have about the five strands of mathematical proficiency?mathematical proficiency?

•How will you increase your How will you increase your understanding?understanding?

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CANCELING ZEROS CANCELING ZEROS MATH TASK MATH TASK

GROUP WORKGROUP WORK•Work individually for 5 minutes.Work individually for 5 minutes.•Share strategies with your Share strategies with your group.group.•Decide how to illustrate the Decide how to illustrate the strategies.strategies.•Record the solution and thinking Record the solution and thinking on chart paper.on chart paper.•Share your solution.Share your solution.

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CLASSROOM CLASSROOM EXAMPLEEXAMPLE

Record evidence that Record evidence that students are developing students are developing

the five strands of the five strands of mathematical mathematical

proficiencyproficiency

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EVIDENCE OF 5 STRANDS FOREVIDENCE OF 5 STRANDS FORCANCELING ZEROS – CLASSROOM CANCELING ZEROS – CLASSROOM

EXAMPLEEXAMPLE

• Return to Stand GroupReturn to Stand Group• Watch video and record Watch video and record

evidence evidence for your strandfor your strand• Discuss with Strand GroupDiscuss with Strand Group

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Mixed Group Discussion

Using Group Number Cards, Locate a Mixed Using Group Number Cards, Locate a Mixed Group representing 1 – 5 strands.Group representing 1 – 5 strands.

Share your strand with others in the group.Share your strand with others in the group.

Debrief Questions with Mixed Groups:Debrief Questions with Mixed Groups: For which strands was there a lot of evidence?For which strands was there a lot of evidence? Which strand were lacking evidence and why?Which strand were lacking evidence and why? What are the implications for your professional What are the implications for your professional

practice?practice?

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LUNCHLUNCH

Teaching is one of the Teaching is one of the most complex human most complex human

endeavors imaginable.endeavors imaginable. - Saphier and Glover

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WATERMELONS AND WATERMELONS AND CANTALOUPESCANTALOUPES•Work the problem independently.Work the problem independently.

•Share your solution with your Share your solution with your group.group.

•Record all solutions on chart Record all solutions on chart paper.paper.

•Be prepared to share your Be prepared to share your solutions with the large group.solutions with the large group.

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INQUIRY-BASED INQUIRY-BASED MATHEMATICSMATHEMATICS

Individually read what the experts Individually read what the experts have to say: Pgs. 15 – 21. have to say: Pgs. 15 – 21.

Think about these questions as you Think about these questions as you read:read:•What implications for teaching and What implications for teaching and learning were alluded to in the learning were alluded to in the reading?reading?•What questions did the reading raise What questions did the reading raise for you?for you?

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PYRAMID PARTNERS PYRAMID PARTNERS PROCESSPROCESS

• Find a “new” partnerFind a “new” partner

• Decide who will be person Decide who will be person A and who will be person A and who will be person BB

• Begin the discussion Begin the discussion when the facilitator when the facilitator indicatesindicates

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PYRAMID PARTNERS DISCUSSIONPYRAMID PARTNERS DISCUSSIONQUESTION ONEQUESTION ONE

• Person B responds to question Person B responds to question one for 15 seconds.one for 15 seconds.

• Person A responds to person B Person A responds to person B for 30 seconds.for 30 seconds.

• Person B responds to person A Person B responds to person A for 45 seconds.for 45 seconds.

• Person A has 60 seconds for a Person A has 60 seconds for a final response.final response.

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PYRAMID PARTNERS DISCUSSIONPYRAMID PARTNERS DISCUSSIONQUESTION TWOQUESTION TWO

•Person A responds to question Person A responds to question two for 15 seconds.two for 15 seconds.•Person B responds to person A Person B responds to person A for 30 seconds.for 30 seconds.•Person A responds to person B Person A responds to person B for 45 seconds.for 45 seconds.•Person B has 60 seconds for a Person B has 60 seconds for a final response.final response.

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LUCKY DRAW• Work in pairs to write a report Work in pairs to write a report that includes your that includes your recommendation to the recommendation to the committee and explains how committee and explains how you came to your conclusion.you came to your conclusion.

•Be prepared to share your Be prepared to share your thinking with the large group.thinking with the large group.

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ANALYZING STUDENT ANALYZING STUDENT WORKWORK•Work in groups at your table.Work in groups at your table.•Look for evidence of student Look for evidence of student progress in each of the five progress in each of the five strands of mathematical strands of mathematical proficiency.proficiency.•Look for evidence of ability to Look for evidence of ability to justify and communicate justify and communicate mathematical reasoning.mathematical reasoning.•Be prepared to share your Be prepared to share your thinking with the large group.thinking with the large group.

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MEANINGFUL PRACTICE

What about basic facts?What about basic facts?• Basic facts are still important.Basic facts are still important.• Practice should be engaging Practice should be engaging

and motivating.and motivating.• Efficiency is more important Efficiency is more important

than speed.than speed.• Mathematics is about sense-Mathematics is about sense-

making.making.

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Questions About Basic Questions About Basic FactsFacts

Number off 1 – 6 and read your Number off 1 – 6 and read your topic. topic. Be ready to share Be ready to share highlights with the group.highlights with the group.1.1.What about basic facts? p. 16What about basic facts? p. 16

2.2.Isn’t speed important in doing math? p. 17Isn’t speed important in doing math? p. 17

3.3.Being in this kind of math program… p. 18Being in this kind of math program… p. 18

4.4.A teacher told me kids don’t… p. 19A teacher told me kids don’t… p. 19

5.5.We can do this kind of math…..p. 21We can do this kind of math…..p. 21

6.6.Teachers have told me that they love….p. 22Teachers have told me that they love….p. 22

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MEANINGFUL MEANINGFUL PRACTICEPRACTICEHow Many Rows? How Many in How Many Rows? How Many in

Each Row?Each Row?• Play with a partner at your Play with a partner at your

table.table.• Continue to play until you Continue to play until you

run out of room on your run out of room on your game board.game board.

• Count the number of Count the number of squares you covered by your squares you covered by your rectangles.rectangles.

• The person with the most The person with the most squares covered wins.squares covered wins.

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THANK YOU FOR THANK YOU FOR PARTICIPATING TODAYPARTICIPATING TODAY

ktaylor@tie.netktaylor@tie.net

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