1. SOUTH DAKOTA COUNTS LEADERSHIP INSTITUTE Brookings, SD - 2012 1

2. ADDING IT UP Strands of Mathematical Proficiency Presented by: Karen Taylor 2

3. TODAY’S OBJECTIVES : Participants will: Have an increased understanding of the five strands of mathematical proficiency. Have an increased understanding of the five strands of mathematical proficiency. Have an introduction to classroom applications of the five strands of mathematical proficiency. Have an introduction to classroom applications of the five strands of mathematical proficiency. Have an increased understanding of the research supporting inquiry-based mathematics in teaching and learning Have an increased understanding of the research supporting inquiry-based mathematics in teaching and learning 3

4. “Adding It Up” 4

5. Connections to Common Core Mathematics 8 Standards of Mathematical Practice “These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” “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 NCTM process standards (2000) The National Research Council’s report Adding It Up (2001) The National Research Council’s report Adding It Up (2001) 5

6. Connections to Common Core CCSS – Mathematics Two Types of Standards Mathematical Practice Mathematical Practice (recurring throughout the grades) (recurring throughout the grades) Mathematical Content Mathematical Content (this will be different at each grade level) (this will be different at each grade level) 6

7. 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. 7 8 Standards of Mathematical Practice

8. Five Stands of Mathematical Proficiency 8

9. Making Connections 8 Standards of Mathematical Practice5 Strands of Mathematical Proficiency Make sense of problems and persevere in solving them Adaptive Reasoning Reason abstractly and quantitatively Strategic Competence Construct viable arguments and critique the reasoning of others Conceptual Understanding Model with mathematics Productive Disposition Use appropriate tools strategically Procedural Fluency Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning 9

10. “ADDING IT UP” - GOALS 1. Represent a synthesis of the research of mathematical learning. 2. Provide research-based recommendations for improving student learning. 3. Provide advice and guidance 10

11. Group Norms Private Think Time: Locate the group norms in your participant packet. Put a star by the norms that will be easy for you to follow Put a star by the norms that will be easy for you to follow Circle the norms you may have difficulty remembering to follow. Circle the norms you may have difficulty remembering to follow.Discussion: Turn and talk to a shoulder partner about the norms you circled. Discuss how you might support each other in following the norms you circled. Turn and talk to a shoulder partner about the norms you circled. Discuss how you might support each other in following the norms you circled. 11

12. Agenda 8:30  Welcome and Introductions  Strands of Mathematical Proficiency  Math Task – Cancelling Zeros Lunch  Making the Case  Math Task – Analyzing Student Work  Meaningful Practice 4:00 Closure 12

13. UNDERSTANDING STRANDS OF MATHEMATICAL PROFICIENCY Assigned Reading All Groups – Pgs. 115 – 118 All Groups – Pgs. 115 – 118 Group 1: Conceptual Understanding – Pgs. 118 – 120 Group 1: Conceptual Understanding – Pgs. 118 – 120 Group 2: Procedural Fluency – Pgs. 121 – 124 Group 2: Procedural Fluency – Pgs. 121 – 124 Group 3: Strategic Competence – Pgs. 124 – 129 Group 3: Strategic Competence – Pgs. 124 – 129 Group 4: Adaptive Reasoning – Pgs. 129 – 131 Group 4: Adaptive Reasoning – Pgs. 129 – 131 Group 5: Productive Disposition – Pgs. 131 - 133 Group 5: Productive Disposition – Pgs. 131 - 133 13

14. GROUP WORK Read assigned pages individually. Read assigned pages individually. Create a Frayer Model that will describe your strand to the large group. Create a Frayer Model that will describe your strand to the large group. 14

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16. REFLECTION QUESTIONS What questions do you still have about the five strands of mathematical proficiency? What questions do you still have about the five strands of mathematical proficiency? How will you increase your understanding? How will you increase your understanding? 16

17. Break 17

18. CANCELING ZEROS MATH TASK GROUP WORK Work individually for 5 minutes. Work individually for 5 minutes. Share strategies with your group. Share strategies with your group. Decide how to illustrate the strategies. Decide how to illustrate the strategies. Record the solution and thinking on chart paper. Record the solution and thinking on chart paper. Share your solution. Share your solution. 18

19. CLASSROOM EXAMPLE Record evidence that students are developing the five strands of mathematical proficiency 19

20. EVIDENCE OF 5 STRANDS FOR CANCELING ZEROS – CLASSROOM EXAMPLE Return to Stand Group Return to Stand Group Watch video and record evidence for your strand Watch video and record evidence for your strand Discuss with Strand Group Discuss with Strand Group 20

21. Mixed Group Discussion  Using Group Number Cards, Locate a Mixed Group representing 1 – 5 strands.  Share your strand with others in the group.  Debrief Questions with Mixed Groups:  For which strands was there a lot of evidence?  Which strand were lacking evidence and why?  What are the implications for your professional practice? 21

22. LUNCH Teaching is one of the most complex human endeavors imaginable. - Saphier and Glover 22

23. WATERMELONS AND CANTALOUPES Work the problem independently. Work the problem independently. Share your solution with your group. Share your solution with your group. Record all solutions on chart paper. Record all solutions on chart paper. Be prepared to share your solutions with the large group. Be prepared to share your solutions with the large group. 23

24. INQUIRY-BASED MATHEMATICS Individually read what the experts have to say: Pgs. 15 – 21. Think about these questions as you read: What implications for teaching and learning were alluded to in the reading? What implications for teaching and learning were alluded to in the reading? What questions did the reading raise for you? What questions did the reading raise for you? 24

25. PYRAMID PARTNERS PROCESS Find a “new” partner Find a “new” partner Decide who will be person A and who will be person B Decide who will be person A and who will be person B Begin the discussion when the facilitator indicates Begin the discussion when the facilitator indicates 25

26. PYRAMID PARTNERS DISCUSSION QUESTION ONE Person B responds to question one for 15 seconds. Person B responds to question one for 15 seconds. Person A responds to person B for 30 seconds. Person A responds to person B for 30 seconds. Person B responds to person A for 45 seconds. Person B responds to person A for 45 seconds. Person A has 60 seconds for a final response. Person A has 60 seconds for a final response. 26

27. PYRAMID PARTNERS DISCUSSION QUESTION TWO Person A responds to question two for 15 seconds. Person A responds to question two for 15 seconds. Person B responds to person A for 30 seconds. Person B responds to person A for 30 seconds. Person A responds to person B for 45 seconds. Person A responds to person B for 45 seconds. Person B has 60 seconds for a final response. Person B has 60 seconds for a final response. 27

28. LUCKY DRAW Work in pairs to write a report that includes your recommendation to the committee and explains how you came to your conclusion. Work in pairs to write a report that includes your recommendation to the committee and explains how you came to your conclusion. Be prepared to share your thinking with the large group. Be prepared to share your thinking with the large group. 28

29. ANALYZING STUDENT WORK Work in groups at your table. Work in groups at your table. Look for evidence of student progress in each of the five strands of mathematical proficiency. Look for evidence of student progress in each of the five strands of mathematical proficiency. Look for evidence of ability to justify and communicate mathematical reasoning. Look for evidence of ability to justify and communicate mathematical reasoning. Be prepared to share your thinking with the large group. Be prepared to share your thinking with the large group. 29

30. Break 30

31. MEANINGFUL PRACTICE What about basic facts? Basic facts are still important. Basic facts are still important. Practice should be engaging and motivating. Practice should be engaging and motivating. Efficiency is more important than speed. Efficiency is more important than speed. Mathematics is about sense-making. Mathematics is about sense-making. 31

32. Questions About Basic Facts Number off 1 – 6 and read your topic. Be ready to share highlights with the group. 1. What about basic facts? p. 16 2. Isn’t speed important in doing math? p. 17 3. Being in this kind of math program… p. 18 4. A teacher told me kids don’t… p. 19 5. We can do this kind of math…..p. 21 6. Teachers have told me that they love….p. 22 32

33. MEANINGFUL PRACTICE How Many Rows? How Many in Each Row? Play with a partner at your table. Play with a partner at your table. Continue to play until you run out of room on your game board. Continue to play until you run out of room on your game board. Count the number of squares you covered by your rectangles. Count the number of squares you covered by your rectangles. The person with the most squares covered wins. The person with the most squares covered wins. 33

34. THANK YOU FOR PARTICIPATING TODAY ktaylor@tie.net 34