Presented by Sara Delano Moore , Ph.D . Director of Mathematics and Science at ETA hand2mind

1. Visual Models in Math: Connecting Concepts with Procedures Overview Tuesday, January 6, 2015 Presented by Sara Delano Moore, Ph.D. Director of Mathematics and Science at ETA hand2mind Join our community on edWeb.net Implementing Common Core Standards in Math www.edweb.net/math

2. Join our community on edWeb.net Implementing Common Core Standards in Math • Invitations to upcoming webinars • Webinar recordings and resources • CE quizzes • Online discussions Join the community www.edweb.net/math

3. Starting in February our community’s name will be changing to • Don’t worry, we will continue to feature great webinars and engaging conversations. Thank you for all your support over the years. We greatly appreciate it.

4. Recognition for your participation today! Attending Live? Your CE Certificate will be emailed to you within 24 hours. Viewing the Recording? Join the community at www.edweb.net/math Go to the Webinar Archives folder Take the CE Quiz to get a personalized CE Certificate CE Certificate provided by

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6. Visual Models in Math: Connecting Concepts with Procedures January 6, 2014: Overview Session Sara Delano Moore, Ph.D. Director of Mathematics & Science ETA hand2mind

7. Visual Models in Math:Series Overview • January 6: Connecting Concepts with Procedures Overview • February 3: Connecting Concepts with Procedures for Whole Number & Decimal Addition & Subtraction • March 3: Connecting Concepts with Procedures for Fraction Addition & Subtraction • April 7: Connecting Concepts with Procedures for Whole Number & Decimal Multiplication & Division • May 5: Connecting Concepts with Procedures for Fraction Multiplication & Division

8. From Principles to Actions In short, we must move from “pockets of excellence” to “systemic excellence” by providing mathematics education that supports the learning of all students at the highest possible level.

9. Realities we need to address • Too much focus on learning procedures without any connection to meaning, understanding, or the applications that require these procedures. • Too many students are limited by the lower expectations and narrower curricula of remedial tracks from which few ever emerge. • Too many teachers have limited access to the instructional materials, tools, and technology that they need. • Too much weight is placed on results from assessments – particularly large-scale, high-stakes assessments – that emphasize skills and fact recall and fail to give sufficient attention to problem solving and reasoning. • Too many teachers of mathematics remain professionally isolated, without the benefits of collaborative structures and coaching, and with inadequate opportunities for professional development related to mathematics teaching and learning. PtA, page 3

10. Mathematics Teaching Practices • Establish mathematics goals to focus learning • Implement tasks that promote reasoning and problem solving • Use and connect mathematical representations • Facilitate meaningful mathematical discourse • Pose purposeful questions • Build procedural fluency from conceptual understanding • Support productive struggle in learning mathematics • Elicit and use evidence of student thinking PtA, page 10

11. Beliefs about teaching and learning mathematics Unproductive Beliefs Productive Beliefs Mathematics learning should focus on developing understanding of concepts and procedures through problem solving, reasoning, and discourse. All students need to have a range of strategies and approaches from which to choose in solving problems, including, but not limited to, general methods, standard algorithms, and procedures. Students can learn mathematics through exploring and solving contextual and mathematical problems. • Mathematics learning should focus on practicing procedures and memorizing basic number combinations. • Students need only to learn and use the same standard computational algorithms and the same prescribed methods to solve algebraic problems. • Students can learn to apply mathematics only after they have mastered the basic skills. PtA, page 11

12. Beliefs about teaching and learning mathematics Unproductive Beliefs Productive Beliefs The role of the teacher is to engage students in tasks that promote reasoning and problem solving and facilitate discourse that moves students toward shared understanding of mathematics. The role of the student is to be actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and considering the reasoning of others. An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics. • The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems. • The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests. • An effective teacher makes the mathematics easy for students by guiding them step-by-step through problem solving to ensure that they are not frustrated or confused. PtA, page 11

13. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. PtA, page 42

14. Being fluent means that students are able to choose flexibly among methods and strategies to solve contextual and mathematical problems, they understand and are able to explain their approaches, and they are able to produce accurate answers efficiently. PtA, page 42

15. Progression to Fluency Add/subtract within 20, multiply/divide within 100 PtA, page 43

16. Teacher and Student Actions What are teachers doing? What are students doing? Making sure that they understand and can explain the mathematical basis for the procedures that they are using. Demonstrating flexible use of strategies and methods while reflecting on which procedures seem to work best for specific types of problems. Determining whether specific approaches generalize to a broad class of problems. Striving to use procedures appropriately and efficiently. • Providing students with opportunities to use their own reasoning strategies and methods for solving problems. • Asking students to discuss and explain why the procedures they are using work to solve particular problems. • Connecting student-generated strategies and methods to more efficient procedures as appropriate. • Using visual models to support students understanding of general methods. • Providing students with opportunities for distributed practice of procedures. PtA pp 47-48

17. Why are manipulatives and visual models the right tools?

18. NCSM Position Statement …in order to develop every student’s mathematical proficiency, leaders and teachers must systematically integrate the use of concrete and virtual manipulatives into classroom instruction at all grade levels.

19. Research Summary

20. Hands-On Learning Instructional Cycle Concrete Representational Abstract

21. Impact on Student Performance

22. An example with whole number multiplication

23. Visual Models in Math:Series Overview • January 6: Connecting Concepts with Procedures Overview • February 3: Connecting Concepts with Procedures for Whole Number & Decimal Addition & Subtraction • March 3: Connecting Concepts with Procedures for Fraction Addition & Subtraction • April 7: Connecting Concepts with Procedures for Whole Number & Decimal Multiplication & Division • May 5: Connecting Concepts with Procedures for Fraction Multiplication & Division

25. Join our community on edWeb.net Implementing Common Core Standards in Math • Invitations to upcoming webinars • Webinar recordings and resources • CE quizzes • Online discussions Join the community www.edweb.net/math

26. Starting in February our community’s name will be changing to • Don’t worry, we will continue to feature great webinars and engaging conversations. Thank you for all your support over the years. We greatly appreciate it.

27. Recognition for your participation today! Attending Live? Your CE Certificate will be emailed to you within 24 hours. Viewing the Recording? Join the community at www.edweb.net/math Go to the Webinar Archives folder Take the CE Quiz to get a personalized CE Certificate CE Certificate provided by

28. Join us for the next webinar Tuesday, February 3rd - 4PM Eastern Time Visual Models in Math: Connecting Concepts with Procedures for Whole Number & Decimal Addition and Subtraction For an invitation to the next webinar Join Implementing Common Core Standards in Mathwww.edweb.net/math

29. Thank you! www.hand2mind.com