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Instructional Shifts and the Common Core Math Practices

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  1. Instructional Shifts and the Common Core Math Practices Ohio Middle Level Association State Conference February 20, 2014 Jean C. Richardson Math Specialist K-8 Mayfield City School District jrichardson@mayfieldschools.org 440-995-7879

  2. Goal of Presentation We will engage in a conversation about the importance of incorporating the eight mathematical practices into our pedagogy with the goal of developing mathematically proficient students.

  3. Turn and Talk After every segment of the presentation, you will be given a few minutes to turn and talk with a person sitting near you. The questions to discuss are on p. 2 and 3 of your packet. Be ready to turn back to these pages as the presentation continues. p. 2-3

  4. The Power of Imagination Ken Robinson, Ph.D. http://www.youtube.com/watch?v=ywtLnd3xOVU

  5. Common Core State Standards for Mathematics “In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures. A lack of mathematical competence keeps those doors closed. All students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding.” NCTM (2000, p.50)

  6. Shifts in Mathematics p. 4

  7. Shifts in Mathematics p. 4

  8. Shifts in Mathematics p. 4

  9. Learning Progressions: Fluency (Automaticity) p. 5

  10. Learning Progressions: Fluency (Automaticity) p. 5

  11. Shifts in Mathematics p. 4

  12. Shifts in Mathematics p. 4

  13. Shifts in Mathematics p. 4

  14. Common Core State Standards Mathematics Standards for Content

  15. Common Core State Standards Learning Goal: To examine the standards for Mathematical Practice Pre-Assessment p. 6-8

  16. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriatetoolsstrategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning. p. 9-11

  17. My Personal Learning Goal p. 12

  18. Standards for Mathematical Practice “The Standards for Mathematical Practicedescribe 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)

  19. Underlying Frameworks 5 Process Standards • Problem Solving • Reasoning and Proof • Communication • Connections • Representations

  20. Underlying Frameworks 5 Proficiency Standards • Conceptual Understanding • Procedural Fluency • Strategic Competence • Adaptive Reasoning • Productive Disposition

  21. Mathematical Proficiency Conceptual Understanding • comprehension of mathematical concepts, operations, and relations Procedural Fluency • skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic Competence • ability to formulate, represent, and solve mathematical problems Adaptive Reasoning • capacity for logical thought, reflection, explanation, and justification Productive Disposition • habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

  22. Six Components ofMathematics Classrooms • Creating an environment that offers all students an equal opportunity to learn • Focusing on a balance of conceptual understanding and procedural fluency • Ensuring active student engagement in the mathematical practices • Using technology to enhance understanding • Incorporating multiple assessments aligned with instructional goals and mathematical practices • Helping students recognize the power of sound reasoning and mathematical integrity

  23. Turn and Talk Individually review the Standards for Mathematical Practice revised in student language in your packet. Then discuss the following question with a partner: What implications might the Instructional Shifts and the Standards for Mathematical Practice have on the culture of your mathematics classroom?

  24. NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

  25. Problem Solving and Precision • Make sense of problems and persevere in solving them. • 6.Attend to precision.

  26. Problem Solving • Make sense of problems and persevere in solving them. • Mathematically proficient students: • understand the problem-solving process and how to navigate through the process from start to finish. • have a repertoire of strategies for solving problems and the ability to select a strategy that makes sense for a given problem. • have the disposition to deal with confusion and persevere until a problem is solved.

  27. Problem Solving • Make sense of problems and persevere in solving them. • I can make sense of math problems and keep trying even when problems are challenging.

  28. Problem-Based or Inquiry Approach When students explore a problem and the mathematical ideas are later connected to that experience. It is through inquiry that students are activating their own knowledge and trying to make new knowledge (meaning). This builds conceptual understanding.

  29. A Three-Part Format for Problem-Based Lessons

  30. Two Machines, One Job Ron's Recycle Shop started when Ron bought a used paper-shredding machine. Business was good, so Ron bought a new shredding machine. The old machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload in only 2 hours. How long will it take to shred a truckload of paper if Ron runs both shredders at the same time? p. 13

  31. Two Machines, One Job

  32. Making Sense = new problem

  33. Problem Solving from NCTM’s Principles and Standards for School Mathematics “Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings.” NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author. (p. 52)

  34. Problem Solving from NCTM’s Principles and Standards for School Mathematics “Students should have frequent opportunities to formulate, grapple with and solve complex problems that require a significant amount of effort and should be encouraged to reflect on their thinking.” NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author. (p. 52)

  35. Ignition Deep Practice Master Coaching Sweet Spot

  36. The Sweet Spot “There is a place, right on the edge of your ability, where you learn best and fastest. It’s called the sweet spot. Here’s how to find it.” D. Coyle, 2012

  37. Traditional vs. Rich Problems

  38. Give It a Try! Focus on the Question Dan Meyer http://www.101qs.com/ p. 14

  39. What’s the first question that comes to your mind?

  40. What’s the first question that comes to your mind?

  41. Open-Ended Questions to Promote Problem Solving Before – During - After p. 15

  42. Precision • 6.Attend to precision. • Mathematically proficient students: • calculate accurately and perform math tasks with precision. • communicate precisely.

  43. Precision • Attend to precision. • I am accurate when I compute and I am specific when I talk about math ideas.

  44. Give It a Try! Translate the Symbol Heads Up/Name That Category Test Analysis

  45. Give It a Try! Translate the Symbol

  46. Turn and Talk Discuss the following question with a partner: What opportunities do your students currently have to grapple with non-routine complex tasks and to reflect on their thinking and consolidate new mathematical ideas and problem solving solutions? Should a student’s ability to be precise in language and computation be calculated into a child’s grade? p. 2-3

  47. Reasoning and Explaining • 2.Reason abstractly and quantitatively. • 3.Construct viable arguments and critique the reasoning of others.

  48. Reasoning • 2.Reason abstractly and quantitatively. • Mathematically proficient students: • Represent quantities in a variety of ways. • Remove the problem context to solve the problem in an abstract way (equation). • Refer back to the problem context, when needed, to understand and evaluate the answer.