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Building Understanding in Math

Building Understanding in Math. Through Backwards Design and Differentiation. Objective. Use a backwards design process to create a math unit that Contains goals for transfer, meaning and acquisition Purposefully addresses a 21 st century skill Includes a performance assessment task

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Building Understanding in Math

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  1. Building Understanding in Math Through Backwards Design and Differentiation

  2. Objective • Use a backwards design process to create a math unit that • Contains goals for transfer, meaning and acquisition • Purposefully addresses a 21st century skill • Includes a performance assessment task • Offers a differentiation plan

  3. Process • September 6: • Stage 1 (Learning Goals) • Stage 2 (Evidence –Performance Task) • On your own –for ½ credit (Sign up on SPOT) • Complete Stage 2 – Other Evidence (Assessments) • October 7: • Stage 3: The Learning Plan • Formative Assessments • Differentiation Plan • On your own – Continued • Complete Unit • Assure alignment between Goals, Evidence, and Learning Plan • Spring Semester – Teach the Unit

  4. What is Understanding? • It’s Probably Understanding if it… From Grant Wiggins & Jay McTigheUnderstanding by Design

  5. It’s probably understanding if it… • Raises additional questions or paths of thought within the discipline • Example: There are similarities and differences between length and time. From Grant Wiggins & Jay McTigheUnderstanding by Design

  6. It’s probably understanding if it… • Can be understood on a continuum, something that kindergarteners through graduate students could study, albeit at different levels of sophistication • Example: Parts of a system are interrelated. • Non-example: A system has more than one part From Grant Wiggins & Jay McTigheUnderstanding by Design

  7. It’s probably understanding if it… • Can be stated as “I want students to understand THAT…” rather than “I want students to understand • Example in math? • Standards! • Standard 1 – THAT At their most basic level, numbers are abstract symbols that represent real world qualities From Grant Wiggins & Jay McTigheUnderstanding by Design

  8. It’s probably understanding if it… • Is a pithy statement that reveals a truth about the study or practice of the discipline. • Example: Math is in all things. From Grant Wiggins & Jay McTigheUnderstanding by Design

  9. It’s probably understanding if it… • Involves multiple layers or multiple meanings • Example: Changing the grouping or the order of addends or factors does not change a sum or product • Non-Example: 2 + 3 = 3 + 2

  10. It’s probably understanding if it… • Is an idea that is especially powerful in understanding the discipline and across topics in the discipline. • Number patterns are based on operations and relationships. (Standard2, Concept 1 5th grade) From Grant Wiggins & Jay McTigheUnderstanding by Design

  11. It’s probably understanding if it… • Provides a purpose for the discipline, the reason for studying the discipline, and why the discipline is valuable. • Computational fluency with fractions is necessary for daily life. From Grant Wiggins & Jay McTigheUnderstanding by Design

  12. Enduring Understandings & Transfer • Group Work: • Look at curriculum mapping work from the A.M. Choose one to address. Write an enduring understanding and transfer

  13. Enduring Understandings & Transfer I want students to understand that _____________________ so that in the long run, without assistance, they can __________________________________. Your Wiki FoothillsUBDPD.pbworks.com 15 Minutes – Then Share Out

  14. Share • What Standard/Gap are you addressing? • What is the Enduring Understanding/Transfer?

  15. Essential Questions Jamie McKenzie: “Most essential questionsareinterdisciplinary in nature. They cut across the lines created by schools and scholars to mark the terrain of departments and disciplines.” “From Trivial Pursuit to Essential Questions” - http://www.fno.org/feb01/pl.html

  16. Essential Questions Jamie McKenzie: “Essential questions probe the deepest issues confronting us . . . complex and baffling matters which elude simple answers: Life - Death - Marriage - Identity - Purpose - Betrayal - Honor - Integrity - Courage - Temptation - Faith - Leadership - Addiction - Invention - Inspiration.” “From Trivial Pursuit to Essential Questions” - http://www.fno.org/feb01/pl.html

  17. Intel Teaching Thinking With Technology Overview: Module 3: Creating Curriculum-Framing Questions to Support Thinking Skills

  18. Ranking Questions • With your group, use the Intel Visual Ranking Tool to rank questions according to their potential for generating deeper thinking in the classroom • Open Visual Ranking: www.intel.com/education/visualranking • Log in with your team ID and password • Click Ranking Questions • Rank questions: • Rank questions • Add comments

  19. Login Information • Teacher ID: nwhite@d20.co.edu • User Name FHE01, FHE02, FHE03, FHE04, FHE05, FHE06, FHE07 • Password: The same

  20. Ranking Questions Step 2: Discuss Your Ranking • Discuss significant variations in rankings • Discuss your ranking experience – what you think of this tool

  21. Asking Questions in the Classroom Understanding Open and Closed Questions • Closed questions • Test factual knowledge • Contain limited range of correct responses • Open questions • Build upon factual knowledge • Promote higher-order thinking Reflecting on Questions Used in Your Classroom • Reflect on the questions used in a typical day in your classroom

  22. Curriculum-Framing Questions Defining Curriculum-Framing Questions • Essential Questions • Are overarching, foundational “big idea” questions • Can help focus several units • Can be used over the course of a year • Example: • What does it take to change the world? • Where can we find order and patterns?

  23. Curriculum-Framing Questions Unit Questions • Are unit-specific, open-ended questions • Help build understanding for the Essential Question • Example: • Why leave one’s home to make a new life in a strange land? • What patterns are repeated in large and small numbers?

  24. Curriculum-Framing Questions Content Questions • Are supporting, fact-based questions • Are categorized as closed questions • Help strengthen and develop students’ understanding of larger questions • Examples: • What route did the early explorer’s take? • What were the explorers looking for? • Why does 1/10 = .1?

  25. Meaning Goals Group Work • Write Your Goals for Meaning-Making: • Understandings • Essential Questions that will help lead to the understandings Your Wiki FoothillsUBDPD.pbworks.com 15 Minutes

  26. Learning Goals for 21st Century Skills

  27. Acquisition Goals: Group Work • Pick ONE 21st Century Skill that you will focus on to model, teach, and assess • Identify the math skills, identified in the curriculum or standards, that students will demonstrate. Your Wiki FoothillsUBDPD.pbworks.com 15 Minutes

  28. Break

  29. Stand Up & Vote! • If you agree with the statement, LEFT side of room • If you disagree with statement, RIGHT side of room • If you are somewhere in the middle –go to the middle! • CHALLENGE! Can you persuade middle-of-the-room folks to join your side?

  30. Issues in Mathematics Teaching • There needs to be a stronger emphasis on the automaticity of math in elementary school.

  31. Issues in Mathematics Teaching • Offering rewards and incentives will help motivate students to try harder at math.

  32. Issues in Mathematics Teaching • The ultimate goal for mathematics is independent and creative problem solving.

  33. Stage 2: Evidence How will you know that they know it?

  34. Performance tasks in math GRASPS method • G – Real World Goal • R – Real World Role • A – Real World Audience • S – Real World Situation • P- Real-world Products or Performances • S – Standards and Criteria Indicators From Grant Wiggins & Jay McTigheUnderstanding by Design

  35. G – Real World Goal • Household budget, travel budget • Building a garden – purchasing the right amount of soil, edging, etc. • What is fair?

  36. R – Real World Role • Head of household, travel agent • Homeowner, landscaper • Teacher

  37. A – Real World Audience • Local travel agent, parents, a younger grade • Readers of publication – blog – wiki - newspaper • School board • Community

  38. S – Real World Situation • Capture their imagination! • Write a clever introduction or story to set the scene.

  39. P – Real World Products or Performances • Travel brochure • Budget spreadsheet for college student • Build a real garden for the school or as a community service project • Letter to the editor

  40. S – Standards & Criteria Indicators • Model a finished product –good and not-so-good –for the students. Allow them to critique. • Consider student input in creating the criteria from this experience

  41. Group Work: Performance Task • Brainstorm and use the GRASPS method to determine what your performance assessment task will be. • Make sure it aligns with your Learning Goals Your Wiki FoothillsUBDPD.pbworks.com 15 Minutes

  42. Share • As teams share, check for alignment between Learning Goals and the Performance Task • Will the performance task demonstrate understanding? Does it require transfer, meaning-making and acquisition of skills?

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