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- 1. Intelligent Adaptive Learning: A Powerful Element for 21st Century Learning & Differentiation Tim Hudson, PhD Senior Director of Curriculum Design DreamBox Learning timh@dreambox.com @DocHudsonMath
- 2. Introduction • Senior Director of Curriculum Design for DreamBox Learning • Over 10 years in public education: o HS math teacher o K-12 Math Curriculum Coordinator o Strategic Planning Facilitator • Consulted for Authentic Education • PhD in Educational Leadership • Co-author of a chapter in NCTM book on Math Intervention Models: Reweaving the Tapestry (I get no royalties)
- 3. How can we leverage technology to improve student learning?
- 4. Which schedule is better? BLOCK • 8 courses/semester • 4 classes/day • Each course meets every other day • 90-minute periods TRADITIONAL • 8 courses/semester • 8 classes/day • Every course meets every day • 45-minute periods Scheduling is a means to what ends? What is happening during class?
- 5. Which blended model is better? FLIPPED-CLASSROOM ENRICHED-VIRTUAL Blending is a means to what ends? What is happening during class? What is happening on the computers? H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012
- 6. The Quality of Digital Learning Experiences is just as important as the Quality of Classroom Learning Experiences
- 7. Plan Schooling Backwards • “Contemporary school reform efforts… typically focus too much on various means: structures, schedules, programs, PD, curriculum, and instructional practices (like cooperative learning) • [or blended learning] • [or flipped learning] • [or iPads, hardware, etc] p. 234-235, Wiggins & McTighe, © 2007
- 8. Plan Schooling Backwards • Certainly such reforms serve as the fuel for the school improvement engine, but they must not be mistaken as the destination…[which is] improved learning.” p. 234-235, Wiggins & McTighe, © 2007
- 9. Plan Curriculum Backwards 1. Identify desired results 2. Determine acceptable evidence 3. Plan learning experiences and instruction Understanding by Design, Wiggins & McTighe, ©2005
- 10. Key Questions 1. What do you want students to accomplish? 2. How will you know they‟ve achieved it? 3. What technologies can help students meet goals?
- 11. Plan Schooling Backwards • “The first stage in the design process calls for clarity about priorities expressed as achievements.” • “…take time to clarify not just goals, but also the needed assessment evidence and initial data before [you] generate a detailed action plan [for blended learning, block scheduling, etc.].” p. 204, 227, Wiggins & McTighe, © 2007
- 12. Let‟s Take a Poll! Question #1: Have you ever used Wolfram Alpha? 12
- 13. Math Learning Goals
- 14. Wolfram|Alpha
- 15. Wolfram|Alpha
- 16. Wolfram|Alpha
- 17. Let‟s Take a Poll! Question #2: If computers can solve math problems so efficiently, why do we drill our students in answering them? 17
- 18. Better Goals for Students David Bressoud, Mathematical Association of America (www.maa.org/columns) Regarding Wolfram|Alpha: • “If computers can solve [math] problems so efficiently, why do we drill our students in answering them? • “There are important mathematical ideas behind these methods, and showing one knows how to solve these problems is one way of exhibiting working knowledge of these ideas.”
- 19. Better Goals for Students David Bressoud, (cont‟d) • “The existence of Wolfram|Alpha does push instructors to be more honest about their use of standard problems executed by memorizing algorithmic procedures. • “If a student feels that she or he has learned nothing that cannot be pulled directly from Wolfram|Alpha, then the course really has been a waste of time.”
- 20. New Teacher Induction What do you offer students in your classroom that they can‟t get online for free?
- 21. Pop Quiz • 3,998 + 4,247 = • 288 + 77 = • 8 + 7 = • What is a good strategy? • What is fluency? • How is fluency learned? • Can you get this from Wolfram|Alpha?
- 22. Compensation
- 23. Learning Principles • “An understanding is a learner realization about the power of an idea.” • “Understandings cannot be given; they have to be engineered so that learners see for themselves the power of an idea for making sense of things.” p. 113, Schooling by Design, Wiggins & McTighe, ©2007
- 24. What do you remember about math from when you were in middle & high school?
- 25. Common Experience From a 5th grade teacher in NY: “I had a lot of good people teaching me math when I was a student – earnest and funny and caring. But the math they taught me wasn‟t good math. Every class was the same for eight years: „Get out your homework, go over the homework, here‟s the new set of exercises, here‟s how to do them. Now get started. I‟ll be around.‟” p. 55, Teaching What Matters Most, Strong, Silver, & Perini, ©2001
- 26. Typical Teaching Cycle Whole Class or Small Group Instruction Guided Practice Whole Class Assessment Use Data Formatively to Plan Use Data Summatively
- 27. Teaching as Content Delivery Whole Class or Small Group Instruction Guided Practice Whole Class Assessment Use Data Formatively to Plan Use Data Summatively
- 28. Let‟s Take a Poll! Question #3: How old were you when you decided whether or not you were a "math person?" 28
- 29. Lichtenberg, 1749-99 “We accumulate our opinions at an age when our understanding is at its weakest.” At what age did you acquire your mental models of how math is taught and learned?
- 30. Transmission View of Learning 30
- 31. High school?
- 32. Thinking Mathematically “They were so concerned with making sure we knew how to do every single procedure we never learned how to think mathematically. I did well in math but I never understood what I was doing. I remember hundreds of procedures but not one single mathematical idea.” p. 55, Teaching What Matters Most, Strong, Silver, & Perini, ©2001
- 33. Let Me Show You How To Do X Now You Go Do X Can You Independently Do X? Maybe You Need to Be Shown X Again You Know X Schooling as Content Delivery
- 34. Let Me Show You How To Do X Now You Go Do X Can You Independently Do X? Maybe You Need to Be Shown X Again You Know X Content Delivery cannot „give understandings‟
- 35. Blended Learning Clarified H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012 “online delivery of content & instruction”
- 36. Time, Place, Path, Pace H. Staker, M. Horn, Classifying K-12 Blended Learning, © 2012 “Learning is no longer restricted to the pedagogy used by the teacher.” Learning IS restricted – and impacted by – the pedagogy used by the online teacher, in the online instruction, or in designs of the learning software.
- 37. Typical Cycle At School: Explicit Instruction & Problem Solving At Home: Practice Problems Whole Class Assessment Maybe You Need to Be Shown X Again Use Data Summatively
- 38. Flipping the classroom? At Home: Explicit Instructional Videos & Online Practice At School: Guided Practice & Problem Solving Whole Class Assessment Maybe You Need to Watch the Video Again Use Data Summatively
- 39. Pros & Cons Benefit of Blending & Flipping Becoming MORE thoughtful and strategic about the use of precious class time Danger of Blending & Flipping Becoming LESS thoughtful and strategic about how students learn and make sense of things
- 40. Transmission View of Learning 40 y = mx + b
- 41. Learning Myth “Presentation of an explanation, no matter how brilliantly worded, will not connect ideas unless students have had ample opportunities to wrestle with examples.” From Best Practices, 3rd Ed., by Zemelman, Daniels, and Hyde, ©2005 From Understanding by Design, Wiggins & McTighe, ©2005 “If I cover it clearly, they will „get it.‟”
- 42. Kid Snippets: “Math Class”
- 43. Don‟t Start by Telling “Providing students with opportunities to first grapple with specific information relevant to a topic has been shown to create a „time for telling‟ that enables them to learn much more from an organizing lecture.” • How People Learn, p. 58
- 44. Let‟s Take a Poll! Question #4: Are you currently working on differentiated instruction in your classroom, school, or district? 44
- 45. Differentiation Defined • Teachers have a responsibility to ensure that all of their students master important content. • Teachers have to make specific and continually evolving plans to connect each learner with key content. • Differences profoundly impact how students learn and the nature of scaffolding they will need at various points in the learning process. • Teachers should continually ask, “What does this student need at this moment in order to be able to progress with this key content, and what do I need to do to make that happen?” Leading and Managing a Differentiated Classroom by C.A. Tomlinson & M.B. Imbeau, ASCD, © 2010, pp. 13-14
- 46. Rethink Differentiation Our mental models of learning often cause us to differentiate in two wrong ways: 1. around knowledge, skills, and procedures rather than ideas, understanding, and complex performance 2. in response to student knowledge AFTER being shown a skill instead of in response to student thinking when solving an unfamiliar problem or at the point of conception formation.
- 47. Formative Assessment • What incorrect answers would we expect on a problem like 29 + 62? • 81 Student does not regroup to the tens place • 81 Student adds columns from left to right • 811 Student adds each column independently • 92 Arithmetic error in ones place • 33 Student believes this is a subtraction problem • How would you score each error? • How would you respond to each error? • What lesson(s) need to come before & after? • Which of these errors are “naturally occurring?”
- 48. Pop Quiz For a bicycle race, Donald’s time was: 3 hours, 4 minutes, and 11 seconds. Keina’s time was: 2 hours, 58 minutes, and 39 seconds. How long was Keina finished before Donald crossed the finish line?
- 49. Hours Minutes Seconds 3 4 11 2 58 39 3 X 71 61 3 2 6 3 5 1 50 2 304 – 298 = ? one strategy
- 50. Oxford University, 1992 “To the person without number sense, arithmetic is a bewildering territory in which any deviation from the known path may rapidly lead to being totally lost. The person with number sense…has, metaphorically, an effective „cognitive map‟ of that same territory.” Ann Dowker, Computational Estimation Strategies of Professional Mathematicians, Journal for Research in Mathematics Education, Vol. 23(1), January 1992
- 51. Constant Difference
- 52. Let‟s Take a Poll! Question #5: Did you learn the Constant Difference strategy for subtracting in elementary school? 52
- 53. How can we leverage technology to improve student learning?
- 54. DreamBox Pedagogical Design Student Engages within a Context Student Transfers & Predicts Student Receives Feedback Engine Adapts & Differentiates Student Independently Transfers
- 55. Engineered for Realizations Student Engages within a Context Student Transfers & Predicts Student Receives Feedback Engine Adapts & Differentiates Student Independently Transfers
- 56. Division with Remainders
- 57. Let‟s Take a Poll! Question #6: How many gumballs would you pack first? 57
- 58. Division with Remainders
- 59. Ma & Pa Kettle
- 60. 3rd Grade
- 61. 3rd Grade
- 62. 4th Grade
- 63. 4th Grade
- 64. A C B Continuous Embedded Assessment
- 65. Multiplying Fractions
- 66. Engaging Learning Experience with Context Individuals are Presented with Accessible Problems or Questions Individuals Make a Prediction, Answer the Problem, Take a Guess Individuals Receive Instant, Specific Feedback Based on their Prediction Data from that Prediction Informs the next Problem Presented or Question Posed Original, Independent, Strategic Thinking
- 67. Engaging Learning Experience with Context Self-Directed, Coherent, Connected Paths Individuals are Presented with Accessible Problems or Questions Individuals Make a Prediction, Answer the Problem, Take a Guess Individuals Receive Instant, Specific Feedback Based on their Prediction Data from that Prediction Informs the next Problem Presented or Question Posed
- 68. Seamless • DreamBox Lessons, Practice, & Assessments look identical to students • These are not banks of practice items. • Students need no prior instruction to engage in the lessons. Original, Independent Thinking Feedback, Realizations Practice or Assessment Feedback, Realizations New Problem or New Lesson
- 69. Assessments throughout the curriculum assess the skills taught in a unit Unit Pretest Lesson1 Lesson3 Lesson4 Lesson2 Lesson5 Students who demonstrate understanding of this concept skip the unit and move to a new skill assessment Lesson 3 Lesson 4 Lesson 1 Lesson 2 Lesson 5 Students who don‟t have these skills work through a unique sequence of lessons in the unit to learn those concepts Why is DreamBox so Effective? Integrated Assessment and Instruction
- 70. Primary Engagement Environment
- 71. Persevere: Build Optimally
- 72. Look for Structure: Quick Images
- 73. Intermediate Engagement Environment
- 74. Sequenced Challenges
- 75. Timely, Specific Feedback
- 76. Kindergarten Data Report
- 77. Student Reporting by Proficiency
- 78. DreamBox Combines Three Essential Elements to Accelerate Student Learning
- 79. Q & A timh@dreambox.com @DocHudsonMath www.dreambox.com

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