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Teaching Problem Solving

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Four principles for developing students as problem solvers in the STEM disciplines, a workshop presented at the King Fahd University of Petroleum and Minerals in Saudi Arabia, October 26, 2015

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Teaching Problem Solving

  1. 1. Teaching Problem Solving Derek Bruff / Vanderbilt University @derekbruff / derekbruff.org
  2. 2. Adaptive Expert Routine Expert Novice EFFICIENCY INNOVATION The goal! Bransford et al. (2000)
  3. 3. Think-Pair-Share Consider a course that you teach. • What is an example of a task that requires routine expertise? • What is an example of a task that requires adaptive expertise?
  4. 4. Misconception Questions Imagine holding two identical bricks under water. Brick A is just beneath the surface of the water, while Brick B is at a greater depth. The force needed to hold Brick B in place is… 1. Larger than 2. The same as 3. Smaller than the force required to hold Brick A in place. Eric Mazur, Physics, Harvard University
  5. 5. Misconception Questions Adam List, Chemistry, Vanderbilt University
  6. 6. Instructor Poses Question (<1 Min) Students Answer Independently (1-3 Min) Instructor Views Results (<1 Min) If Most Answer Correctly, Briefly Discuss Question (1-3 Min) If Most Answer Incorrectly, Backtrack (5+ Min) If Students Are Split, Have Students Discuss in Pairs and Revote (1-5 Min) Instructor Leads Classwide Discussion (2-15 Min) Peer Instruction
  7. 7. Force Concept Inventory Mazur & Crouch (2001)
  8. 8. Force Concept Inventory Mazur & Crouch (2001) 70 70 78 86 0 100 Lectures (1990) Peer Instruction (1993) Pre-Test Post-Test
  9. 9. Mental Models
  10. 10. Principle #1: Students’ mental models shape how they make sense of new information.
  11. 11. A Private Universe
  12. 12. “A Private University,” Harvard-Smithsonian Center for Astrophysics, 1987 A Private Universe
  13. 13. Writing Activity Consider a course you teach. • Identify a common student misconception that serves as a roadblock to learning. • Draft a multiple-choice question that might surface this misconception.
  14. 14. Alignment Wiggins & McTighe (2005)
  15. 15. Principle #2: How students organize their knowledge affects their ability to solve problems.
  16. 16. Knowledge Organizations
  17. 17. Concept Maps Jennifer Osterhage, Biology, University of Kentucky
  18. 18. Concept Maps Jennifer Osterhage, Biology, University of Kentucky
  19. 19. Multi-Scale Concept Maps Tamara Carley, Earth Science, Lafayette College
  20. 20. Pair-Share • What “multi-scale” content do you have in one of your courses? Identify at least three scales.
  21. 21. Multi-Scale Concept Maps Harrison Dreves, Vanderbilt University
  22. 22. Graphic Organizers
  23. 23. Signposts
  24. 24.  An Introduction  Is this manufacturing process out of control?  Central LimitTheorem  Understanding Confidence Intervals  Example: Baby birth weight  What CIs are not  Constructing Confidence Intervals  Formula  Checking the intuition  Special Cases
  25. 25.  An Introduction  Is this manufacturing process out of control?  Central LimitTheorem  Understanding Confidence Intervals  Example: Baby birth weight  What CIs are not  Constructing Confidence Intervals  Formula  Checking the intuition  Special Cases
  26. 26.  An Introduction  Is this manufacturing process out of control?  Central LimitTheorem  Understanding Confidence Intervals  Example: Baby birth weight  What CIs are not  Constructing Confidence Intervals  Formula  Checking the intuition  Special Cases
  27. 27.  An Introduction  Is this manufacturing process out of control?  Central LimitTheorem  Understanding Confidence Intervals  Example: Baby birth weight  What CIs are not  Constructing Confidence Intervals  Formula  Checking the intuition  Special Cases
  28. 28. Signposts for this workshop…
  29. 29. Principle #3: Learning new concepts or skills requires iterative practice and feedback.
  30. 30. “Active Learning Increases Student Performance in Science, Engineering, and Mathematics,” Scott Freeman et al., Proceedings of the National Academy of Sciences, 2014. Freeman et al. (2014) • 228 studies comparing active learning to traditional lecturing • Failure Rates: – Lecturing: 34% – Active Learning: 22% • Exam Scores: – Active Learning: 6 points higher
  31. 31. Instructor Poses Question (<1 Min) Students Answer Independently (1-3 Min) Instructor Views Results (<1 Min) If Most Answer Correctly, Briefly Discuss Question (1-3 Min) If Most Answer Incorrectly, Backtrack (5+ Min) If Students Are Split, Have Students Discuss in Pairs and Revote (1-5 Min) Instructor Leads Classwide Discussion (2-15 Min) Peer Instruction
  32. 32. The Challenge Generate Ideas Multiple Perspectives Research & Revise Test Your Mettle Go Public Challenge Cycles Cordray, Harris, & Klein (2009)
  33. 33. Generate Ideas • What kind of challenge might you give your students that would structure one or more class sessions? • What learning objectives would be aligned with this challenge? • What would be difficult about implementing this challenge during class?
  34. 34. Case Studies
  35. 35. Research & Revise • Visit http://sciencecases.lib.buffalo.edu/cs/ and identify a case study relevant to a course you teach. • How might you implement this case study as an in-class activity? What would be difficult about doing so?
  36. 36. Formative Assessment Angelo & Cross (1998)
  37. 37. Summative Assessment Walvoord & Anderson (2009)
  38. 38. Test Corrections
  39. 39. Principle #4: Developing adaptive expertise requires answering open-ended questions.
  40. 40. What is the most helpful radiologic study? A. Ultrasound B. Angiography C. Hepatobiliary Scan D. Sulfur colloid scan Stephanie Spottswood, • 17-year-old male • Pruritic foot rash • Severe joint pain • High fevers to 104°F • CT abdomen requested Critical Thinking Questions
  41. 41. Counterfactual Questions Rob MacDougall, History, Univ. of • If a Viking and a samurai fought, who would win? A. Viking B. Samurai • When and where would you rather have lived? A. 18th-century France B. 15th-century China C. 8th-century Ghana D. 1st-century Rome
  42. 42. Be cautious using questions that are too open-ended.
  43. 43. Application Projects
  44. 44. Poster Sessions
  45. 45. Analytic Rubrics
  46. 46. Derek Bruff @derekbruff / derekbruff.org derek.bruff@vanderbilt.edu Flickr (CC) Photo Credits • “Choices,” Derek Bruff • “No Ordinary Tourist,” Derek Bruff • “Look Right,” Derek Bruff • “Parallel to nowhere,” Daniel Kulinski • “Macro,” Derek Bruff • “Stop for Directions,” Derek Bruff • “Young Skateboarder,” Tony Alter • “Macbook X-Ray,” Jason de Villa • “It’s all for this moment,” Sebastian Mary • “up!”, Ryan Heaney • “Traction,” Derek Bruff

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