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

1. Teaching Problem Solving
Derek Bruff / Vanderbilt University
@derekbruff / derekbruff.org

3. Adaptive
Expert
Routine
Expert
Novice
EFFICIENCY
INNOVATION
The goal!
Bransford et al. (2000)

4. 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?

5. 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

6. Misconception Questions
Adam List, Chemistry, Vanderbilt University

7. 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

8. Force Concept Inventory
Mazur & Crouch (2001)

9. Force Concept Inventory
Mazur & Crouch (2001)
70 70
78
86
0
100
Lectures (1990) Peer Instruction
(1993)
Pre-Test
Post-Test

10. Mental Models

11. Principle #1:
Students’ mental models shape how
they make sense of new information.

12. A Private Universe

13. “A Private University,” Harvard-Smithsonian Center for Astrophysics, 1987
A Private Universe

14. 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.

17. Alignment
Wiggins & McTighe (2005)

18. Principle #2:
How students organize their knowledge
affects their ability to solve problems.

20. Knowledge Organizations

22. Concept Maps
Jennifer Osterhage, Biology, University of Kentucky

25. Concept Maps
Jennifer Osterhage, Biology, University of Kentucky

26. Multi-Scale Concept Maps
Tamara Carley, Earth Science, Lafayette College

27. Pair-Share
• What “multi-scale” content do you have in
one of your courses? Identify at least three
scales.

28. Multi-Scale Concept Maps
Harrison Dreves, Vanderbilt University

29. Graphic Organizers

31. Signposts

32.  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

33.  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

34.  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

35.  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

36. Signposts for this workshop…

37. Principle #3:
Learning new concepts or skills requires
iterative practice and feedback.

39. “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

40. 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

42. The
Challenge
Generate
Ideas
Multiple
Perspectives
Research &
Revise
Test Your
Mettle
Go Public
Challenge Cycles
Cordray, Harris, & Klein (2009)

43. 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?

44. Case Studies

45. 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?

46. Formative Assessment
Angelo & Cross (1998)

47. Summative
Assessment
Walvoord & Anderson (2009)

48. Test Corrections

49. Principle #4:
Developing adaptive expertise requires
answering open-ended questions.

50. 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

51. 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

52. Be cautious using questions
that are too open-ended.

54. Application Projects

55. Poster Sessions

56. Analytic Rubrics

60. 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