Framing, Epistemology, and all that Jazz: Why it Matters


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Invited talk at AAPT National Meeting, Philadelphia, PA, July 2012

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Framing, Epistemology, and all that Jazz: Why it Matters

  1. 1. Outline •  What can we learn from psychology that can help us understand our students? •  Examples and anecdotes •  So what? Implications   For teaching / affect-epist impl on e-c-r   For researchJuly 30, 2012 AAPT PHILADELPHIA 2
  2. 2. Psychology •  One-step thinking – fast thinking and slow   Experiment 1: Linda the bank teller •  Selective attention – framing   Experiment 2: The basketball illusion •  Expectations   Experiment 3: The Lyell-Muller illusionJuly 30, 2012 AAPT PHILADELPHIA 3
  3. 3. Experiment 1: Which is more likely?•  Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.•  Which is more probable? A.  Linda is a bank teller. B.  Linda is a bank teller and is active in the feminist movement. Tversky and Kahneman (1983) Psychological Review 90 (4): 293–315. DOI:10.1037/0033-295X.90.4.293.July 30, 2012 AAPT PHILADELPHIA 4
  4. 4. Implications of Experiment 1 •  Most people (typically up to 85%!) choose answer B. •  One-step reasoning / “fast thinking” Bank Feminist teller Kahnemann argues that most of our thinking is “fast” – not carefully considered or reasoned out. We tend to choose answers quickly and by seeing what comes to mind most easily and quickly – how naturally a plausible story can be generated. The speed and ease of generating the response is associated withJuly 30, 2012 how confident we are of the result. AAPT PHILADELPHIA 5
  5. 5. Experiment 2: Count the passes Simons & Chabris (1999) Perception. 28:9, 1059-1074.July 30, 2012 AAPT PHILADELPHIA 6
  6. 6. How many passes did you see? A.  14 or fewer B.  15 C.  16 D.  17 or moreJuly 30, 2012 A A P T P H I L A D E L P H I7 A
  7. 7. How many gorillas did you see? A.  None! (You’re kidding, right?) B.  One C.  More than oneJuly 30, 2012 A A P T P H I L A D E L P H I8 A
  8. 8. How many players were on the court at the end of the video? A.  More than 6 B.  6 C.  5 D.  4 or fewerJuly 30, 2012 A A P T P H I L A D E L P H I9 A
  9. 9. Implications of Experiment 2 •  Typically, more than half of the observers will not see the gorilla.   For those who do, in the version shown, most will not notice that the curtain has changed color or that one of the players on the black team left the court when the gorilla appeared. •  Demonstrates the power of selective attention.   What you think is relevant plays a large role in what you notice.   “I wouldn’t have seen it if I hadn’t believed it.”July 30, 2012 AAPT PHILADELPHIA 10
  10. 10. Experiment 3: Which line is longeron the paper you have been given?(Ignore the arrowheads) A.  Line (a) B.  Line (b) C.  they are the same length AAPT PHILADELPHIA 11
  11. 11. Implications of Experiment 3 •  When I did this in a class of ~200, 70% said they were the same length.   After they were asked to compare with their neighbors, it dropped to 45%.   I heard some discussions where students said, “Oh, don’t bother. I know this one. They’re the same.” •  Their expectation about what was happening was so strong, that many of them weren’t even able to consider the possibility that something else might be going on.July 30, 2012 AAPT PHILADELPHIA 12
  12. 12. Key concepts •  Framing – “What’s going on here?”*   “choosing” a subset of data to pay attention to   “deciding” what to do about it   “deciding” what can be safely ignored. •  Epistemology – Knowledge about knowledge: both global and local   What is the nature of the knowledge I am going to learn in this class and what is it that I need to do to learn it?   What of the knowledge that I have is appropriate to use in a particular problem or situation? * The “scare quotes” are because theseJuly 30, 2012 processes are often not conscious. A A P T PHILADELPHIA 13
  13. 13. Example 1: Tutorials in Intro Physics•  Tutorials are research-based lessons done in small groups.•  Students are guided through expressing their own ideas, comparing them with observations and reasoning qualitatively.•  Students are often challenged by questions that activate common misconception: “elicit / confront / resolve.”•  The critical component of the environment is independent small group discussion, lightly facilitated by an instructor. July 30, 2012 AAPT PHILADELPHIA 14
  14. 14. TutorialsL. C. McDermott, et al., Tutorials In Introductory Physics (Prentice Hall, 1998)M. Wittmann, R. Steinberg, E. Redish, Activity-Based Tutorials (Wiley, 2003)A. Elby et al., Open Source Tutorials (UMd, 2008). July 30, 2012 AAPT PHILADELPHIA 15
  15. 15. The context •  In our first tutorial of the year, students are asked to analyze speed. •  Paper tapes are made beforehand by a machine tapping at regular intervals (6 times/sec). A cart attached to the tape slowly accelerates down a long ramp.July 30, 2012 AAPT PHILADELPHIA 16
  16. 16. The task•  The TA describes the equipment and how it works.•  Then each group of students is given 4 tapes containing 6 dots and asked “Which tape took the longest time to make?”July 30, 2012 AAPT PHILADELPHIA 17
  17. 17. The result B. Frank, PhD Dissertation, U. of Maryland, 2010July 30, 2012 AAPT PHILADELPHIA 18
  18. 18. A few minutes laterJuly 30, 2012 AAPT PHILADELPHIA 19
  19. 19. Implication: Epistemological Framing •  In their first look, the students activated a common primitive element – “more is more”. They framed the task as appropriate for “fast thinking”: one-step-answer-making; that the result could be found directly and did not require considering the mechanism of the process carefully. •  Later, in a new context, they reframed the task as physical sense-making; one that required “slow thinking” carefully about the mechanism.July 30, 2012 AAPT PHILADELPHIA 20
  20. 20. A Misconception?•  This looks like a misconception –   Brought into the class   Commonly held   Quickly and naturally generated.•  I am happy to refer to such an error as a misconception. But...•  Despite looking simple it has a structure.   It depends on what the students think they are doing.   Sometimes, these are robust and hard to undo;   But sometimes, they are created on the spot and are context dependent. In the case here it is a framing error.July 30, 2012 AAPT PHILADELPHIA 21
  21. 21. Example 2: Upper division problem solving •  Imagine two non-interacting particles, each of mass m, in the infinite square well. If one is in the state ! n and the other is in state ! m orthogonal to ! n, calculate ( x ! x ) , assuming that 1 2 2 (a) they are distinguishable particles, (b) they are identical bosons, and (c) they are identical fermions. D. Griffiths, Introduction to Quantum Mechanics, prob. 5.56/9/08 G R C B R YA N T U , R I 22
  22. 22. Student response •  We observed a group of 6 students working on this problem. At some point, someone realized they had to evaluate integrals of the form "x 2 2 1 ! n (x1 ) dx1 or more explicitly 2 2 2 " n!x $ L & x sin # L % dx They turned to Mathematica to do so. T.J. Bing and E. F. Redish, Am. J. Phys. 76, 418-424 (2008).6/9/08 G R C B R YA N T U , R I 23
  23. 23. One student takes the lead •  Over about 10 minutes, she attempts to evaluates the integral " # x 2 sin 2 x dx !" in a variety of ways:   Using Mathematica   With her programmable calculator   By hand after integrating by parts, doing the indefinite integral and plugging in the limits and convinces herself the result is ∞.July 30, 2012 AAPT PHILADELPHIA 24
  24. 24. She has done a lot of good work, but..•  She has framed the task as a purely mathematical one solvable with symbolic analysis alone (no graphs).•  As a result, she has not noticed that she is doing the wrong integral. July 30, 2012 AAPT PHILADELPHIA 25
  25. 25. The resolution S3: Hey, it’s not negative infinity to infinity. S1: What is it? S3: Is it? Well, we just have to integrate it over the square well, ‘cause it’s the infinite square well. S2: Oh yeah, so it’s zero to [L]. S1: (chuckling) You’re right. S3: Yeah, that’s why it’s not working. ... 38. S5: Oh. We’re awesome. (sarcasm)July 30, 2012 AAPT PHILADELPHIA 26
  26. 26. Implication: Epistemological Framing •  In their first look, the students framed the task as appropriate for calculation: algorithmically following a set of established computational steps should lead to a trustable result. •  Later, they reframed the task as physical mapping; one that required blending their physical knowledge with the setting up of the mathematical model.July 30, 2012 AAPT PHILADELPHIA 27
  27. 27. Broadening our instructional goals•  We not only want our students to learn concepts and processes, we want them to learn appropriate epistemological framing –  How to recognize what are the appropriate tools and concepts to bring to a task  How to blend conceptually different tools to create a coherent and powerful approach.   In example 1: mathematical concepts (the idea of velocity) with physical mechanism (understanding how the machine works)   In example 2: mathematical manipulations (calculation) with physical modeling.July 30, 2012 AAPT PHILADELPHIA 28
  28. 28. Instructional implications •  We have to be careful not to have our conceptual instruction undermine our epistemological goals. •  If “elicit-confront-resolve” is not implemented carefully, it can result in   students rejecting their own intuitions (“Whatever I think is always wrong in physics class.”)   students becoming hostile (“I’ll give them their answer on the test, but they’ll never convince me that that’s right!”)“Why having a theory of learning changes what I do in class on Monday”, E. F. Redish[2010, invited talk, Workshop for New Phys and Astron. Fac., Reunion Meeting] July 30, 2012 AAPT PHILADELPHIA 29
  29. 29. The take away message•  Students bring a lot of knowledge into our classes.   Some of it is misinterpretations and misgeneralizations of their physical everyday experience – “common misconceptions”.•  But they also bring epistemological expectations– assumptions about what they will be learning and what they have to do to learn it.   If we assume every common error is a “misconception” we may miss what is really going on and not respond appropriately. July 30, 2012 AAPT PHILADELPHIA 30