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

2. 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 research
July 30, 2012 AAPT PHILADELPHIA 2

3. 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 illusion
July 30, 2012 AAPT PHILADELPHIA 3

4. 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

5. 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 with
July 30, 2012 how confident we are of the result. AAPT PHILADELPHIA 5

6. Experiment 2: Count the passes
Simons & Chabris (1999) Perception. 28:9, 1059-1074.
July 30, 2012 AAPT PHILADELPHIA 6

7. How many passes
did you see?
A. 14 or fewer
B. 15
C. 16
D. 17 or more
July 30, 2012 A A P T P H I L A D E L P H I7
A

8. How many gorillas
did you see?
A. None!
(You’re kidding, right?)
B. One
C. More than one
July 30, 2012 A A P T P H I L A D E L P H I8
A

9. How many players were on the court
at the end of the video?
A. More than 6
B. 6
C. 5
D. 4 or fewer
July 30, 2012 A A P T P H I L A D E L P H I9
A

10. 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

11. Experiment 3: Which line is longer
on the paper you have been given?
(Ignore the arrowheads)
A. Line (a)
B. Line (b)
C. they are the same length
AAPT PHILADELPHIA 11

12. 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

13. 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 these
July 30, 2012 processes are often not conscious. A A P T PHILADELPHIA 13

14. 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

15. Tutorials
L. 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

16. 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

17. 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

18. The result
B. Frank, PhD Dissertation, U. of Maryland, 2010
July 30, 2012 AAPT PHILADELPHIA 18

19. A few minutes later
July 30, 2012 AAPT PHILADELPHIA 19

20. 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

21. 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

22. 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. 5.5
6/9/08 G R C B R YA N T U , R I 22

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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