framing, epistemology, and all that jazz: why it matters

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 A A P T P H I L A D E L P H I A 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 illusion

July 30, 2012 A A P T P H I L A D E L P H I A 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.

July 30, 2012 A A P T P H I L A D E L P H I A 4

Tversky and Kahneman (1983) Psychological Review 90 (4): 293–315. DOI:10.1037/0033-295X.90.4.293.

Implications of Experiment 1 •  Most people (typically up to 85%!)

choose answer B. •  One-step reasoning / “fast thinking”

July 30, 2012 A A P T P H I L A D E L P H I A 5

Bank teller Feminist

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 how confident we are of the result.

July 30, 2012 6

Experiment 2: Count the passes

A A P T P H I L A D E L P H I A

Simons & Chabris (1999) Perception. 28:9, 1059-1074.

How many passes did you see?

A.   14 or fewer B.  15 C.   16 D.  17 or more

7 July 30, 2012 A A P T P H I L A D E L P H I A

How many gorillas did you see?

A.   None! (You’re kidding, right?)

B.  One C.   More than one

8 July 30, 2012 A A P T P H I L A D E L P H I A

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

9 July 30, 2012 A A P T P H I L A D E L P H I A

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 A A P T P H I L A D E L P H I A 10

Experiment 3: Which line is longer on the paper you have been given? (Ignore the arrowheads)

A A P T P H I L A D E L P H I A 11

A.  Line (a) B.  Line (b) C.  they are the same length

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 A A P T P H I L A D E L P H I A 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?

13 July 30, 2012 A A P T P H I L A D E L P H I A

* The “scare quotes” are because these processes are often not conscious.

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 A A P T P H I L A D E L P H I A 14

Tutorials

July 30, 2012 A A P T P H I L A D E L P H I A 15

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).

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 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 17

The result

B. Frank, PhD Dissertation, U. of Maryland, 2010 July 30, 2012 A A P T P H I L A D E L P H I A 18

A few minutes later

July 30, 2012 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 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 and the other is in state orthogonal to , calculate , assuming that (a) they are distinguishable particles, (b) they are identical bosons, and (c) they are identical fermions.

6/9/08 G R C B RYA N T U , R I 22

D. Griffiths, Introduction to Quantum Mechanics, prob. 5.5

! n

! m

! n

x1 ! x2( )2

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

or more explicitly They turned to Mathematica to do so.

6/9/08 G R C B RYA N T U , R I 23

x12! n (x1)

2dx1"

2L

x 2 sin2 n!xL

" #

$ % dx&

T.J. Bing and E. F. Redish, Am. J. Phys. 76, 418-424 (2008).

One student takes the lead •  Over about 10 minutes, she attempts to

evaluates the integral

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 A A P T P H I L A D E L P H I A 24

x2 sin2 xdx!"

"

#

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 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 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 A A P T P H I L A D E L P H I A 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!”)

July 30, 2012 A A P T P H I L A D E L P H I A 29

“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] 

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 A A P T P H I L A D E L P H I A 30