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					     How a Problem’s Context
      Influences Students to
          Construct FBDs*

David Rosengrant,
Eugenia Etkina, Alan Van Heuvelen
Rutgers, The State University of New Jersey

AAPT 2006, Syracuse, New York
* Supported in part by NSF grants DUE 0241078, DUE 0336713
Summary of Previous Findings
If we teach students to solve problems
using FBDs, do they use FBDs to solve
    846 problems (58%) with
    619 problems (42%) without

                42% w/o

                          58% With
 Summary of Previous Findings
Are those who use FBD’s more successful?
– YES – Average success rate of 12 questions:
  Correct FBD       85%      FBD Needs Improvement 71%
  FBD is Inadequate 38%      No Evidence of an FBD 49%
  Success Rate      60%
                                     Correct FBD
                                     FBD Needs
      60                             Improvement
      50                             FBD is
      40                             inadequate
      30                             No Evidence of
      20                             an FBD
      10                             Average
                                     Success Rate
           Average of 12 Questions
Summary of Previous Findings
Why do students use free-body diagrams
to help them solve problems?
– High achieving students used representations to
    clarify problem situation
    evaluate other representations
    evaluate the answer
– Low achieving students used them because their
  instructor used them.
         Research Questions
Previous research has shown that if we create an
  environment where the instructor models the
  use of FBDs in problem solving then students
  will construct FBDs and those who construct a
  correct FBD are more successful in solving the


What features of a problem could influence a
 student to construct an FBD?
            Course Format
Algebra-based Physics course, 500 students/year.
Two 55-min large-room meetings, one 55-min recitation
and one 3-h laboratory per week.
Used Investigative Science Learning Environment ISLE
(Etkina & Van Heuvelen, 2001).
 – Inquiry-based learning system
   and incorporates them in concept construction and
   problem solving
 – Active Learning Guide
 – Model solutions for the homework
 – Multiple Representation tasks in Recitation
               Free body diagrams (FBD)
You are riding to the top floor of your residence hall. As the
elevator approaches your floor, it slows to a stop. Construct
an FBD for the cable car [with you inside] as the object of
interest as the car slows down to a stop.
       Cable            FCableon Car
                                             v        
                                            
                                             v       v
      Earth             FEarthon Car
 Sample and Data Sources
    Quantitative Study
– 125 Students randomly selected (25%) Year 1
– 120 Students randomly selected (29%) Year 2
– 2 Midterms, 1 Final per semester
– 5 Multiple-choice problems Year 1
– 7 Multiple-choice problems Year 2
– no credit for diagrams!
         An Example Problem
Difficult, Picture Present, Mechanics
   Block A of mass 6.0 kg rests on a smooth table
   and is connected by a string that passes over
   an ideal pulley to block B of 4.0 kg. Block B is
   released from rest. Which answer below is
   closest to the time interval that block A, initially
   at rest, needs to travel 0.80 m?
   a 0.40 s                   A

   b 0.78 s
   c 0.88 s
   d 0.49 s
   e 0.63 s
         An Example Problem
Difficult, Picture Present, Mechanics
 The three charged metal balls each have charge
 of magnitude Q but of different sign, as shown.
 The positive direction is toward the right. Which
 expression below is the net electric force exerted
 on the right charged ball.
 a +3kQ2/4d2
 b +5kQ2/4d2                     +Q   -Q   -Q

 c -3kQ2/4d2                        d    d

 d -5kQ2/4d2
 e None of the other answers
      An Example Problem
 No Picture Present, Mechanics,
    Problem asks for a Force
A 1000-kg elevator moving down at 4.0 m/s
slows to a stop in 2.0 m. Which answer below is
closest to the magnitude of the force exerted by
the cable on the elevator as the elevator’s speed
is decreasing?
a 16,000 N
b 14,000 N
c 10,000 N
d 6000 N
e 4000 N
  What are possible relationships between the type of
  problem and how likely students will draw an FBD for it?
    Category      # of    Conceptual        Average     Problem      Picture
[% of FBD Drawn] Quest.     Area            Success    asks for a    Present
                                             Rate        Force

      Low           4     2 Mechanics       52.75%       2 No         2 with
     [<50%]                 2 Electro.                   2 Yes        2 w/o

    Medium          3     1 Mechanics        65.7%       1 No         2 with
    [50-60%]                2 Electro.                   2 Yes        1 w/o

      High          5     4 Mechanics        63.8%       0 No         0 with
     [>60%]                 1 Electro.                   5 Yes        5 w/o

          Pearson Correlation for Low Med High groupings
          Comparison Conceptual Success Force              Picture
                     Area       Rate                       Present
          Pearson       -.278        .395       .502       -.479
          Significance .382          .204       .096       .116
What are possible relationships between the
type of problem and how likely a student will
draw an FBD for it?
– We found 2 key factors
   Positive - Problem asks for a magnitude of force
   Negative - Pictorial representation of the
   problem situation is provided to the students
            Future Work
In the fall we will conduct a study where
we will create isomorphic problems to give
to the same class. Half of the students will
receive one problem, half of the students
will receive the other.
                Example Problem
A 100–kg fireman starts at rest   A 100–kg fireman starts at rest
and slides down a vertical pole   and slides down a vertical
with a constant downward          pole. The magnitude of the
acceleration of 4.0 m/s2. The     upward friction force that the
magnitude of the friction force   pole exerts on the fireman is
that the pole exerts on the       600 N. What is the magnitude
fireman is closest to:            of the fireman’s downward

a)   1000 N                       a)   15.0 m/s2
b)   1400 N                       b)   9.80 m/s2
c)   400 N                        c)   3.00 m/s2
d)   1600 N                       d)   6.00 m/s2
e)   600 N                        e)   4.00 m/s2