How a Problem

1
How a Problems 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
2
Summary of Previous Findings

• If we teach students to solve problems using
  FBDs, do they use FBDs to solve problems?
• YES
• 846 problems (58) with
• 619 problems (42) without

42 w/o
58 With
3
Summary of Previous Findings

• Are those who use FBDs 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

4
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.

5
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 problem.
• However
• What features of a problem could influence a
  student to construct an FBD?

6
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
• ISLE emphasizes MULTIPLE REPRESENTATIONS and
  incorporates them in concept construction and
  problem solving
• Active Learning Guide
• Model solutions for the homework
• Multiple Representation tasks in Recitation

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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
Earth
8
Sample and Data SourcesQuantitative Study

• Sample
• 125 Students randomly selected (25) Year 1
• 120 Students randomly selected (29) Year 2
• Source
• 2 Midterms, 1 Final per semester
• 5 Multiple-choice problems Year 1
• 7 Multiple-choice problems Year 2
• no credit for diagrams!

9
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
• b 0.78 s
• c 0.88 s
• d 0.49 s
• e 0.63 s

10
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
• c -3kQ2/4d2
• d -5kQ2/4d2
• e None of the other answers

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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 elevators speed
  is decreasing?
• a 16,000 N
• b 14,000 N
• c 10,000 N
• d 6000 N
• e 4000 N

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What are possible relationships between the type
of problem and how likely students will draw an
FBD for it?
Category of FBD Drawn of Quest. Conceptual Area Average Success Rate Problem asks for a Force Picture Present
Low lt50 4 2 Mechanics 2 Electro. 52.75 2 No 2 Yes 2 with 2 w/o
Medium 50-60 3 1 Mechanics 2 Electro. 65.7 1 No 2 Yes 2 with 1 w/o
High gt60 5 4 Mechanics 1 Electro. 63.8 0 No 5 Yes 0 with 5 w/o
Pearson Correlation for Low Med High groupings Pearson Correlation for Low Med High groupings Pearson Correlation for Low Med High groupings Pearson Correlation for Low Med High groupings Pearson Correlation for Low Med High groupings
Comparison Conceptual Area Success Rate Force Picture Present
Pearson -.278 .395 .502 -.479
Significance .382 .204 .096 .116
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Discussion

• 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

14
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.

15
Example Problem

• A 100kg fireman starts at rest and slides down
  a vertical pole with a constant downward
  acceleration of 4.0 m/s2. The magnitude of the
  friction force that the pole exerts on the
  fireman is closest to
• a) 1000 N
• b) 1400 N
• c) 400 N
• d) 1600 N
• e) 600 N

• A 100kg fireman starts at rest and slides down
  a vertical pole. The magnitude of the upward
  friction force that the pole exerts on the
  fireman is 600 N. What is the magnitude of the
  firemans downward acceleration?
• a) 15.0 m/s2
• b) 9.80 m/s2
• c) 3.00 m/s2
• d) 6.00 m/s2
• e) 4.00 m/s2