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

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.

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

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  1. 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

  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 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%

  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

  7. 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. A B 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. -Q -Q +Q d d 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

  11. 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

  12. What are possible relationships between the type of problem and how likely students will draw an FBD for it?

  13. 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. A 100–kg 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 100–kg 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 fireman’s 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 Example Problem

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