July 26–30, 2014
79
Monday afternoon
PST1C03: 8:30-9:15 p.m. To Use or Not to Use Diagrams: The
Effect of Drawing a Diagram in Solving Introductory
Physics Problems
Poster – Alexandru Maries, University of Pittsburgh, 5813 Bartlett St., Pitts-
burgh, PA 15217;
Chandralekha Singh, University of Pittsburgh
Drawing appropriate diagrams is a useful problem solving heuristic that
can transform a given problem into a representation that is easier to exploit
for solving it. A major focus while helping introductory physics students
learn problem solving is to help them appreciate that drawing diagrams
facilitates problem solution. We conducted an investigation in which 111
students in an algebra-based introductory physics course were subjected
to two different interventions during recitation quizzes throughout the
semester. They were either (1) asked to solve problems in which the
diagrams were drawn for them or (2) explicitly told to draw a diagram. A
comparison group was not given any instruction regarding diagrams. We
developed a rubric to score the problem-solving performance of students
in different intervention groups. We investigated two problems involving
electric field and electric force and found that students who drew produc-
tive diagrams were more successful problem solvers and that a higher
level of relevant detail in a student’s diagram corresponded to a better
score. We also compared students’ facility in calculating electric field vs.
electric force and in calculating force on a point charge at a point efficiently
from the electric field computed at the same point both immediately after
instruction (quiz) and a few weeks after instruction (midterm). We found
that the student performance on electric field remains stagnant while the
performance on electric force improves significantly over time. Finally,
think-aloud interviews were conducted with nine students who were at
the time taking an equivalent introductory algebra-based physics course.
These interviews supported some of the interpretations for the quantita-
tive results, and were very useful in identifying some difficulties students
still exhibited after having learned the concepts of electric field and electric
force and after having been tested on it (in a midterm exam). The difficul-
ties identified and instructional implications are discussed.
*Work supported by the National Science Foundation
PST1C04: 9:15-10 p.m. Student Difficulties in Translating
Between Mathematical and Graphical Representations
in Electrostatics: Impact of Increasing Levels of
Scaffolding on Student Performance
Poster – Alexandru Maries, University of Pittsburgh, 5813 Bartlett, Pitts-
burgh, PA 15217;
Chandralekha Singh, University of Pittsburgh
Shih-Yin Lin Georgia, Institute of Technology
Prior research suggests that introductory physics students have difficulty
with graphing and interpreting graphs. In this paper, we investigate intro-
ductory physics students’ difficulties in translating between mathematical
and graphical representations and the effect of increasing levels of scaf-
folding on students’ performance. Ninety-five calculus-based introduc-
tory physics students were given a typical problem that can be solved
using Gauss’s law involving a spherically symmetric charge distribution (a
conducting sphere concentric with a conducting spherical shell) in which
they were asked to write a mathematical expression for the electric field in
various regions and then graph the electric field. Previous preliminary re-
search indicated that students have great difficulty in graphing the electric
field as a function of the distance from the center of the sphere consistent
with the mathematical expressions in various regions. Therefore, two scaf-
folding interventions with increasing levels of support were implemented
in order to help them. Students who received the scaffolding support were
either (1) asked to sketch the electric field in each region first (before hav-
ing to plot it as a function of distance from the center of the sphere) or (2)
asked to sketch the electric field in each region after explicitly evaluating
the electric field at the beginning, mid and end points of each region. The
comparison group was not given any scaffolding support and only asked
to plot the electric field in all regions at the end of the problem. Analysis
of student performance with different levels of scaffolding reveals that the
appropriate level of scaffolding is not necessarily the one that involves more
support (which is considered beneficial from an expert’s perspective) and
analyses. The chosen experiments are easy to perform in classroom and
allow students to contrast their knowledge of free-fall motion with vertical
motion at an acceleration greater than g, or no acceleration at all.
C – PER Posters
PST1C01: 8:30-9:15 p.m. A Good Diagram Is Valuable Despite
Choice of Mathematical Approach to Problem Solving*
Poster – Alexandru Maries, University of Pittsburgh, 5813 Bartlett St., Pitts-
burgh, PA 15217;
Chandralekha Singh, University of Pittsburgh
Drawing appropriate diagrams is a useful problem solving heuristic that
can transform a problem into a representation that is easier to exploit for
solving the problem. A major focus while helping introductory physics
students learn problem solving is to help them appreciate that drawing
diagrams facilitates problem solution. We conducted an investigation in
which 118 students in an algebra-based introductory physics course were
subjected to two different interventions during the problem solving in
recitation quizzes throughout the semester. Here, we discuss the problem
solving performance of students in different intervention groups for two
problems involving standing waves in tubes, one which was given in a quiz
and the other in a midterm exam. These problems can be solved using two
different methods, one involving a diagrammatic representation and the
other involving mostly mathematical manipulation of equations. In the
quiz, students were either (1) asked to solve the problem in which a partial
diagram was provided or (2) explicitly asked to draw a diagram. A com-
parison group was not given any instruction regarding diagrams. Students
in group (1), who were given the partial diagram, could not use that partial
diagram by itself to solve the problem. The partial diagram was simply
intended as a hint for students to complete the diagram and follow the
diagrammatic approach. However, we find an opposite effect, namely, that
students given this diagram were less likely to draw productive diagrams
and performed worse than students in the other groups. Moreover, we
find that students who drew a productive diagram performed better than
those who did not draw a productive diagram even if they primarily used
a mathematical approach. We also find that many introductory physics
students in algebra-based courses struggle with relatively simple algebraic
manipulations while solving physics problems but are capable of doing
equivalent algebra when the manipulations are stand-alone tasks not tied
to problem solving in physics.
*Work supported by the National Science Foundation
PST1C02: 9:15-10 p.m. Should Students be Provided Diagrams
or Asked to Draw Them While Solving Introductory
Physics Problems?
Poster – Alexandru Maries, University of Pittsburgh, 5813 Bartlett St., Pitts-
burgh, PA 15217;
Chandralekha Singh, University of Pittsburgh
Drawing appropriate diagrams is a useful problem0solving heuristic that
can transform a given problem into a representation that is easier to exploit
for solving it. A major focus while helping introductory physics students
learn problem solving is to help them understand that drawing diagrams
facilitates problem solution. We conducted an investigation in which 111
students in an algebra-based introductory physics course were subjected
to two different interventions during recitation quizzes throughout the
semester. They were either (1) asked to solve problems in which the
diagrams were drawn for them or (2) explicitly told to draw a diagram. A
comparison group was not given any instruction regarding diagrams. We
developed a rubric to score the problem-solving performance of students
in different intervention groups and found that students who were pro-
vided diagrams performed worse than the other students on two problems
in electricity which involve considerations of initial and final conditions.
We developed a hypothesis to explain why this counterintuitive result
occurred and conducted interviews with fourteen students to evaluate this
hypothesis. We found evidence which supports our hypothesis, which was
that students provided with diagrams spent less time on the conceptual
planning stage and sometimes jumped into the implementation stage
without fully understanding the problem.
*Work supported by the National Science Foundation
