July 26–30, 2014

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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.

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

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