aapt_program_final_sm13 - page 100

Tuesday afternoon
ways that math as it is taught in math classes is different from math as it
is used in introductory physics classes. In this talk I will describe some of
these differences.
*This work is supported by NSF DUE-1045227, NSF DUE-1045231, NSF DUE-
4:20-4:30 p.m. Discourse Analysis of Students’ Use of
Mathematical Idioms in Physics*
Contributed – Ying Chen, Kansas State University, 116 Cardwell Hall,
Manhattan, KS 66506-2601;
Eleanor C. Sayre, Kansas State University
As students develop their physics identity, their ability to successfully
understand the relationship between mathematics and physics plays an
integral role. What are their expectations about how mathematics should
be done in physics classes? How do they understand typical idiomatic ex-
pressions such as “far away” or “blows up”? In this talk, these questions will
be discussed using observational video-based data of upper-division phys-
ics students using micro-genetic analysis of discourse. Starting with how
students become aware of mathematical idioms and use them in problem
solving and sense-making, this analysis will give insight into how students
understand mathematics in physics using mathematical idioms as a lens.
*This material is based upon work supported by the National Science Foundation
under Grant No. 1240782.
4:30-4:40 p.m. Understanding External Representations
as Computational Tools
Contributed – Elizabeth Gire, University of Memphis, 421 Manning Hall,
Memphis, TN 38152;
Edward Price, California State University, San Marcos
In physics, external representations (like graphs or free-body diagrams)
are used to document and communicate information about a physical situ-
ation, and also as tools for computation. An important instructional goal
is to teach students to solve problems using physical representations. Yet,
while experts use representations fluently and productively, novices often
struggle to interpret them and may not value their utility. In addressing
this, we use conceptual blending theory and distributed cognition to gain
insight into how meaning and computational power arise from the mate-
rial and conceptual features of representations. In this talk, we apply these
ideas to understanding how students create and use external representa-
tions for solving problems. In particular, we discuss how conflicts among
material and conceptual elements of representations may lead students to
misuse or misunderstand external representations, and how looking for
such conflicts may help to identify potential areas of student difficulties.
4:40-4:50 p.m. Student Difficulties in Translating
between Mathematical and Graphical Representations
Contributed – Alexandru Maries, University of Pittsburgh, 5813 Bartlett St.,
Pittsburgh, PA 15217;
Shih-Yin Lin, Chandralekha Singh, University of Pittsburgh
We investigate introductory physics students’ difficulties in translating
between mathematical and graphical representations and the effect of
scaffolding on students’ performance. We gave a typical problem that can
be solved using Gauss’s law to 96 calculus-based introductory physics
students. Students were asked to write an expression for the electric field
in various regions and graph it. We implemented two scaffolding inter-
ventions to help them: (1) students were asked to draw the electric field in
each region first (before having to plot it at the end) or (2) asked to draw
the electric field in each region and asked to evaluate the electric field at
the beginning, mid and end points of each region. The comparison group
was only asked to plot the electric field at the end of the problem. We also
conducted interviews in order to better understand how the interventions
impacted them. We will present some surprising results.
4:50-5 p.m. Student Interpretation of Multi-Variable
Expressions: Transfer Between Different Contexts
Contributed – Mila Kryjevskaia, North Dakota State University, Department
of Physics, PO Box 6050, Fargo, ND 58108-6050; mila.kryjevskaia@ndsu.
Student reasoning difficulties with applying and interpreting multi-
variable expressions have been reported previously. In the context of a
math course, for example, it may be appropriate to reason that, for the
given relationship
y = x/a,
increases, y must also increase; in such
cases, it is commonly assumed that variables (e.g.,
) and constants
(e.g., positive a) have been clearly established. However, a direct mapping
of the same reasoning in the context of physics (namely, for the given
f= v
, if the propagation speed
increases, frequency f must
also increase) leads to an erroneous conclusion. In this investigation we
are probing the impact of targeted instruction on student ability to apply
multi-variable expressions and to transfer their knowledge and skills
between different contexts. Data from introductory calculus-based physics
courses will be presented and discussed.
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