100

Portland

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-

104525.

EI03:

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.

EI04:

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.

EI05:

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.

EI06:

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.

edu

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,

if

x

increases, y must also increase; in such

cases, it is commonly assumed that variables (e.g.,

x

and

y

) 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

relationship

f= v

/

l

, if the propagation speed

v

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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