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July 13–17, 2013

CE07:

8:40-8:50 a.m. EBAPS Correlations: The Importance of

Epistemology

Contributed – Cameron G. Summers,* BYU-Idaho, Department of Physics,

Provo, UT 84604;

Brian A. Pyper, BYU, Idaho

In looking at correlations between subsets of the EBAPS (Epistemological

Beliefs Assessment for Physical Science) and various other measures of stu-

dent abilities and conceptual understanding, we found some surprisingly

strong correlations with some predictable and some unexpected aspects of

the students’ background, attitudes, and conceptual understanding. We’ll

report on these data, as well as implications for instruction.

*Sponsored by Brian Pyper

Location: Galleria II

Sponsor: Committee on Research in Physics Education

Date: Tuesday, July 16

Time: 7:30–9 a.m.

Presider: Warren Christensen

CF01:

7:30-8 a.m. Analyzing Student Understanding in Linear

Algebra Through Mathematical Activity

Invited – Megan Wawro,* Virginia Tech, Mathematics Department, 460 Mc-

Bryde Hall, Blacksburg, VA 24061;

The purpose of this study is to investigate how students conceptualize span

and linear (in)dependence, and to utilize the construct of mathematical

activity to provide insight into these conceptualizations. The data under

consideration are portions of individual interviews with students in an

inquiry-oriented linear algebra course. Through grounded analysis via the

framework of concept image (Tall & Vinner, 1991), the range of student

conceptions of span and linear (in)dependence are organized into four

concept image categories: travel, geometric, vector algebraic, and matrix

algebraic. To further illuminate participants’ conceptions, a framework

was developed to classify engagement in types of mathematical activity:

defining, proving, relating, example generating, and problem solving. The

coordinated analysis of concept image with engagement in mathematical

activity facilitates a nuanced and rich characterization of students’ connec-

tions within and between the concepts of span and linear (in)dependence.

*Sponsored by Warren Christensen

CF02:

8-8:30 a.m. Beliefs and Strategies for Comprehending

Mathematical Arguments

Invited – Keith Weber, Rutgers University, 10 Seminary Place, New Bruns-

wick, NJ 08901;

In the upper-level collegiate mathematics courses taught for mathemat-

ics majors, lectures largely consist of having professors prove theorems

for their students. An important assumption behind this instruction is

that students can learn mathematics from studying the proofs of others.

Unfortunately, both mathematics educators and mathematicians question

whether this assumption is true. In this talk, I present strategies that stu-

dents can use to understand the mathematical arguments that they read as

well as unproductive beliefs that students hold that may inhibit them from

gaining this understanding. These strategies and beliefs were hypothesized

based on qualitative studies in which students were observed reading

proofs and confirmed by a quantitative survey with 83 mathematicians and

175 mathematics majors that demonstrated that mathematicians desired

that their students use strategies that they did not hold and that students

held beliefs that mathematicians found undesirable.

CF03:

8:30-9 a.m. Three Interpretations of the Matrix

Equation Ax=b

Invited – Michelle Zandieh, Arizona State University, Tempe, AZ 85284;

Christine Larson, Florida State University

Over the past years we have come to reflect on the nature of the cognitive

demands that a sophomore or junior level linear algebra course places on

students. Many of the central ideas in introductory linear algebra can be

interpreted through the lens of the matrix equation Ax=b where A is an

mxn matrix, x is a vector, and b is a vector. We describe a framework that

highlights the challenges involved in interpreting Ax=b both symbolically

and graphically as (1) a system of equations, (2) a vector equation, and (3)

as a linear transformation. In particular we note how differently the vector

x must be viewed in each of these interpretations. We present vignettes of

student thinking that illustrate how the framework may be used to make

sense of the ways in which students blend ideas as they begin learning

linear algebra.

Location: Parlor A/B

Sponsor: Committee on Science Education for the Public

Date: Tuesday, July 16

Time: 7:30–9 a.m.

Presider: Amber Stuver

CG01:

7:30-8 a.m. Practical Approaches to Evaluating

Informal Science Learning

Invited – Scott Pattison,* Oregon Museum of Science and Industry, 1945 SE

Water Ave., Portland, OR 97214;

The opportunities for science learning outside of school are rich and

varied, including visits to museums and science centers, after-school pro-

grams and science clubs, outdoor experiences, conversations with families

and friends, reading, surfing the web, watching educational television

programs, and more. As educators and researchers increasingly recog-

nize, these experiences are a critical part of the nation’s science education

infrastructure. In this session, the speaker will draw upon over a decade of

experience in informal science education to discuss the unique opportu-

nities and challenges associated with evaluating and studying informal

learning and describe a variety of evaluation strategies used at the Oregon

Museum of Science and Industry as part of program and exhibit develop-

ment. He will also introduce a more practical approach for non-evaluation

professionals, called team-based inquiry, designed to empower educators

to incorporate evaluation into their work in order to create more effective

informal science learning experiences.

*Sponsored by Amber Stuver

CG02:

8-8:30 a.m. Little Shop of Physics: It’s Fun, But Is It

Effective?

Invited – Brian Jones, Colorado State University, Physics Department, Fort

Collins, CO 80523;

Michael Lacy, Matthew Aronson, Leonard Albright, Andrea Weinberg, Colo-

rado State University

A glance at the energy and enthusiasm levels of the K-12 students working

with Little Shop of Physics hands-on experiment stations reveals an obvi-

ous fact: They are having fun. But a decade of careful assessment shows

that they are learning science concepts as well. In this talk I’ll share the

progress of our assessment program, from informal early efforts to our lat-

er more formal testing. I will also discuss how assessment of all aspects of

our program has guided our efforts. How much time does a student spend

with one of our experiment stations? What is the best level of engagement

of our undergraduate interns? What is the best way to engage both male

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