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5:25 – 6:20 pm Grand Foyer 
Poster
Session 

Impact of advanced mathematical knowledge on the teaching
and learning of secondary mathematics Eileen Murray, Debasmita
Basu, Matthew Wright This
poster presents preliminary data from an exploratory study that aims to
advance our understanding of the nature of mathematics offered to prospective
mathematics teachers by looking at mathematical connections. In this study,
we investigate how inservice and preservice middle school teachers make
connections between tertiary and secondary mathematics as well as if and how
the understanding of connections influences teachersÕ thoughts about teaching
and learning mathematics. 

Analyzing classroom developments of language and notation
for interpreting matrices as linear transformations. Ruby Quea, Christine
AndrewsLarson As
part of a larger study of students reasoning in linear algebra, this research
analyzes how students make sense of language and notation introduced by
instructors when learning matrices as linear transformations. This paper
examines the implementation of an inquiryoriented instruction that consists
of students generating, composing, and inverting matrices in the context of
increasing the height and leaning a letter ÒNÓ placed on a 2dimensional
Cartesian coordinate system (Wawro et. al., 2012). I analyzed two classroom
implementations and noted how instructors introduced and formalized
mathematical language and notation in the context of this particular
instructional sequence, and then related that to the ways that language and
notation were subsequently taken up by students. This work was conducted in
order to enable me to build theory about the relationship between student
learning and the ways in which language and notation are introduced. 

What do students attend to when first graphing in R3? Allison Dorko This
poster considers what students attend to as they first encounter R3
coordinate axes and are asked to graph functions with free variables. Graphs
are critical representations, yet students struggle with graphing functions
of more than one variable. Because prior work has revealed that studentsÕ
conceptions of multivariable graph are often related to their conceptions
about single variable functions, we used an actororiented transfer
perspective to identify what students see as similar between graphing
functions with free variables in R2 and R3. We considered what students
attended to mathematically, and found that they focused on equidistance,
parallelism, and coordinate points. 

Support for mathematicians' teaching reform in an online
working group for inquiry oriented differential equations Nicholas Fortune There
is more need for research on how mathematicians can alter their teaching
style to a reform approach (Speer, Smith, & Horvath, 2010), especially if
they have always been teaching the same way (Speer & Wagner, 2009;
Wagner, Speer, & Rossa, 2007). One particular area that needs more work
is investigations of support structures for mathematicians hoping to reform
their teaching practice. This poster focuses on supports designed to aid in the
reform of teaching practice and specifically discusses the Teaching
Inquiryoriented Mathematics: External Supports (TIMES) project and one
online working group (OWG) used as a mode of support in the project. Results
indicate that facets of the OWG are successful support structures for
mathematicians who desire to align their practice to an inquiry oriented (IO)
approach to undergraduate differential equations (Rasmussen & Kwon, 2007;
Rasmussen, 2003). 

StudentsÕ understanding of mathematics in the context of
chemical kinetics Kinsey Bain, Alena Moon
and Marcy Towns This
work explores general chemistry studentsÕ use of mathematical reasoning to
solve quantitative chemical kinetics problems. Personal constructs, a
variation of constructivism, provides the theoretical underpinning for this
work, asserting that students engage in a continuous process of constructing
and modifying their mental models according to new experiences. The study
aimed to answer the following research question: How do nonmajor students in
a secondsemester general chemistry course and a physical chemistry course
use mathematics to solve kinetics problems involving rate laws? To answer
this question, semistructured interviews using a thinkaloud protocol were
conducted. A blended processing framework, which targets how problem solvers
draw from different knowledge domains, was used to interpret studentsÕ
problem solving. Preliminary findings describe instances in which students
blend their knowledge to solve kinetics problems. 

A comparative study of calculus I at a large research
university Xiangming Wu, Jessica
Deshler, Marcela Mera Trujillo, Eddie Fuller and Marjorie Darrah In
this report, we describe the results of analyzing data collected from 502
Calculus I students at a large research university in the U.S. Students were
enrolled in one of five different versions of Calculus I offered at the
university. We are interested in (i) whether the different characteristics of
each version of the course affect studentsÕ attitudes toward mathematics and
(ii) how each course might affect studentsÕ intentions of pursuing science,
technology, engineering and mathematics (STEM) degrees. We examine data
related to these two issues gathered from students via surveys during one
semester in Calculus I. 

Active learning in undergraduate precalculus and
singlevariable calculus Naneh Apakarian and Dana
Kirin The
study presented here examines the active learning strategies currently in place
in the Precalculus through single variable calculus sequence. While many
lament the lack of active learning in undergraduate mathematics, our work
reveals the reality behind that feeling. Results from a national survey of
mathematics departments allow us to report the proportion of courses in the
mainstream sequence utilizing active learning strategies, what those
strategies are, and how those strategies are being implemented. 

A Proposed Framework for Tracking Professional Development
Through GTAÕs Hayley Milbourne and Susan
Nickerson There
are several different models of graduate teaching assistant programs in
mathematics departments across the nation (Ellis, 2015). One particular
public university has recently reformatted their calculus program toward a
peermentor model and this is the first year of implementation. In the
peermentor model, there is a lead TA who serves as a support for the other
TAs in the program. Because of this, the professional development in which
the TAs are engaged is formally directed by both faculty and a peer. We are
interested in discussing a framework known as the Vygotsky Space as a
methodology for tracking the appropriation and sharing of pedagogical
practices among those responsible for calculus instruction. 

How Calculus students at successful programs talk about
their instructors Annie Bergman and Dana
Kirin The
CSPCC (Characteristics of Successful Programs in College Calculus) project
was a 5year study focused on Calculus I instruction at colleges and
universities across the United States with overarching goals of identifying
the factors that contribute to successful programs. In this poster, we draw
from student focus group interview data collected from schools that were
identified by the CSPCC project as being successful. The analyses we will
present in this poster will characterize the ways in which calculus students
talk about their instructors in an attempt to understand how their
perceptions shape their experience. 

Investigating university students difficulties with algebra Sepideh Stewart and Stacy
Reeder Algebra
is frequently referred to as the ÒgatewayÓ course for high school
mathematics. Even among those who complete high school Algebra courses, many
struggle with more advanced mathematics and are frequently underprepared for
college level mathematics. For many years, college instructors have viewed
the final problem solving steps in their respective disciplines as Òjust
AlgebraÓ, but in reality, a weak foundation in Algebra maybe the cause of
failure for many college students. The purpose of this project is to identify
common algebraic errors students make in college level mathematics courses
that plague their ability to succeed in higher level mathematics courses. The
identification of these common errors will aid in the creation of a model for
intervention. 

A qualitative study of the ways students and faculty in the
biological sciences think about and use the definite integral William Hall In
this poster, I share my methods and pilot interview results concerning a
qualitative study of the ways undergraduate students and faculty from the
biological sciences think about and use the definite integral. In this
research, I utilize taskbased interviews including five applied calculus
tasks in order to explore how students and faculty think about area,
accumulation, and the definite integral. Early results from pilot interviews
helped me revise the interview protocols and indicate that student reasoning
may be affected by experience and context. In presenting this poster, I hope
to gain feedback from the community on my research methodology and potential
analytical strategies. 

Root of Misconceptions – the Incorporation of
Mathematical Ideas in History KuoLiang Chang The
evolution of a mathematical concept in history has been the process of
merging different ideas to form a more rich, general, and rigorous concept.
Ironically, students, when learning such welldeveloped concepts, have
similar difficulties and make the same misconceptions again and again. To
illustrate, despite the welldeveloped and defined concept of real numbers,
many students still have difficulties in comparing fractions or doing basic
operations on irrational numbers. In this poster, the incorporation of
different ideas to form a general and rigorous mathematical concept in
history is examined. StudentsÕ struggles and misconceptions in learning the
concepts are investigated from the perspective of the incorporation process.
Finally, a model for differentiating and validating the variations of a
general mathematical concept is suggested for resolving learning difficulties
and misconceptions. 

Student Experiences in a ProblemCentered Developmental
Mathematics Class Martha Makowski Given
the large numbers of students who enroll each year in developmental
mathematics classes, community colleges have started creating developmental
classes that both engage students in meaningful mathematics and provide them
with an efficient pathway to the collegelevel curriculum. This study
examines how community college students enrolled in a problembased
developmental algebra class experience the curriculum and instruction. Eight
students from a target classroom were interviewed about their experiences in
the class, focusing on how they experienced group work, problem solving, and
the role of the teacher. Surveys were also used to measure their attitudes
towards mathematics along several dimensions at the beginning and end of the
semester. Students who liked group work were energized by the opportunity to
work with people while learning and valued the multiple opportunities group
work provided for them to check their work. Few students saw group work as an
opportunity to explore conceptual ideas. The results suggest that implementations
of such classes could benefit from structured discussion about group work
norms and explicit discussion about the purpose of solving problems. 

A collaborative effort for improving calculus through
better assessment practices Justin Heavilin, Hodson
Kyle and Brynja Kohler Like
many institutions across the country, Utah State UniversityÕs Department of
Mathematics and Statistics has embarked on an effort to improve the calculus
sequence with the following objectives: (1) improve our studentsÕ
comprehension and application of key topics, (2) retain/recruit more students
into STEM majors, and (3) provide more consistency across sections. After
initial planning and preparation in the 201415 academic year, new practices
were ready for implementation. In the fall of 2015, teams of instructors
worked from common guided course notes, and met weekly to discuss instruction
and develop common assessments. This poster displays the methodology of test
design and item analysis we employed in the Calculus 2 course. While our team
is only at the beginning stages of this work, the methods for creating
reliable and relevant measures of student learning hold promise for achieving
the goals of our reform. 

Exploring student understanding of the negative sign in
introductory physics contexts Suzanne Brahmia and Andrew
Boudreaux Recent
studies in physics education research demonstrate that although physics
students are generally successful executing mathematical procedures, they
struggle with the use of mathematical concepts for sense making. In this
poster we investigate student reasoning about negative numbers in contexts
commonly encountered in calculusbased introductory physics. We describe a
largescale study (N > 900) involving two introductory physics courses:
calculusbased mechanics and calculusbased electricity and magnetism (E&M).
We present data from six assessment items (3 in mechanics and 3 in E&M)
that probe student understanding of negative numbers in physics contexts. Our
results reveal that even mathematically wellprepared students struggle with
the way that we symbolize in physics, and that the varied uses of the
negative sign in physics can present an obstacle to understanding that
persists throughout the introductory sequence. 

Classroom observation, instructor interview, and instructor
selfreport as tools in determining fidelity of implementation for an
intervention Shandy Hauk, Katie
Salguero and Joyce Kaser A
webbased activity and testing system (WATS) has features such as adaptive
problem sets, instructional videos, and datadriven tools for instructors to
use to monitor and scaffold student learning. Central to WATS adoption and
use are questions about the implementation process: What constitutes ÒgoodÓ
implementation and how far from ÒgoodÓ is good enough? Here we report on a
study about implementation that is part of a statewide randomized controlled
trial examining student learning in community college algebra when a
particular WATS suite of tools is used. Discussion questions for conference
participants dig into the challenges and opportunities in researching
fidelity of implementation in the community college context, particularly the
role of instructional practice as a contextual component of the research. 

Separating issues in the learning of algebra from
mathematical problem solving R. Cavender Campbell,
Kathryn Rhoads and James A. Mendoza Epperson StudentsÕ
difficulty in learning school algebra has motivated a plethora of research on
knowledge and skills needed for success in algebra and subsequent
undergraduate mathematics courses. However, in gateway mathematics courses
for science, technology, engineering, and mathematics majors, student success
rates remain low. One reason for this may be to the lack of understanding of
thresholds in student mathematical problem solving (MPS) practices necessary
for success in later courses. Building from our synthesis of the literature
in MPS, we developed Likert scale items to assess undergraduate studentsÕ
MPS. We used this emerging assessment and individual, taskbased interviews
to better understand studentsÕ MPS. Preliminary results suggest that
studentsÕ issues in algebra do not prohibit them from using their typical
problem solving methods. Thus, the assessment items reflect studentsÕ MPS,
regardless of possible misconceptions in algebra, and provide a mechanism for
examining MPS capacity separate from procedural and conceptual issues in
algebra. 

Communicative artifacts of proof: Transitions from
ascertaining to persuading David Plaxco and Milos
Savic With
this poster, we wish to highlight an important aspect of the proving process.
Specifically, we revisit Harel and SowderÕs (1998, 2007) proof schemes to
extend the authorsÕ constructs of ascertaining and persuading. With this
discussion, we reflect on the original theoretical framework in light of more
recent research in the field and draw focus to a critical aspect of the
proving process in which the prover generates the communicative artifacts of
proof (CAP) critical to shifts between ascertaining to persuading. We also
discuss possible ways in which an attention to the psychological and social
activities involved in the development of the CAP might inform research and
instruction. 

On the variety of the multiplication principleÕs
presentation in college texts Zackery Reed and Elise
Lockwood The
Multiplication Principle is one of the most foundational principles of
counting. Unlike foundational concepts in other fields, where there is
uniformity in presentation across text and instruction, we have found that
there is much variety in the presentation of the Multiplication Principle.
This poster highlights the multiple aspects of this variety, specifically
those with implications for the combinatorial research and education
community. Such topics include the statement types, language and
representation of statements, and mathematical implications. 

Assessing studentsÕ understanding of eigenvectors and
eigenvalues in linear algebra Kevin Watson, Megan Wawro,
and Michelle Zandieh Many
concepts within Linear Algebra are extremely useful in STEM fields; in
particular are the concepts of eigenvector and eigenvalue. Through examining
the body of research on student reasoning in linear algebra and our own
understanding of eigenvectors and eigenvalues, we are developing preliminary
ideas about a framework for eigentheory. Based on these preliminary ideas, we
are also creating an assessment tool that will test studentsÕ understanding
of eigentheory. This poster will present our preliminary framework, and
examples of the multiplechoice extended questions we have created to assess
student understanding. 
6:30 – 9:00 pm Grand Ballroom Salons 24 
Using adjacency matrices to analyze a proposed linear
algebra assessment Hayley Milbourne,
Katherine Czeranko, Chris Rasmussen and Michelle Zandieh An
assessment of student learning of major topics in linear algebra is currently
being created as part of a larger study on inquiryoriented linear algebra.
This includes both the assessment instrument and a way to understand the
results. The assessment instrument is modeled off of the Colorado
Upperdivision Electrostatics (CUE) diagnostic (Wilcox & Pollock, 2013).
There are two parts to each question: a multiplechoice part and an
explanation part. In the explanation part, the student is given a list of
possible explanations and is asked to select all that could justify their
original choice. This type of assessment provides information on the
connections made by students. However, analyzing the results is not
straightforward. We propose the use of adjacency matrices, as developed by
Selinski, Rasmussen, Wawro, & Zandieh (2014), to analyze the connections
that students demonstrate. 