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6:10 – 7:00 pm Grand Foyer |
Poster Session & Reception |
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Clearing the way for mindset changed through formative
assessment Rebecca Dibbs and Jennie
Patterson One of the reasons for the exodus in STEM majors is the introductory
calculus curriculum. Although there is evidence that curricula
like CLEAR calculus promoted significant gains in studentsÕ growth mindset, it is unclear how this curriculum promotes mindset changes. The purpose of this case study was to
investigate which features of CLEAR Calculus promoted positive changes in
studentsÕ mindsets. After administering the
Patterns of Adaptive Learning Scale to assess studentsÕ initial mindset in one section of calculus, four students were
selected for interviews. Although participants were selected for maximal
variation in their mindset at the beginning of the
course, there were a lot of similar themes in their interviews. Students
cited that CLEAR Calculus curriculum challenges them in ways that facilitates
deeper comprehensive learning than that of a traditional calculus course. 128 |
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Student interest in calculus I Derek Williams This reports on a secondary analysis of data collected by the
Mathematical Association of AmericaÕs Characteristics of Successful Programs
in College Calculus (2015). Survey data were collected from more than 700
instructors, and roughly 14,000 students making these data ideal for multiple
level analysis techniques (Raudenbush & Bryk, 2002). Here, these data are used to analyze studentsÕ interest in Calculus I. Results suggest
that students with higher frequencies of presenting to their classmates,
collaborating with peers, working individually, explaining their work, and
taking Calculus I with an experienced instructor tend to be more interested
in class |
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Using reading journals in calculus Tara Davis and Anneliese
Spaeth In
parallel studies during the Fall 2015 semester, we examined the effects of
assigning reading journals in a first semester calculus course. At the
beginning of the semester, students were given instructions about how to read
the textbook. On alternating weeks, students were asked to complete journal
assignments - these included taking reading notes, responding to a prompt
question, and reflecting upon any confusing portions of the reading. A
comparison between student quiz scores from weeks during which journals were
assigned and quiz scores from weeks during which no journals were assigned
will be given, and implications for teaching will be discussed. |
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Enriching studentÕs online homework experience in pre-calculus
courses: Hints and cognitive supports Nathan Wakefield and Wendy
Smith As
part of reforming our Pre-Calculus courses, we realized that reforms to
instruction needed to be accompanied by reforms to the homework. We utilized
the online homework system WeBWorK but recognized our students wanted more
support on missed questions. WebWorK ÒhintsÓ provided us an avenue to ask
students leading questions to prompt thinking over procedures. Preliminary
data show many students are using these hints and the hints are working as
intended. We plan to expand hints beyond our Pre-Calculus courses. The open
source nature of WeBWorK provides an opportunity for hints to be implemented
on a wide scale. 134 |
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Calculus studentsÕ understanding of the vertex of the
quadratic function in relation to the concept of derivative Annie Childers and Draga
Vidakovic The
purpose of this study was to gain insight into thirty Calculus I studentsÕ
understanding of the relationship between the concept of vertex of a
quadratic function and the concept of the derivative. APOS
(action-process-object-schema) theory (Asiala et al., 1996) was used in
analysis on student written work, think-aloud, and follow up group
interviews. StudentsÕ personal meanings of the vertex, including
misconceptions, were explored, and how students relate the vertex to the
understanding of the derivative. Results give evidence of studentsÕ lack of
connection between different problem types which use the derivative to find
the vertex. Implications and suggestions for teaching are made based on the
results. Future research is suggested as a continuation to improve student
understanding of the vertex of quadratic functions and the derivative. |
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An insight from a developmental mathematics workshop Eddie Fuller, Jessica
Deshler, Marjorie Darrah, Xiangming Wu and Marcela Mera Trujillo In
this report, we present data from 404 students in a developmental mathematics
course at a large research university and try to better understand academic
and non-academic factors that predict their success. This work is the first
step in a larger project to understand when science, technology, engineering,
and mathematics (STEM) intending students who begin in developmental
mathematics courses are successful and continue to be successful in
higher-level mathematics courses. To gain some preliminary insight, we analyze
SAT and ACT mathematics scores for STEM and non-STEM majors who succeeded in
our developmental mathematics course and also look at personality traits and
anxiety levels in these students. Specifically, we sought to answer the
following questions for STEM intending students: (i) what SAT and ACT
mathematics scores correlate with success in developmental mathematics? and
(ii) what other non-academic factors predict success in developmental
mathematics? 138 |
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College-educated adults on the autism spectrum and
mathematical thinking Jeffrey Truman This
study examines the mathematical learning of adults on the autism spectrum,
currently or formerly undergraduate students. I aim to expand on previous
research, which often focuses on younger students in the K-12 school system.
I have conducted various interviews with current and former students. The
interviews involved a combination of asking for the interviewee's views on
learning mathematics, self-reports of experiences (both directly related to
courses and not), and some particular mathematical tasks. I present some
preliminary findings from these interviews and ideas for further research. |
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Colloquial mathematics in mathematics lectures Kristen Lew, Victoria
Krupnik, Joe Olsen, Timothy Fukawa-Connelly and Keith Weber In
this poster, we focus on mathematics professorsÕ use of colloquial
mathematics where they express mathematical ideas using informal English. We
analyzed 80-minute lectures in advanced mathematics from 11 different
mathematics professors. We identified each instance where mathematicians
expressed a mathematical idea using informal language. In the poster, we use
this as a basis to present categories of the metaphorical images that
professors use to help students comprehend the mathematics that they are
teaching. |
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Talking about teaching: Social networks of instructors of
undergraduate mathematics Naneh Apkarian The RUME community has focused on studentsÕ understandings of and
experiences with mathematics. This project sheds light on another part of the
higher education system – the departmental culture surrounding
undergraduate mathematics instruction. This paper reports on the interactions
of members of a single mathematics department, centered
on their conversations about undergraduate mathematics instruction. Social
network analysis of this group sheds important light on the informal
structure of the department. |
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Preliminary genetic decomposition for implicit
differentiation and its connections to multivariable calculus Sarah Kerrigan Derivatives
are an important concept in undergraduate mathematics and across the STEM
fields. There have been many studies on student understanding of derivatives,
from graphing derivatives to applying them in different scientific areas.
However, there is little research on how students construct an understanding
of multivariable calculus from their understanding of single variable
calculus. This poster uses APOS theory to hypothesize the mental reflections
and constructions students need to make in order to solve and interpret an
implicit differentiation problem and examine the connections to multivariable
calculus. Implicit differentiation is often the first time students are
introduced to the notion of a function defined by two dependent variables, a
concept vital in multivariable calculus. Investigating how students initially
reconcile this new idea of two variable functions can provide knowledge of how
students thing about multivariable calculus. |
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Physics Students' Construction and Use of Differential
Elements in Multivariable Coordinate Systems Benjamin Schermerhorn and
John Thompson As
part of an effort to examine studentsÕ understanding of non-Cartesian
coordinate systems when using vector calculus in the physics topics of
electricity and magnetism, we interviewed four pairs of students. In one
task, developed to force them to be explicit about the components of specific
coordinate systems, students construct differential length and volume
elements for an unconventional spherical coordinate system. While all pairs
eventually arrived at the correct elements, some unsuccessfully attempted to
reason through spherical or Cartesian coordinates, but recognized the error
when checking their work. This suggests studentsÕ difficulty with
differential elements comes from an incomplete understanding of the systems. |
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Supporting undergraduate teachersÕ instructional change George Kuster and William
Hall Teaching
Inquiry-oriented Mathematics: Establishing Supports (TIMES) is an NSF-funded
project designed to study how we can support undergraduate instructors as
they implement changes in their instruction. One factor in the disconnect
between the development and dissemination of student-centered curricula are
the challenges that instructors face as they work to implement these
curricular innovations. For instance, researchers investigating
mathematiciansÕ efforts to teach in student-centered ways have identified a
number of challenges including: developing an understanding of student
thinking, planning for and leading whole class discussions, and building on
studentsÕ solution strategies and contributions. This research suggests a
critical component needed to take curricular innovations to scale: supports
for instructional change. In this poster we address our current research
efforts to support undergraduate teachersÕ instructional change. |
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RUME- and Non-RUME-track studentsÕ motivations of enrolling
in a RUME graduate course Ashley Berger, Rebecca
Grider, Juliana Bucher, Mollie Mills-Weis, Fatma Bozkurt, and Milos Savic The
purpose of this ongoing study is to investigate studentsÕ motivations in
taking a graduate-level RUME course. Seven individual semi-structured
interviews were conducted with graduate students enrolled in a RUME course at
a large Midwestern university that has a RUME Ph.D. option in the mathematics
department. Our analysis of those interviews utilized two theoretical
frameworks: Self-Determination Theory (Ryan & Deci, 2000) and HannulaÕs
(2006) needs and goals structure. Preliminary analysis of the interviews
indicates that non-RUME-track students are extrinsically, need-motivated,
while RUME-track students are intrinsically, goal-motivated when taking a
RUME course. The researchers conjecture that knowing what influences
non-RUME-track students may aid in closing the gap between the mathematical
and RUME communities. |
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Teaching and learning linear algebra in terms of community
of practice Deniz Kardes Birinci,
Karen Bogard Givvin and James W. Stigler Communities
of practice (CoP) are defined as groups of people who share a concern, a set
of problems, or a passion about a topic, and who interact in an ongoing basis
to deepen their knowledge and expertise. The purpose of this study is to
examine the process of teaching and learning linear algebra within this
theoretical framework. In this research, we used an ethnographic case study
design to study three linear algebra instructors and their students at a
large public university. The instructors have different educational and
cultural backgrounds. Data included observations, a Linear Algebra Questionnaire,
and semi-structured interviews. We observed significant differences in
teaching methods between the instructors. |
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Using the chain rule to develop secondary school teachersÕ
Mathematical Knowledge for Teaching, focused on the rate of change Zareen Rahman, Debasmita
Basu, Karmen Yu and Aminata Adewumi The
unit described in this study was designed to connect secondary and advanced
mathematical topics. It focused on how the knowledge of chain rule impacts
secondary teachersÕ understanding and teaching of rate of change so that they
can address studentsÕ misconceptions. This project is informed by the idea of
Mathematical Knowledge for Teaching, which encompasses both subject-matter
knowledge and pedagogical content knowledge of teachers. The goal was to
enhance secondary school teachersÕ teaching of the rate of change and the
unit featured tasks connecting rate of change problems as seen in high school
algebra to the concept of chain rule. The unit was designed to engage
mathematics teachers in discourse about the content learned at the college
level to content that is taught at the secondary school level. |
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Exploring the factors that support learning with
digitally-delivered activities and testing in community college algebra Shandy Hauk and Bryan
Matlen A
variety of computerized interactive learning platforms exist. Most include
instructional supports in the form of problem sets. Feedback to users ranges
from ÒCorrect!Ó to offers of hints and partially to fully worked examples.
Behind-the-scenes design of such systems varies as well – from static
dictionaries of problems to ÒintelligentÓ and responsive programming that
adapts assignments to usersÕ demonstrated skills, timing, and an array of
other learning theory-informed data collection within the computerized
environment. This poster presents background on digital learning contexts and
invites lively conversation with attendees on the research design of a study
aimed at assessing the factors that influence teaching and learning with such
systems in community college elementary algebra classes. |
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What would the research look like? Knowledge for teaching
mathematics capstone courses for future secondary teachers Shandy Hauk, Eric Hsu and
Natasha Speer Mathematics
Capstone Course Resources is a 14-month proof-of-concept development project.
Collaborators across three sites aim to: (1) develop and pilot two
multi-media activities for advanced pre-service secondary mathematics teacher
learning, (2) create guidance for college mathematics faculty for effective
use of the materials with target audiences, and (3) gather information from
instructors and students to inform future work to develop additional modules
and to guide subsequent research on the implementation of the materials. The
goal of this poster presentation is to provide information about capstone
module development and brainstorm research design suggestions with the long
term aim of developing a grant proposal to research the knowledge college
mathematics faculty use to effectively teach mathematics to future teachers. |
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StudentsÕ experiences and perceptions of an inquiry-based
model of supplemental instruction for calculus Karmen Yu The
Inquiry-Based Instructional Support (IBIS) workshop model is part of an
innovative degree program designed to prepare elementary mathematics
teachers. The reason behind IBIS workshops was to support students enrolled
in Òhistorically difficultÓ mathematics courses, such as Calculus I and
Calculus II. The design of IBIS workshop was framed and guided by Peer-Led
Team Learning (PLTL) (Gosser & Roth, 1998) and Complex Instruction
(Cohen, 1994). During workshop, students work in small groups and engage in
ÒgroupworthyÓ mathematical tasks that promote their conceptual understanding
of Calculus topics (Cohen, 1994). A pilot study was conducted to evaluate the
workshop structure and these tasks. In order to assess studentsÕ workshop
experiences, follow-up interviews were conducted. StudentsÕ responses
indicated that their workshop experiences helped to promote the development
of their problem solving skills and highlighted the critical roles of
thinking and reasoning in learning Calculus with understanding. |
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An overview of
research on the arithmetic mean in university introductory statistics courses Sam Cook There is a dearth of research on the arithmetic mean
at the university level. This
poster will cover overlap of several studies (some unpublished) on university
studentsÕ understanding of the mean and university statistics instructorsÕ
beliefs about their studentsÕ understandings of the mean. |
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Reasoning about changes: a frame of reference approach Surani Joshua In
a RUME 18 Theoretical Report my co-authors and I presented our cognitive
description of a conceptualized frame of reference, consisting of mental
commitments to units, reference points, and directionality of comparison when
thinking about measures. Here I present a pilot study on how a focus on
conceptualizing a frame of reference impacts studentsÕ ability to reason
quantitatively about changes. The two-part empirical study consisted of
clinical interviews with several students followed by teaching interviews
with three students chosen because of their varying abilities to
conceptualize a frame of reference. My initial evidence shows that the
ability to conceptualize a frame of reference greatly benefits students as
they attempt to reason with changes. |