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Thursday

6:10 – 7:00 pm

Grand Foyer

Poster Session & Reception

 

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 students’ 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 students’ mindsets. After administering the Patterns of Adaptive Learning Scale to assess students’ 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.

Paper

128

 

Student interest in calculus I

Derek Williams

This reports on a secondary analysis of data collected by the Mathematical Association of America’s 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 students’ 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

 

Paper

 

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.

Paper

 

 

Enriching student’s 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 “hints” 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.

Paper

134

 

Calculus students’ 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 students’ 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. Students’ 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 students’ 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.

Paper

 

 

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?

Paper

138

 

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.

Paper

 

 

Colloquial mathematics in mathematics lectures

Kristen Lew, Victoria Krupnik, Joe Olsen, Timothy Fukawa-Connelly and Keith Weber

In this poster, we focus on mathematics professors’ 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.

Paper

 

 

Talking about teaching: Social networks of instructors of undergraduate mathematics

Naneh Apkarian

The RUME community has focused on students’ 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.

Paper

 

 

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.

Paper

 

 

Physics Students' Construction and Use of Differential Elements in Multivariable Coordinate Systems

Benjamin Schermerhorn and John Thompson

As part of an effort to examine students’ 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 students’ difficulty with differential elements comes from an incomplete understanding of the systems.

Paper

 

 

 

 

Supporting undergraduate teachers’ 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 mathematicians’ 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 students’ 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 teachers’ instructional change.

Paper

 

 

RUME- and Non-RUME-track students’ 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 students’ 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 Hannula’s (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.

Paper

 

 

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.

Paper

 

 

Using the chain rule to develop secondary school teachers’ 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 teachers’ understanding and teaching of rate of change so that they can address students’ 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 teachers’ 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.

Paper

 

 

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 “Correct!” 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 “intelligent” and responsive programming that adapts assignments to users’ 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.

Paper

 

 

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.

Paper

 

 

Students’ 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 “historically difficult” 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 “groupworthy” 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 students’ workshop experiences, follow-up interviews were conducted. Students’ 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.

Paper

 

 

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 students’ understanding of the mean and university statistics instructors’ beliefs about their students’ understandings of the mean.

Paper

 

 

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 students’ 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.

Paper