Conference Program/Abstracts

Abstracts for Working Groups

All working groups will meet from 8:00am-11:30 am on Thursday, February 21st. Contact the organizers for information about additional meeting times.

Working Group for Research on College Mathematics Instructor Professional Growth

Location: Denver 5

Organizers
Jessica Deshler, West Virginia University
Shandy Hauk, Wested & University of Northern Colorado

Abstract
Formerly the Working Group for Research on Novice Teachers of College Mathematics, we now extend the focus of the group to include research on the professional development of all college mathematics instructors regardless of their level of experience or expertise. Therefore, this year we will solicit proposals from researchers in all areas of the professional development of college mathematics instructors including but not limited to research on factors that shape instructional practices and the experiences of instructors as they attend to student thinking in their instruction. We expect the expansion of the group to include research focused on instructors not considered ‘novice’ to result in a new set of researchers providing perspectives to the group and providing richer feedback to presenters as well as expanding the network of potential collaborations to be formed among members of the group.

The group’s goals (historically defined) continue to drive the focus of annual meetings. They include providing informed support and feedback for researchers, providing opportunities for networking and collaboration among mathematics educators interested in the professional development of collegiate mathematics instructors, and continuing the discussion of issues central to the field and ways to address and contribute to these concerns. The intended participants of this group include researchers in all of these areas, whether new to the field, to research in general (early career researchers) or experienced in both. Researchers need not present their work to participate in the group or provide feedback to others. Allotted time will be structured to provide feedback on projects in the early stages of development. The working group is not meant to be a forum for presenting completed studies, but rather an opportunity to get feedback from peers on projects in any stage from the refinement of research questions to study design, data collection & analysis to discussion of venues for future presentation of completed projects. We will also discuss strategies for sharing our work with the practice-oriented college mathematics instructor professional development community, the needs of the working group, and ways of sustaining collaborations and communication among group participants during the year.

Working Group: Research on the Learning and Teaching of Combinatorics
Location: Denver 6

Organizers
Elise Lockwood, University of Wisconsin – Madison
Aviva Halani, Arizona State University

Abstract
The teaching and learning of combinatorics is, on the whole, an underdeveloped aspect of mathematics education research. Despite the fact combinatorics has a variety of applications in probability and computer science, and is clearly a context for rich problem solving situations, there has been relatively little research conducted on this aspect of the field. Interest in this domain is growing, but to this point combinatorics education researchers have largely worked in isolation. The working group is an ideal setting in which to facilitate face-to-face meetings and collaboration, and much progress could be made through in-person discussions over an extended period of time. The working group also provides an excellent opportunity to get others involved and to connect people with similar research interests, including those who might be new to (or simply curious about) research in combinatorics education. By organizing a working group, we hope to bring researchers together in an effort to move toward a more coherent research agenda in combinatorics education. Specific goals include: (1) getting a clearer picture of the current state of combinatorics education research, (2) involving more people in combinatorics education research, and (3) identifying specific goals and directions as we look to develop an overall corpus of literature on combinatorics education.

The overall structure of the session is to explore and discuss past, present, and future work related to research on the teaching and learning of combinatorics. First, we will look at previous work in the existing literature through a presentation by the organizers, then we will explore present research by having current combinatorics education researchers share their work, and finally we will look at future avenues of study by having overall discussions on how we might synthesize and move forward from past and present work. Since this is the first time a research on combinatorics education working group will be held, we will do our best to advertise it widely and invite many interested parties to participate.

Working Group: Infinity and Limits in Undergraduate Mathematical Learning
Location: Gold Coin

Organizers
Rob Ely, University of Idaho
Timothy Boester, Wright State University

Abstract
In our fourth meeting of the infinity and limits group, we will continue to develop and refine research goals pertaining to the undergraduate learning of infinite processes (including series and sequences), infinite sets, limits of real-valued functions, and other domains that significantly incorporate limits and infinity. While existing research has substantially charted out misconceptions and obstacles to infinity and limits, there is still great need for further understanding of the functioning of student knowledge of limits and infinity in context, the development of instructional goals and curricular implications, and the building of these ideas into learning trajectories. With these needs in mind, we have organized our research goals along four general themes: (a) the interaction of function and limit, (b) how limits manifest themselves throughout the calculus curriculum, (c) formalization of limit, and (d) mathematizing the “...”. Although we plan to pursue these themes, we welcome participants interested in any areas related to limits and infinity.

Most of the working group time will be for presentations of completed, ongoing, or preliminary work, with ample time for discussion, analysis, and planning of participants’ research. Each research presentation will be allowed significant opportunities for questions and feedback, but need to be categorized as being at one of the following steps:

1. Developing a research question from a research topic (and literature in the field)
2. Determining methodology for answering a particular research question
3. Refining categories for analysis of collected data
4. Interpreting the meaning and significance of analyzed data

Our primary goal for the working group is to nurture collaborative studies and publications based on the vision of all participants in the undergraduate learning of infinity and limits.

Working Group on Investigating Student Understanding of Cross-Cutting Concepts within Undergraduate Mathematics and Physics
Location: Matchless

Organizers
Megan Wawro, Virginia Tech
Warren Christensen, North Dakota State University

Abstract
Mathematics and physics have an inextricably linked history, with work in one field often motivating the other and facilitating its procession into new and unexplored areas of inquiry. An opportunity exists to welcome in a new era of such collaboration. Significant overlap exists between the practitioners of Research in Undergraduate Mathematics Education (RUME) and Physics Education Research (PER), and interested researchers have the chance to leverage both fields for a broader and deeper conversation about teaching and learning.

The purpose of this working group is to lay the groundwork for collaborations among RUME and PER members regarding research into students’ understanding of cross-cutting key concepts in undergraduate mathematics and physics. Within this exist goals such as the following:

• To better communicate about instructional goals and methods within undergraduate mathematics and physics content courses
• To improve communication between the RUME and PER fields regarding common research methods, valued research topics, underlying theories, key results about student thinking in the respective fields, etc.
• To begin to generate opportunities for collaborations across research communities.

We will focus our conversations on topics from Calculus 2+, Differential Equations, and Linear Algebra. Outcomes from the working group will be a compilation of ample literature from both RUME and PER that will be centrally informative to someone wishing to work across disciplines. Substantial time will be dedicated to establishing testable research questions. Also, venues for grant applications for this type of work will be discussed. We hope to find enough synergy among participants that a number of plans for future research grow out of the working group.

This proposal is for a new working group at RUME, so participants from a variety of experiences and viewpoints are extremely encouraged. Intended participants are researchers or practitioners with interest and/or experience in investigating students’ understanding of content common to physics and mathematics. Participants with interest or experience in explicitly studying their overlap are particularly welcome. Those participants who wish to present short presentations of their own relevant research during the working group should contact the organizers at least two weeks prior to the session.

Working Group: Realistic Mathematics Education in Research in Undergraduate Mathematics Education
Location: Colorado G

Organizers
Jason Martin, University of Central Arkansas
Michael Oehrtman, University of Northern Colorado
Craig Swinyard, University of Portland

Abstract
The number and diversity of research projects in undergraduate mathematics education that have employed design heuristics and the theoretical framing of Realistic Mathematics Education (RME) have grown significantly. The RME in RUME working group will devote equal time to deriving general principles from prior research and to applying these principles to guide new and ongoing projects. The first half of our session will provide opportunities for researchers who have completed studies within the RME framework to share their experiences related to the insights afforded by RME and the methodological and theoretical considerations involved in its use. These brief reports will be interspersed with group discussions to clearly articulate important issues in the use of RME in RUME and to identify themes, strategies, and questions common to multiple research projects. The second half of our working group session will be devoted to discussing new research projects and to discussing how lessons learned from our collective experience can strengthen the design and implantation of this work.

Working Group on Community College Mathematics Research
Location: Colorado H

Organizers
Irene M. Duranczyk, University of Minnesota
April Strom, Scottsdale Community College
John T. Smith, Pellissippi State Community College
Claire Wladis, Borough of Manhattan Community College at the City University of New York
Mark Yannotta, Clackamas Community College
Ann Sitomer, Portland Community College
Vilma Mesa, University of Michigan

Abstract
We will bring together researchers of community college mathematics teaching and learning. Over the past two years we have made progress growing a cadre of community college researchers and establishing an agenda for advancing community college teaching and learning research in mathematics. As a group we have identified and submitted for publication three articles on moving from anecdotal to evidence-based research for community college teaching and learning. We have developed one collaborative research proposal for collecting evidence based research across the nation, and we are working on developing a second collaborative research proposal for advancing evidence-based professional development activities for community college mathematics faculty. This working group is intended for active scholars in community college mathematics education, new researchers or researchers in other areas who are interested in investigating teaching and learning, and research-practitioners (i.e. community college faculty who have earned, or are in the process of earning, a doctoral degree) who see research and teaching at the community college as their primary focus.

The agenda of the Working Group session includes the following activities: (1) provide a summary of the work done at RUME 2001 and 2012, including an outline of ongoing plans for continued submission of research commentaries to journals and other outlets; (2) report on and discuss the results of the Institute of Educational Sciences proposal, Student success in mathematics: An exploratory investigation of students, instructors, and content at community colleges; (3) discuss a logic model for advancing an evidence based professional development project for community college faculty involving classroom-based research; (4) discuss and outline plans for ongoing and future collaborations on specific research questions among working group members; and (5) generate ideas and topics for advancing an special issue of a research journal focused on community college mathematics education. We anticipate working group outcomes to include: (1) a report for the RUME Proceedings; (2) a report for the research committee of the American Mathematical Association of Two-Year Colleges (AMATYC); (3) continued collaboration between the professional organizations for community college faculty (MAA, AMATYC, and NCTM); (4) the outline of a special issue of a research journal focused on community college mathematics education; and (5) a cadre of educators to continue engagement in research of community college mathematics education, with specific plans for collaborative research projects, grant proposals, and article submissions throughout the 2013-2014 academic year.