Volume 29, Issues 8 and 9 of the journal PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studues) were a 2-part special issue on Interdisciplinary Conversations, Edited by Susan Ganter, Stella Hofrenning, Carrie Diaz-Eaton, and Victor Piercey
Susan Ganter, Stella Hofrenning, Carrie-Diaz Eaton, and Victor Piercey
Abstract:
The two parts in this special issue address interdisciplinary conversations involving mathematics courses in the first two years of undergraduate work. The special issue was inspired by work funded by the National Science Foundation under a grant titled “SUMMIT-P.” The special issue includes papers written about projects both from SUMMIT-P and from outside of SUMMIT-P. Part I focuses on frameworks and models of interdisciplinary collaboration.
Fabiana Cardetti and Steven LeMay
Abstract:
In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the undergraduate level. Using these categories, we present and discuss rich learning tasks that meaningfully engage students in mathematical argumentation. In addition, these argumentation tasks support the development of students’ communication and critical thinking skills - all essential to learning in partner disciplines. Finally, recognizing that collaboration with colleagues from other disciplines is crucial to understand and address learning objectives beyond mathematics, we also present lessons learned from our successful interdisciplinary collaborations.
Carrie Diaz-Eaton, Hannah Callender Highlander, Kam D. Dahlquist, Glenn Ledder, M. Drew LaMar, and Richard Schugart
Abstract:
Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the “Rule-of-Four,” initially used in calculus reform efforts, to a “Rule-of-Five” framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.
Tevian Dray, Elizabeth Gire, Mary Bridget Kustusch, Corinne A. Manogue, and David Roundy
Abstract:
Calculus, as commonly taught, describes certain operations on explicit functions, but science relies on experimental data, which is inherently discrete. In the face of this disparity, how can we help students transition from lower-division mathematics courses to upper-division coursework in other STEM disciplines? We discuss here our efforts to address this issue for upper-division physics majors by introducing a new representation for derivatives in terms of experiments to go along with the traditional symbolic, graphical, verbal, and numerical representations, and by emphasizing infinitesimal reasoning through the use of differentials. These ideas culminate in the concept of thick derivatives. By providing examples of “physics” reasoning about both ordinary and partial derivatives, and methods for incorporating such reasoning into the classroom, we hope to give instructors of calculus new insight into the needs of many of their students.
Lorraine F. Dame, Binil Aryal, Aminul Huq, and Xavier Prat-Resina
Abstract:
Students entering health sciences programs may face challenges on their road to successful completion and possible entry to medical school in the area of preparedness in quantitative skills. At our institution, faculty analyzed evidence of these challenges including performance on the ACT Math Test, an in-house math placement test and quantitative tasks for physics and chemistry courses. The authors have used the ARCS (Attention, Relevance, Confidence, Satisfaction) conceptual framework developed by John M. Keller to examine a collaborative effort by our faculty from mathematics, chemistry and physics to design and deliver an interdisciplinary quantitative curriculum in the first 2 years. Preliminary results show high levels of attention, an improvement in student perceptions regarding the relevance of math to science, significant improvements to student confidence in their ability to learn and apply algebra, and reasons for student satisfaction. Faculty reflections indicate that this was a significant and rewarding effort.
Ruthmae Sears, Frances Hopf, Ana Torres-Ayala, Casey Williams, and LesLaw Skryzpek
Abstract:
We describe how faculty and staff used improvement science design Plan-Do-Study-Act (PDSA) cycles and engaged in interdisciplinary conversations in an effort to improve students’ performance in introductory mathematics courses. This initiative started with College Algebra a course with a large enrollment of students that had a high failure rate. We engaged in PDSA cycles over a period of 4 years. From 2011–2015, we used data from student assessment scores, course evaluations, lab surveys, and instructors’ observations to inform decisions to transform introductory mathematics courses. The transformative efforts positively enhanced students’ performance. Furthermore, to reflect on our PDSA cycles and the broader implications of institutionalized change to mathematics courses, we engaged in frequent interdisciplinary conversations to discuss complexities and challenges. These meetings provided an opportunity to build a common vision about the nature and delivery of the mathematics taught to better serve students The themes of the conversations were on curriculum, assessment, instruction, the complexities of the change process, cultivating a growth mindset, and the need to engage in research in general education mathematics courses. Therefore, in this article we provide insights as to how interdisciplinary conversations were used to implement evidence-based teaching practices and also pedagogical approaches that can be used to facilitate students learning.
Susan Ganter, Stella Hofrenning, Carrie Diaz-Eaton, and Victor Piercey
Abstract:
The two parts in this special issue address interdisciplinary conversations involving mathematics courses in the first 2 years of undergraduate work. The special issue was inspired by work funded by the National Science Foundation under a grant titled “SUMMIT-P.” The special issue includes papers written about projects both from SUMMIT-P and from outside of SUMMIT-P
Cardboard Cities, Real Mathematics: Employing Quantitative Literacy to Study Gentrification in NYC
Forest Fisher, Jared Warner, and Nate Mickelson
Abstract:
Gentrification is a complex issue with very real repercussions for urban youth. Games make learning fun and provide a way for students to explore complex systems through recursive play. We describe a board game designed to help students explore ratios and proportional reasoning while simultaneously engaging the causes and effects of gentrification. Situated within a multidisciplinary first-semester learning community course, the game provides a model for later experiential learning opportunities as students are asked to study the effects of gentrification in one New York City neighborhood.
Interdisciplinarity and Inclusivity: Natural Partners in Supporting Students
Meredith L. Greer
Abstract:
Mathematics Across the Sciences is an applications-based course designed to strengthen students’ mathematical skills in preparation for calculus or for a major in the sciences. Its development relied heavily on input from faculty members in several science departments. This article describes the course; many of the scientific applications taught; pedagogical strategies; and scholarship on inclusion, equity, and diversity in education. These descriptions make clear that the goals of inclusion and academic excellence are intertwined, and an interdisciplinary approach can help each to improve.
Revising General Education Math Courses with Partner Discipline Input
Holly Hirst and Katrina Palmer
Abstract:
The authors describe working with partner disciplines during the process of updating mathematics courses for the general education quantitative literacy requirement. The conversations resulted in significant changes to the business calculus course and a rich listing of applications to be incorporated into the college algebra course from technical fields such as industrial design, exercise science, and building science.
Collaborative Effort to Develop Middle School Preservice Teachers’ Mathematical Knowledge
Ruthmae Sears, Gladis Kersaint, Fernando Burgos, and Rebecca Wooten
Abstract:
This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses, two in mathematics and one in mathematics education, worked together to more explicitly link course materials, assignments, and the pedagogical approaches. Collectively, the courses were designed to address the five components of preservice teachers’ mathematical knowledge for teaching (PT-MKT), and to model effective teaching practices. Using their collective experiences co-planning and implementing these course adjustments were made in the subsequent year. The instructors were pleased by their implementation and student outcomes in all three courses.
We describe how each component of the PT-MKT framework was approached in these courses and discuss challenges experienced by the instructors, who were part of a larger effort to develop and implement a middle school teacher preparation program. The information shared is based on data collected as part of a program evaluation effort, and is bolstered by the instructors’ recollection of events. Overall, the instructors enhanced the curricula and their instructional practices and found that the attention placed on developing PT-MKT support the mathematical development of middle school mathematics preservice teachers.
Linking Mathematics and Psychological Science
Mike Pinter and Linda Jones
Abstract:
We describe a successful collaboration between mathematics and psychological science faculty members to create a learning community for our students that linked sections of introductory mathematical reasoning and psychological science courses. The students in our learning community were in their second or third semester. The learning community is designed so that, throughout the semester, students regularly move across the border between the two linked disciplines by completing common assignments, including a group project. We modified our existing course topics and frameworks to be intentional about building connections between the courses.
A Project-Based Approach to Statistics and Data Science
David White
Abstract:
In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills.
Cryptography in Context: Co-teaching Ethics and Mathematics
Nathaniel Karst and Rosa Slegers
Abstract:
Many of the applied mathematics courses we teach touch upon a range of rich and important ethical issues – issues that, for a number of reasons, are rarely openly discussed in class. In this work, we describe a sequence of activities co-designed and co-taught by philosophy and mathematics faculty in the hopes of bridging the divide between the application and implementation of modern cryptography and the ethical dilemmas it creates. Although we have specifically focused on one area of applied mathematics at one particular type of institution, we highlight throughout the work the areas in which our approach can be changed to suit different content areas and student populations.