Digital Commons Network^™

Calculus I Companion, Beth Campbell Hetrick, Kimberly R. Spayd

Open Educational Resources

A course pack for supplementing Calculus 1 with algebra, geometry, trigonometry, and precalculus topics, including reading material, activities, and practice problems assembled from various OER texts.

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part Ii, Janet H. Barnett, Dominic Klyve, Dave Ruch

Euleriana

This article and its prequel together highlight a set of nine classroom-ready projects that draw on the remarkable writing of Leonhard Euler (1707--1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom use.

Leveraging The "Large" In Large Lecture Statistics Classes, Kady Schneiter, Kimberleigh Felix Hadfield, Jenny Lee Clements

Mathematics and Statistics Faculty Publications

Being a teacher or a student in a class with a large enrollment can be intimidating. Often, teachers view comforts that are common to small classes as unattainable in a larger class, including knowing students’ names, using active learning, employing group work, and creating group discussion. Students in large classes may find that the class size leads to isolation. At Utah State University, we offer introductory statistics classes for various audiences using a large lecture format. The authors have collectively led these large lectures dozens of times and found that, despite its shortcomings, the large lecture format can be an …

Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark

Journal of Humanistic Mathematics

In peer Instruction, students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first authot began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the “Goldilocks Zone” – not too hard …

What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher

Journal of Humanistic Mathematics

We describe students’ learning practices in an online asynchronous PreCalculus course during Fall 2020, the first complete semester of distance learning induced by the COVID-19 pandemic. Results were compiled using a thematic analysis of a questionnaire administered to 43 students enrolled in PreCalculus at a university in the Midwest (United States). Students were given opportunities for active learning and various synchronous Q&A sessions, yet they primarily learned through watching videos and reading worked examples, minimizing interactions with the instructor and available tutors. The questionnaire results show that students knew active learning was helpful, but they were unable to curtail unproductive …

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker

Euleriana

This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …

Supporting Student Success And Persistence In Stem With Active Learning Approaches In Emerging Scholars Classrooms, David Miller, Jessica Deshler, Tim Mceldowney, John Stewart, Edgar Fuller, Matt Pascal, Lynnette Michaluk

Faculty & Staff Scholarship

Over the last several decades, Emerging Scholars Programs (ESPs) have incorporated active learning strategies and challenging problems into collegiate mathematics, resulting in students, underrepresented minority (URM) students in particular, earning at least half of a letter grade higher than other students in Calculus. In 2009, West Virginia University (WVU) adapted ESP models for use in Calculus I in an effort to support the success and retention of URM STEM students by embedding group and inquiry-based learning into a designated section of Calculus I. Seats in the class were reserved for URM and first- generation students. We anticipated that supporting students …

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

An Experiential Report On The Thayer Method Of Teaching Across College-Level Chemistry, Biology, Math, And Physics Courses, Kevin P. O'Halloran, Sairam Tangirala, Fengjie Sun, Leonard E. Anagho, Gerald Agbegha, Clay Runck, David Roth, Amy H. Erickson

Georgia Journal of Science

The Thayer method of instruction is a little-known active learning technique that dates back to 1817 at the U.S. Military Academy. This study describes the implementation and statistical evaluation of an adaptation of the Thayer method in a variety of college science and math courses. All courses had five characteristics in common: (i) students were given a daily reading schedule and instructed to prepare before class, (ii) each class started with a question and answer session, (iii) class time minimized the use of lecture, (iv) class time maximized the use of active learning, and (v) students were frequently quizzed. A …

Linear Algebra And Applications: An Inquiry-Based Approach, Feryal Alayont, Steven Schlicker

Open Textbooks

Linear Algebra and Applications: An Inquiry-Based Approach provides a novel open-source inquiry-based learning approach to linear algebra. The emphasis is on active learning and developing intuition through investigation of examples. The content is introduced through inquiry-based activities, starting with experimentation with hands-on concrete examples and continuing on to developing a deep understanding of the topics through working with conceptual questions. To provide motivation and context for the linear algebra content, the text includes 35 real-life applications projects. While working through all of this material in the text, readers are actively DOING mathematics instead of being passive learners. Although it is …

Active Prelude To Calculus, Matthew Boelkins

Open Textbooks

Active Prelude to Calculus is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. The reader will find that …

The Mathematics Of Gossip, Jessica Deters, Izabel P. Aguiar, Jacquie Feuerborn

CODEE Journal

How does a lie spread through a community? The purpose of this paper is two-fold: to provide an educational tool for teaching Ordinary Differential Equations (ODEs) and sensitivity analysis through a culturally relevant topic (fake news), and to examine the social justice implications of misinformation. Under the assumption that people are susceptible to, can be infected with, and recover from a lie, we model the spread of false information with the classic Susceptible-Infected-Recovered (SIR) model. We develop a system of ODEs with lie-dependent parameter values to examine the pervasiveness of a lie through a community.

The model presents the opportunity …

Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

CODEE Journal

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.

On The Removal Of Motivation And Structural Barriers In The Classroom And Across The Mathematics Curriculum, Benjamin Wiles, Chantal Levesque-Bristol

IMPACT Presentations

Presentation at the research roundtable discussion at the 2018 Critical Issues in Math Education Workshop, Mathematical Sciences Research Institute, in Berkeley, CA.

Presents data on the ability of active learning methods to impact motivation and promote learning outcomes in mathematics courses.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

How Does The Structure Of A College Chemistry Examination Affect Pedagogy, Rajeev R. Pandey, John Mayberry, Jace Hargis

College of the Pacific Faculty Articles

This study examines variations of assessment and connections to active learning methods, which may enhance both the accuracy of assessment, engagement and retention. Correlation data relating instruction and assessment in a multiple dimensions are presented. Multiple choice (MC) and free response (FR) exams were provided and students were also given the option to provide FR answers to the MC items. This study suggests there is little overall difference in mean or median student scores on the MC vs. FR portions of the exam, but that there is some evidence to believe that student scores on MC portions are more variable …

Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Engineering education is facing many challenges: a decline in core mathematical skills; lowering entry requirements; and the diversity of the student cohort. One approach to confronting these challenges is to make subject content appropriate to the communication styles of today’s student. To achieve this, a pedagogical shift from the traditional hierarchical approach to learning to one that embraces the use of technology as a tool to enhance the student learning experience is required. By including the student as co-creator of course content, a greater sense of engagement is achieved and a change to one where students become agents of their …

Work In Progress: Online Resource Platform For Mathematics Education, Marisa Llorens, Edmund Nevin, Eileen Mageean

Conference papers

Mathematics is intrinsic to engineering and as such plays an integral role in the education of engineers. New challenges are being faced in higher education particularly in the areas of student motivation, engagement and attainment. As a result mathematics is often the focus of engineering education research. Traditional methods of delivery such as lectures and tutorials need to evolve to counter these challenges with new pedagogical approaches explored including the use of new technologies. Today’s students are immersed in an increasingly technological world and are willing to adapt to new technological advances. This paper describes a study being undertaken in …

Promoting Active Studying: The Study Challenge, Christopher K. Storm, Salvatore Petrilli, Susan Petry

Journal of Humanistic Mathematics

We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.