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Dawkins, Paul Christian; Zazkis, Dov; Cook, John Paul – PRIMUS, 2022
Many mathematics departments have transition to proof (TTP) courses, which prepare undergraduate students for proof-oriented mathematics. Here we discuss how common TTP textbooks connect three topics ubiquitous to such courses: logic, proof techniques, and sets. In particular, we were motivated by recent research showing that focusing on sets is…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Undergraduate Students
Koss, Lorelei – PRIMUS, 2022
In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…
Descriptors: Mathematics Instruction, Learning Activities, Mathematics Tests, Teamwork
Boudreaux, Gregory M.; Haugh, Janine; Johnson, Ed; Tinney, Laura; Whitlock, Cathy – PRIMUS, 2022
Several publishing companies now offer competing brands of online homework (OHW) software. Students rarely have a voice in choosing their required course materials, even though, ultimately, they will be asked to use and pay for these systems. In this study, Calculus I students each tested three different OHW systems. The students were then asked…
Descriptors: Mathematics Instruction, Calculus, Homework, Educational Technology
Grundmeier, T. A.; Retsek, D.; Berg, A.; Mann, S.; Hamlin Prieto, A. – PRIMUS, 2022
Students' proof abilities were explored in the context of an inquiry-based learning (IBL) approach to teaching an introductory proofs course. IBL is a teaching method that puts the responsibility for proof on students and focuses on student discussion and exploration. Data collected from each of the 70 participants included a portfolio consisting…
Descriptors: Mathematics Instruction, Inquiry, Validity, Mathematical Logic
DeOrsey, Philip; von Renesse, Christine – PRIMUS, 2022
We introduce a ruler and compass activity designed around Islamic Geometry and provide a detailed description of the various components of the activity along with ideas for students exhibitions in both digital and print form. In our experience, this activity helps students to "buy into" actively doing mathematics, making it an ideal…
Descriptors: Geometry, Mathematics Instruction, Learning Activities, Inquiry
Melhuish, K.; Lew, K.; Hicks, M. – PRIMUS, 2022
Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K-12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra…
Descriptors: Mathematics Instruction, Teaching Methods, Best Practices, Algebra
Kerrigan, John; Prendergast, Lydia – PRIMUS, 2022
As part of a departmental reform project, a large University converted a "Precalculus College Mathematics" lecture-based course for 97 students into an active learning flipped classroom for first-year engineering students. The curriculum was designed specifically to provide applications of pre-calculus in various engineering subjects.…
Descriptors: Flipped Classroom, Calculus, Mathematics Education, Engineering Education
Clement, Geoff; Swars Auslander, Susan – PRIMUS, 2022
This mixed-methods study examined prospective elementary teachers' (N = 32) mathematical knowledge and mathematics self-efficacy while learning about the Singapore Modeling Method in a university mathematics course. Pre- and post- quantitative data were collected via two content knowledge assessments and one belief survey, and qualitative data…
Descriptors: Preservice Teachers, Mathematics Education, Preservice Teacher Education, Student Attitudes
Hwang, Jihye; Castle, Sarah D.; Karunakaran, Shiv Smith – PRIMUS, 2022
Collegiate mathematics instructors are moving away from traditional lecture-based teaching practices to accommodate the pedagogies that support more active student learning. As part of the movement, groupwork has been increasingly implemented. At the same time, mathematics classrooms have become increasingly diverse and also in the distribution of…
Descriptors: College Faculty, Mathematics Teachers, College Mathematics, Teaching Methods
Álvarez, James A. M.; Kercher, Andrew; Turner, Kyle; Arnold, Elizabeth G.; Burroughs, Elizabeth A.; Fulton, Elizabeth W. – PRIMUS, 2022
We describe the design and implementation of lessons in undergraduate abstract algebra that integrate applications to teaching high school mathematics. Each lesson consists of a pre-activity, class activity, homework set, assessment questions and detailed instructor notes. The included applications intend to bridge advanced mathematics concepts to…
Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Algebra
Fulton, Elizabeth W.; Arnold, Elizabeth G.; Burroughs, Elizabeth A.; Álvarez, James A. M.; Kercher, Andrew; Turner, Kyle – PRIMUS, 2022
This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into…
Descriptors: High Schools, Secondary School Mathematics, Mathematics Instruction, Undergraduate Study
Dahma, Alfred M.; Long, Valerie N.; Flowers, Timothy B. – PRIMUS, 2022
This article describes the revision of a Business Calculus course at a medium-sized, northwestern university. The purpose of this manuscript is to describe the need for a redesign of the Business Calculus course, conversations among math and business faculty about the course changes, the development of the new course, and the addition of a…
Descriptors: Business Education, Calculus, Instructional Design, College Faculty
Moyer, Todd O. – PRIMUS, 2022
This article describes the application of technology to the van Hiele Model for Geometric Thought to increase the van Hiele levels in an undergraduate Euclidean geometry course. Following the model with activities and phase-based instruction, students showed significant gains in the van Hiele levels in five different sections over the course of…
Descriptors: College Mathematics, Mathematics Achievement, Geometry, Undergraduate Students
Pair, Jeffrey; Calva, Gabe – PRIMUS, 2022
For a semester within a transition-to-proof course, mathematics majors explored two famous conjectures: The Twin Primes Conjecture and the Collatz Conjecture. Students were scaffolded into exploring the conjectures through directed activities but were also expected to create their own methods of exploration. We documented students' experiences…
Descriptors: Undergraduate Students, College Mathematics, Majors (Students), Mathematics Skills
Frank, K.; Kolesnikov, A.; Wang, X. – PRIMUS, 2022
Placement policies are intended to match students with appropriate courses in order to improve student success, but how do you evaluate these policies? In this article, we evaluate four placement policies at Towson University by considering three categories of outcomes: long-term outcomes such as graduation and retention rates, short-term or…
Descriptors: Student Placement, Courses, School Policy, Program Effectiveness