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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

Palmer, Katrina; Bauldry, William; Bossé, Michael J.; Post, Jaehee – PRIMUS, 2022

Most any students can explain the meaning of "a[superscript b]", for "a" ? R and for "b" ? Z. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" ? R and for "c" ? Z. However, few may be able to explain "a[superscript di]" or…

Descriptors: Mathematics Instruction, Mathematical Concepts, Secondary School Mathematics, College Mathematics

Lucas, Krista L.; Lucas, Timothy A. – PRIMUS, 2022

It is increasingly important for mathematics students to engage in active learning along with discussion of material with their peers. "Slopes" is a mobile application designed to visualize solutions to differential equations and support active learning in the classroom. We implemented group activities using "Slopes" into an…

Descriptors: Mathematics Instruction, Equations (Mathematics), Active Learning, Computer Oriented Programs

Venkatesh, Anil; Bagley, Spencer – PRIMUS, 2022

To address a deteriorating classroom climate at the midpoint of a two-semester course sequence, we employed a novel intervention: reading a research manuscript together with students as an invitation to legitimate peripheral participation in scholarly reflection on teaching and learning. This intervention resolved many student complaints about the…

Descriptors: Classroom Environment, Intervention, Student Participation, Publications

Gaines, Benjamin – PRIMUS, 2022

In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts…

Descriptors: Introductory Courses, Mathematics Instruction, Cues, Writing (Composition)

Ledder, G.; Homp, M. – PRIMUS, 2022

The COVID-19 pandemic has made mathematical epidemiology a topic of critical importance, providing mathematics educators with an unparalleled opportunity. This opportunity is accompanied by a challenge: how do mathematics educators, some of whom have little personal experience with mathematical modeling, teach mathematical epidemiology to their…

Descriptors: COVID-19, Pandemics, Mathematics Instruction, Epidemiology

Rahmoeller, Margaret; Steinweg, J. Megan – PRIMUS, 2022

We explored the impact a new quantitative biology course for biology majors had on their ability and confidence to utilize hypothesis testing. Students currently in the quantitative biology course and the first cohort of students who took the course (currently seniors) were surveyed on ability and confidence regarding four types of hypothesis…

Descriptors: Biology, Science Instruction, Self Esteem, Student Attitudes

Bennoun, Steve – PRIMUS, 2022

Cornell University has long offered a Calculus for Life Sciences course. In this case study, we report on how a team of pure mathematicians has modernized both the content and teaching methods of this course. The content went from a standard calculus course with few genuine applications in the life sciences to a course focusing on dynamical…

Descriptors: Mathematics Instruction, Calculus, Biological Sciences, Interdisciplinary Approach

Ryu, Hwayeon; Zhu, Bin – PRIMUS, 2022

Biology students need analytical and critical thinking skills to analyze data and apply their knowledge to real-life situations. To meet this growing need while helping students to discover the relevance of learning through applications, we created an academic learning community (LC) between Ecology and Biostatistics courses. Selected case-studies…

Descriptors: Biology, Science Instruction, Statistics Education, Thinking Skills

Jungck, John R. – PRIMUS, 2022

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Models, Learning Modules