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Klima, V. – PRIMUS, 2019

As teachers of mathematics we encourage our students to ask good questions, and we strive to help our students find and understand answers to these questions. This journey can be made more meaningful if students conclude by reflecting on their learning process. If we find careful questioning and reflection important, we should include such…

Descriptors: Homework, Mathematics Instruction, College Mathematics, Color

Isihara, Paul; Congdon, Elisabeth; Perciante, Terry – PRIMUS, 2018

Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from…

Descriptors: Undergraduate Study, College Mathematics, Mathematics Instruction, Least Squares Statistics

Combs, Randy; Bingham, Teri; Roper, Taylor – PRIMUS, 2018

In this paper I discuss my experience in using the inverted classroom structure to teach a proof-based, upper level Advanced Calculus course. The structure of the inverted classroom model allows students to begin learning the new mathematics prior to the class meeting. By front-loading learning of new concepts, students can use valuable class time…

Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic

Williams, Kristopher – PRIMUS, 2018

This article describes a system of specifications-based grading used in an introduction to proofs course. The system was introduced to address two issues that arose in the course: how to spend less time grading and how to encourage use of feedback. We describe the implementation of the system and the results on grading and on students.

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Validity

Hendrickson, Anders O. F. – PRIMUS, 2018

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…

Descriptors: Mathematical Concepts, Mathematics Instruction, College Mathematics, Algebra

Shannon, Kathleen – PRIMUS, 2018

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

Descriptors: Mathematics Instruction, Textbooks, Mathematics, Portfolio Assessment

Herrera, Christine A.; McCabe, Terrance; Strictland, Sharon; White, Alexander – PRIMUS, 2018

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Mathematics Skills

El Turkey, Houssein; Tang, Gail; Savic, Milos; Karakok, Gulden; Cilli-Turner, Emily; Plaxco, David – PRIMUS, 2018

A growing body of mathematics education research points to the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Creativity

Dorée, Suzanne Ingrid – PRIMUS, 2017

How can we teach inquiry? In this paper, I offer practical techniques for teaching inquiry effectively using activities built from routine textbook exercises with minimal advanced preparation, including rephrasing exercises as questions, creating activities that inspire students to make conjectures, and asking for counterexamples to reasonable,…

Descriptors: Inquiry, Mathematics Instruction, Learning Activities, Problem Solving

Robertson, Robert L. – PRIMUS, 2017

Calculating Laplace transforms from the definition often requires tedious integrations. This paper provides an integration-free technique for calculating Laplace transforms of many familiar functions. It also shows how the technique can be applied to probability theory.

Descriptors: Mathematics Instruction, Teaching Methods, Probability, Computation

Garcia, Stephan Ramon – PRIMUS, 2017

A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by…

Descriptors: Algebra, Mathematics Instruction, Numbers, College Mathematics

Howell, Russell W.; Schrohe, Elmar – PRIMUS, 2017

Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Mathematical Logic

Newton, Paul K. – PRIMUS, 2017

The subject of fluid mechanics is a rich, vibrant, and rapidly developing branch of applied mathematics. Historically, it has developed hand-in-hand with the elegant subject of complex variable theory. The Westmont College NSF-sponsored workshop on the revitalization of complex variable theory in the undergraduate curriculum focused partly on…

Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Mechanics (Physics)

Bolt, Michael – PRIMUS, 2017

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Physics

Garcia, Stephan Ramon; Ross, William T. – PRIMUS, 2017

We hope to initiate a discussion about various methods for introducing Cauchy's Theorem. Although Cauchy's Theorem is the fundamental theorem upon which complex analysis is based, there is no "standard approach." The appropriate choice depends upon the prerequisites for the course and the level of rigor intended. Common methods include…

Descriptors: Mathematics Instruction, College Mathematics, Mathematical Logic, Undergraduate Study