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Martin, Taylor E. – PRIMUS, 2019

My goal in crafting homework in calculus is twofold: to provide scaffolding for students to develop a theoretical understanding of calculus concepts and to incorporate good mathematical exposition, including justification and proof when appropriate. I achieve these goals by creating weekly homework sets that students work on in groups of three or…

Descriptors: Calculus, Homework, Mathematics Instruction, Mathematical Concepts

Dunmyre, Justin R. – PRIMUS, 2019

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

Descriptors: Educational Technology, Technology Uses in Education, Homework, Video Technology

OShaughnessy, J. – PRIMUS, 2019

This paper investigates the advantages of using a two-step homework system. First, technology is used to collect and grade traditional homework. Then, students are expected to present and explain problems from their assignments in class. Several versions of implementation are discussed for different course levels and sizes. Through these methods,…

Descriptors: Mathematics Instruction, College Mathematics, Homework, Educational Technology

Melkonian, Vardges – PRIMUS, 2019

This paper discusses a game that can be used for introducing the binary representation of integers in an interactive and fun environment. The game is introduced in the way it is presented in an undergraduate Discrete Mathematics class. Variations of the game are discussed, particularly its extension to base-three representation of integers. It is…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Educational Games

Rasmussen, Chris; Dunmyre, Justin; Fortune, Nicholas; Keene, Karen – PRIMUS, 2019

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Descriptors: Mathematical Models, Teaching Methods, Mathematics Instruction, Inquiry

Singh, Satyanand – PRIMUS, 2019

We show that the total distance traveled by an under-damped oscillating spring mass system with sinusoidal displacement results in a nice, closed-form expression.

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

Greer, M. L. – PRIMUS, 2019

"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…

Descriptors: Interdisciplinary Approach, Inclusion, Mathematics Skills, Calculus

Dray, Tevian; Gire, Elizabeth; Kustusch, Mary Bridget; Manogue, Corinne A.; Roundy, David – PRIMUS, 2019

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…

Descriptors: Calculus, Physics, Majors (Students), Science Instruction

Bliss, Karen M.; Galluzzo, Benjamin J.; Kavanagh, Kathleen R.; Skufa, Joseph D. – PRIMUS, 2019

To promote and facilitate the teaching of math modeling throughout the K-16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the…

Descriptors: Mathematical Models, Undergraduate Study, Mathematics Instruction, Elementary Secondary Education

Ludwig, Patrice; Tongen, Anthony; Walton, Brian – PRIMUS, 2018

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Descriptors: Mathematics Instruction, Science Instruction, Case Studies, Interdisciplinary Approach

Lynch, Frank H.; Page, Breeanna S. – PRIMUS, 2018

This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show "Car Talk," hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1…

Descriptors: Calculus, Problem Solving, Word Problems (Mathematics), Mathematics Instruction

AsKew, A.; Kennedy, K.; Klima, V. – PRIMUS, 2018

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Descriptors: Arithmetic, Music Theory, Correlation, Numbers

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

Berger, Lisa – PRIMUS, 2018

In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers' understanding of mathematical definitions. We discuss teachers' work in developing definitions for students at various…

Descriptors: Mathematics Instruction, Mathematical Concepts, Definitions, Preservice Teachers

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