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Gordon, Sheldon P.; Gordon, Florence S. – PRIMUS, 2023
This article makes a case for introducing moving averages into introductory statistics courses and contemporary modeling/data-based courses in college algebra and precalculus. The authors examine a variety of aspects of moving averages and draw parallels between them and similar topics in calculus, differential equations, and linear algebra. The…
Descriptors: College Mathematics, Introductory Courses, Statistics Education, Algebra
Glassmeyer, David – PRIMUS, 2023
This article presents a task providing college students opportunities to build on their high school knowledge of trigonometry to explore parametric equations and inverse trigonometric relationships within a contextual learning ladder problem.
Descriptors: Trigonometry, Equations (Mathematics), College Students, High Schools
Reed, Zackery; Tallman, Michael A.; Oehrtman, Michael; Carlson, Marilyn P. – PRIMUS, 2022
We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…
Descriptors: Calculus, College Mathematics, Mathematical Logic, Mathematics Instruction
Reed, Zackery; Tallman, Michael A.; Oehrtman, Michael – PRIMUS, 2023
We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…
Descriptors: Mathematics Instruction, Calculus, Mathematical Concepts, Concept Formation
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
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
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
Cook, S. A.; Hartman, J.; Pierce, P. B.; Seaders, N. S. – PRIMUS, 2017
As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…
Descriptors: Mathematics, Mathematics Teachers, Algebra, Problem Solving
Selby, Christina – PRIMUS, 2016
Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Algebra
Zandieh, Michelle; Wawro, Megan; Rasmussen, Chris – PRIMUS, 2017
In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…
Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education
Andrews-Larson, Christine – PRIMUS, 2015
There is a long-standing tradition in mathematics education to look to history to inform instruction. An historical analysis of the genesis of a mathematical idea offers insight into: (i) the contexts that give rise to a need for a mathematical construct; (ii) the ways in which available tools might shape the development of that mathematical idea;…
Descriptors: Algebra, Mathematics Instruction, Teaching Methods, History
Slavit, David; Lesseig, Kristin – PRIMUS, 2017
Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…
Descriptors: Inquiry, Mathematics Instruction, Mathematics Education, Teacher Education
Pankavich, Stephen; Swanson, Rebecca – PRIMUS, 2015
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…
Descriptors: Factor Analysis, Mathematics Instruction, College Mathematics, Algebra
Sylvestre, Jeremy – PRIMUS, 2014
This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…
Descriptors: Problem Based Learning, Matrices, Algebra, Mathematical Concepts
Cook, John Paul – PRIMUS, 2015
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
Descriptors: Mathematics Instruction, Liberal Arts, College Mathematics, Undergraduate Study