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Soosloff, Elisa; Huey, Maryann; Alexander, Daniel S. – PRIMUS, 2023
In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…
Descriptors: Mathematics Instruction, Visual Aids, Prior Learning, Teaching Methods
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
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)
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
Engelke Infante, N. – PRIMUS, 2021
In calculus, related rates problems are some of the most difficult for students to master. This is due, in part, to the nature of the problems, which require constructing a nuanced mental model and a solid understanding of the function. Many textbooks present a procedure for their solution that is unlike how experts approach the problem and elide…
Descriptors: Mathematics Instruction, College Mathematics, Calculus, Schemata (Cognition)
Adiredja, Aditya P. – PRIMUS, 2021
The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…
Descriptors: Mathematics Instruction, College Mathematics, Teaching Methods, Calculus
Carlisle, Sylvia – PRIMUS, 2020
Specifications grading is a version of mastery grading distinguished by giving students clear specifications that their work must meet, and grading most things pass/fail based on those specifications. Mastery grading systems can get quite elaborate, with hierarchies of objectives and various systems for rewriting and retesting. In this article I…
Descriptors: Grading, Standards, Mathematics Instruction, Calculus
Weir, Rachel J. – PRIMUS, 2020
Like many math educators, I have spent much of my career bound to traditional methods of instruction and assessment. In recent years, motivated by a growing understanding that such approaches may not result in equitable or inclusive classroom environments, my teaching philosophy has shifted radically. In this article, I describe how I transformed…
Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Student Centered Learning
Durst, Susan; Kaschner, Scott R. – PRIMUS, 2020
We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…
Descriptors: College Mathematics, Mathematics Instruction, Undergraduate Study, Misconceptions
Breen, Sinéad; O'Shea, Ann – PRIMUS, 2019
Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…
Descriptors: Undergraduate Students, Mathematics Instruction, College Mathematics, Learning Activities
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
Buell, Catherine A.; Greenstein, Steven; Wilstein, Zahava – PRIMUS, 2017
It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…
Descriptors: Inquiry, Active Learning, Mathematics, Mathematics Instruction
Greene, M.; von Renesse, C. – PRIMUS, 2017
This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks…
Descriptors: Mathematics Instruction, Learning Activities, Mathematics Activities, Inquiry
Rash, Agnes M.; Fillebrown, Sandra – PRIMUS, 2016
This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed "math beauty" courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to…
Descriptors: Mathematics Curriculum, General Education, Mathematics Instruction, Mathematics Education