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Case, Joshua; Speer, Natasha – PRIMUS, 2021
In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…
Descriptors: Calculus, Mathematics Instruction, Logical Thinking, Teaching Methods
David, Erika J.; Hah Roh, Kyeong; Sellers, Morgan E. – PRIMUS, 2020
This paper offers instructional interventions designed to support undergraduate math students' understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students' understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are…
Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Students, Calculus
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
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
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
Swenson, Daniel – PRIMUS, 2015
We walk through a module intended for undergraduates in mathematics, with the focus of finding the best strategies for competing in the Showcase Showdown on the game show "The Price Is Right." Students should have completed one semester of calculus, as well as some probability. We also give numerous suggestions for further questions that…
Descriptors: Mathematics Instruction, Probability, Calculus, Undergraduate Students
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
Shipman, Barbara A. – PRIMUS, 2013
Traditional definitions, language, and visualizations of convergence and the Cauchy property of sequences convey a sense of the sequence as a potentially infinite process rather than an actually infinite object. This has a deep-rooted influence on how we think about and teach concepts on sequences, particularly in undergraduate calculus and…
Descriptors: College Mathematics, Mathematics Instruction, Mathematical Concepts, Undergraduate Study
Robertson, Robert L. – PRIMUS, 2013
The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)
Descriptors: Mathematics Instruction, College Mathematics, Validity, Mathematical Logic
Goins, Edray Herber; Washington, Talitha M. – PRIMUS, 2013
We discuss a general formula for the area of the surface that is generated by a graph [t[subscript 0], t[subscript 1] [right arrow] [the set of real numbers][superscript 2] sending t [maps to] (x(t), y(t)) revolved around a general line L : Ax + By = C. As a corollary, we obtain a formula for the area of the surface formed by revolving y = f(x)…
Descriptors: Mathematical Formulas, College Mathematics, Mathematics Instruction, Calculus
Shipman, Barbara A.; Shipman, Patrick D. – PRIMUS, 2013
We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more…
Descriptors: College Mathematics, Undergraduate Study, Mathematics Instruction, Misconceptions
Tesman, Barry – PRIMUS, 2012
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
Descriptors: Geometric Concepts, Mathematics Curriculum, Probability, Calculus
Beaver, Scott – PRIMUS, 2011
The Sequences and Series calculus course (S&S) can be structured to provide students with a unique opportunity to build their proofs skills prior to or concurrently with a bridge course. This article offers a framework for S&S which places logical reasoning on equal footing with content, by employing the theorems and convergence tests as axioms,…
Descriptors: Calculus, Mathematical Logic, Validity, College Freshmen
Lesser, Lawrence M.; Guthrie, Joe A. – PRIMUS, 2012
Undergraduate students who are pre-service teachers need to make connections between the college mathematics they are learning and the pre-college mathematics they will be teaching. Spanning a broad range of undergraduate curricula, this article describes useful lesser-known connections, explorations, and original proofs involving fractions. In…
Descriptors: Calculus, Mathematics Instruction, College Mathematics, Undergraduate Students
Cullinane, Michael J. – PRIMUS, 2011
Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key "stumbling blocks" for students as they attempt to make this transition? How do differences in faculty expectations for students…
Descriptors: Calculus, Mathematics, Mathematics Instruction, Mathematics Education
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