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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

Cline, K.; Fasteen, J.; Francis, A.; Sullivan, E.; Wendt, T. – PRIMUS, 2020

We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, but we also discuss several alternate types of projects. We describe a model that incorporates projects at all stages across the undergraduate mathematics…

Descriptors: Student Projects, Mathematics Curriculum, Mathematics Activities, Mathematics Skills

Capaldi, Mindy – PRIMUS, 2020

Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors' lecture notes, and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors' Calculus I lecture notes are…

Descriptors: Mathematics Instruction, College Mathematics, Definitions, Textbooks

Calkins, Susanna; Grannan, Sharisse; Siefken, Jason – PRIMUS, 2020

This study explores the impact of Peer-Assisted Reflection (PAR), a structured active learning strategy that emphasizes peer feedback and reflection, on students' perceptions of mathematical thinking, and of the roles their peers and their instructors play in their learning process. This study also examines the impact of PAR on the students'…

Descriptors: Reflection, Peer Influence, Active Learning, Feedback (Response)

Robinson, Samantha – PRIMUS, 2020

This quasi-experimental, pre-post study with non-equivalent comparison groups explores the potential for resequencing of course content to affect positive change in an undergraduate, introductory statistics course at a mid-sized, flagship university that is located in a southern state. Quantitative analyses suggest that the implementation of…

Descriptors: Sequential Approach, Instructional Effectiveness, Introductory Courses, Statistics

Das, Tushar; George, Whitney; Warnberg, Nathan – PRIMUS, 2020

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

Descriptors: Mathematics Education, Mathematical Concepts, Symbols (Mathematics), College Mathematics

Boyce, Steven; O'Halloran, Joyce – PRIMUS, 2020

We describe the process of adjusting the balance between computer-based learning and peer interaction in a college algebra course. In our first experimental class, students used the adaptive-learning program ALEKS within an emporium-style format. Comparing student performance in the emporium format class with that in a traditional lecture format…

Descriptors: Active Learning, College Students, Algebra, Mathematics Instruction

Coggins, Porter E., III; Glatzer, Tim – PRIMUS, 2020

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

Descriptors: Mathematics Instruction, Matrices, Technology, Addition

Bruder, Andrea; Kohler, Brynja R. – PRIMUS, 2020

Although modeling is an integral process in applied mathematics, students rarely encounter modeling opportunities in their calculus courses. We introduce a laboratory experience as a starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients…

Descriptors: Calculus, Mathematics Instruction, Climate, Food

Seager, Suzanne – PRIMUS, 2020

For many of my students, Real Analysis I is the first, and only, analysis course they will ever take, and these students tend to be overwhelmed by epsilon-delta proofs. To help them I reordered Real Analysis I to start with an "Analysis Boot Camp" in the first 2 weeks of class, which focuses on working with inequalities, absolute value,…

Descriptors: Mathematics Instruction, Teaching Methods, Mathematical Concepts, Concept Formation

Yao, Guangming; Black, Kelly; Ramsdell, Michael; Skufca, Joseph – PRIMUS, 2020

Improving student success rates in introductory calculus and physics courses is critically important for our students' path in STEM fields. Many of the students who have an intuitive understanding of physics fail calculus and are pushed to delay or drop their majors in technical fields. One way of addressing this issue is by adopting a program…

Descriptors: STEM Education, Undergraduate Students, Success, Mathematics Achievement

Reinholz, Daniel L. – PRIMUS, 2020

This article describes an inquiry-oriented real analysis classroom in which students were guided to discover mathematics for themselves. To support student inquiry, the framework of "five practices" from K-12 education was used. To illustrate this framework, two case examples are given from actual discussions that took place in this…

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

Bossé, Michael J.; Cook, William J.; Castonguay, Joseph M. – PRIMUS, 2020

Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Educational Technology

Flórez, Rigoberto; Mukherjee, Antara – PRIMUS, 2020

We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

Descriptors: Mathematics Instruction, College Mathematics, Secondary School Mathematics, Undergraduate Study

Peters, Travis; Johnston, Elgin; Bolles, Heather; Ogilvie, Craig; Knaub, Alexis; Holme, Thomas – PRIMUS, 2020

Team-Based Learning (TBL) uses a flipped classroom model and involves students working collaboratively in small groups, with peer assessments to promote group accountability. We implemented TBL in Calculus I in both large (N [tilde] 150) and small (N [tilde] 35) class settings. We investigated the impact of this form of instruction over two…

Descriptors: Teamwork, Mathematics Instruction, Homework, Video Technology