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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

Klima, V. – PRIMUS, 2019

As teachers of mathematics we encourage our students to ask good questions, and we strive to help our students find and understand answers to these questions. This journey can be made more meaningful if students conclude by reflecting on their learning process. If we find careful questioning and reflection important, we should include such…

Descriptors: Homework, Mathematics Instruction, College Mathematics, Color

Jordan, Daniel R. – PRIMUS, 2019

Workshops can be a powerful tool to support students as they develop proof-writing skills. In a workshop, each student writes a proof, provides feedback on other students' work, and reflects on critiques from peers. Workshops can be used in any class that emphasizes writing proofs or other forms of mathematical writing. They are highly efficient…

Descriptors: Workshops, Mathematical Logic, Mathematics Skills, Mathematics Instruction

Sears, Ruthmae; Kersaint, Gladis; Burgos, Fernando; Wooten, Rebecca – PRIMUS, 2019

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…

Descriptors: Middle School Mathematics, Preservice Teachers, Knowledge Level, Mathematics Education

Pinter, Mike; Jones, Linda – PRIMUS, 2019

We describe a successful collaboration between mathematics and psychological science faculty members to create a learning community for our students that linked sections of introductory mathematical reasoning and psychological science courses. The students in our learning community were in their second or third semester. The learning community is…

Descriptors: Mathematics Instruction, College Mathematics, Interdisciplinary Approach, College Faculty

Cardetti, Fabiana; LeMay, Steven – PRIMUS, 2019

In this article we present the results of a study focused on engaging students in argumentation to support their growth as mathematical learners, which in turn strengthens their science learning experiences. We identify five argumentation categories that promote the learning of argumentation skills and enrich mathematical reasoning at the…

Descriptors: Persuasive Discourse, Abstract Reasoning, Mathematics Skills, Science Process Skills

Stange, Katherine E. – PRIMUS, 2018

Standards-based grading, in which grading should be designed to communicate to students their current level of mastery with regards to well-articulated standards, is becoming popular at the K-12 level. As yet, the literature addressing standards-based grading at the university level is scarce. In this paper, I document my attempts to put into…

Descriptors: Academic Standards, Grading, Introductory Courses, College Mathematics

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

Williams, Kristopher – PRIMUS, 2018

This article describes a system of specifications-based grading used in an introduction to proofs course. The system was introduced to address two issues that arose in the course: how to spend less time grading and how to encourage use of feedback. We describe the implementation of the system and the results on grading and on students.

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Validity

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

Shannon, Kathleen – PRIMUS, 2018

This paper describes, as an alternative to the Moore Method or a purely flipped classroom, a student-driven, textbook-supported method for teaching that allows movement through the standard course material with differing depths, but the same pace. This method, which includes a combination of board work followed by class discussion, on-demand brief…

Descriptors: Mathematics Instruction, Textbooks, Mathematics, Portfolio Assessment

Pourciau, Bruce – PRIMUS, 2018

In a first proof-oriented mathematics course, students will often ask questions--for example, "What is this problem asking me to do?" or "What would a proof of this even look like"--that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms--such as "p…

Descriptors: Mathematical Logic, Problem Solving, Undergraduate Students, Majors (Students)

Herrera, Christine A.; McCabe, Terrance; Strictland, Sharon; White, Alexander – PRIMUS, 2018

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Mathematics Skills

El Turkey, Houssein; Tang, Gail; Savic, Milos; Karakok, Gulden; Cilli-Turner, Emily; Plaxco, David – PRIMUS, 2018

A growing body of mathematics education research points to the importance of fostering students' mathematical creativity in undergraduate mathematics courses. However, there are not many research-based instructional practices that aim to accomplish this task. Our research group has been working to address this issue and created a formative…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Creativity