PRIMUS

Extended Calculus Using Standards-Based Grading: A Case Study This is a case study of a two-semester Extended Calculus course that utilizes standards-based grading. The course integrates Intermediate Algebra, College Algebra, Pre-calculus, and Calculus I, mak...

New Release: "Extended Calculus Using Standards-Based Grading: A Case Study" by Szanizslo & Van Sickle about persistence in and after a course without prerequisites.

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Fitting Models to Data as an Application of Optimization in Calculus The teaching and learning of calculus is enhanced by applications to real-world problems. The topic of optimization (finding the maximum or minimum of a function) is a place where many calculus ins...

New Release: "Fitting Models to Data as an Application of Optimization in Calculus" by Brown, Shea & Harrington about how fitting a model to data as an application of optimization techniques in single/multivariable calculus classes.

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Instructional Design of an Online Upper-Level Undergraduate Geometry Course Using Hands-On Pedagogy This article describes the design and implementation of an upper-level undergraduate geometry course at a Canadian university, employing hands-on pedagogy through interactive online workshops. Thes...

New Release: "Instructional Design of an Online Upper-Level Undergraduate Geometry Course Using Hands-On Pedagogy" by Shi & Shahbazi about tangible activities and interactive engagement.

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Capstone Studies on Roots of Hyperbolic Numbers To help students develop a more creative and inquisitive mathematical mindset, we present capstone-style explorations on finding roots of hyperbolic numbers, a generalization of the complex numbers...

New Release: "Capstone Studies on Roots of Hyperbolic Numbers" by Easley & Shipman about helping students develop a more creative and inquisitive mathematical mindset with a capstone-style exploration of a generalization of complex numbers.

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Game-Based Learning in an Introduction to Mathematics of Computer Science Course: A Case Study Utilizing active learning, especially game- based learning, within a mathematics classroom can help increase retention, motivation, and overall positive emotions about mathematics. This article pre...

New Release: "Game-Based Learning in an Introduction to Mathematics of Computer Science Course: A Case Study" by S. Johnson about in-class learning activities based on popular card games.

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An Initial Study of the Success of a Winter Break Calculus 1 Course In an effort to keep students on track in their degree programs, the Department of Applied Mathematics at the University of Colorado Boulder offers a Winter Break Calculus 1 course for students who...

New Release: "An Initial Study of the Success of a Winter Break Calculus 1 Course" by Benim & Chang about an effort to keep students on track in their degree programs.

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Inspiring Linear Algebra Topics Using Radiography and Tomography In this paper, we describe how we use the medical imaging processes of radiography and tomography to motivate concepts in an introductory linear algebra course.

"Inspiring Linear Algebra Topics Using Radiography and Tomography" by Snipes, Moon & Asaki about using medical imaging processes to motivate concepts in an introductory linear algebra course.

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A Blended Teaching Sequence for Introducing Eigentheory in a Large University Class We present the design and implementation of a teaching sequence on eigentheory that aims at encouraging at facilitating students’ active participation in a class attended by a high number of studen...

"A Blended Teaching Sequence for Introducing Eigentheory in a Large University Class" by Piroi & Cattabriga about how the use of the online noticing board Padlet facilitates the implementation of activities in small groups.

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An Inquiry-Oriented Approach to Determinants In introductory linear algebra classrooms, determinants are often taught in a formulaic way that obscures their rich connections to graphical interpretations of linear transformations. As an altern...

"An Inquiry-Oriented Approach to Determinants" by Mauntel, Wawro & Plaxco about an innovative task sequence exploring the determinant conceptualized as a measure of the distortion of space.

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An Application Approach to Teaching Linear Algebra This paper shares insights and experiences in developing and teaching a first-year applied linear algebra course. In addition to incorporating innovative pedagogical techniques like active and inqu...

"An Application Approach to Teaching Linear Algebra" by Harsy & Smith about a first-year applied linear algebra course with applications such as computer graphics and sports analytics.

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Inquiry-Based Linear Algebra Teaching and Learning in a Flipped Classroom Framework: A Case Study Flipped Classroom (FC) approaches, which utilize video distribution via modern internet platforms, have recently gained interest as a pedagogical framework. Inquiry Based Mathematics Education (IBM...

"Inquiry-Based Linear Algebra Teaching and Learning in a Flipped Classroom Framework: A Case Study" by Fredriksen, Rebenda, Rensaa & Petersen about a practical combination of introductory videos and inquiry-based activities for stimulating students’ exploration.

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Problem-Solving Before Instruction: A Case Study of a Matrix Theory Course The paper describes a matrix theory course that was taught using Problem-Solving before Instruction (PS-I) pedagogy. At the beginning of each course week, homework was explained but not solved. The...

"Problem-Solving Before Instruction: A Case Study of a Matrix Theory Course" by Berman, Mahagna, Ram & Wolf about analyzing the impacts of a PS-I course.

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Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics Linear algebra is one of the service mathematics courses that students in many programs take as part of their undergraduate study. Previous studies indicate that linear algebra courses are often ch...

"Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics" by Farzad Radmehr about analyzing digital resources for learning eigentheory.

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The Power of Randomly Concrete Examples and Numerical Demonstrations Householder reflector is a must-taught special unitary matrix in numerical linear algebra. It has plentiful theoretical as well as numerical properties, and it plays a significant role in practical...

"The Power of Randomly Concrete Examples and Numerical Demonstrations" by Yunkai Zhou about Householder reflectors as the linking thread to deriving needed formulas, avoiding numerical cancellation errors, and implementing efficient code.

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The Art of Linear Algebra All teachers know the power of “visual understanding” and the literature on this topic is overwhelming. In this article, we focus on the visual image of linear algebra and elaborate on two related ...

"The Art of Linear Algebra" by Strang, Hiranabe & Fernandes about insightful but perhaps less well known visual images of linear algebra.

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Teaching Matrix Multiplication with Impactful and Productive Meaning What is the meaning of matrix multiplication? In this article, I outline a sequence of lessons for an introductory linear algebra course to teach matrix multiplication with impactful and productive...

"Teaching Matrix Multiplication with Impactful and Productive Meaning" by Jeffrey S. Meyer about developing core mathematical mental actions such as meaning-making, symbolizing, interpreting, and justifying.

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A Student-Centered Lesson on Eigenvalues and Eigenvectors Informed by Harel's DNR theoretical framework, this paper describes the design, incorporation, and analysis of two teaching and learning strategies into a particular lesson on eigentheory. The stud...

"A Student-Centered Lesson on Eigenvalues and Eigenvectors" by McDonald, Stewart & Harel about a blended undergraduate–graduate course using a digital worksheet with interactive figures and encouraging student questions.

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Analogy and Generalization as a Driving Force of Learning Mathematics – the Case of a Matrix Analog of a Zero of a Polynomial The concepts of polynomials and matrices essentially expand and enhance the elementary arithmetic of numbers. Once introduced, polynomials and matrices open up new interesting mathematical challeng...

"Analogy and Generalization as a Driving Force of Learning Mathematics – the Case of a Matrix Analog of a Zero of a Polynomial" by D. Kobal about polynomials and matrices as expanding and enhancing the elementary arithmetic of numbers.

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Promoting Linear Algebraic Reasoning among Students: Affordances and Challenges As students transition from the mathematics they learn in school years, including their first-year calculus courses, to the first course in linear algebra, they experience discontinuities in their ...

"Promoting Linear Algebraic Reasoning among Students: Affordances and Challenges" by Gershon Harel about pedagogical approaches oriented within a particular theoretical framework for the learning and teaching of mathematics.

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Linear Algebra Education: An International Perspective This editorial presents the special issue titled Linear Algebra Education: An International Perspective. We highlight the significant role of linear algebra in undergraduate mathematics curricula a...

"Linear Algebra Education: An International Perspective" by Cronin, McDonald, Quilan, Stewart & Strong. This editorial gives an overview of the Special Issue.

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PRIMUS Teaching Linear Algebra: An International Perspective. Volume 35, Issue 9-10 of PRIMUS

New Release: Volume 35.9-10! This is a special issue on Teaching Linear Algebra: An International Perspective, guest edited by Cronin, McDonald, Quilan, Stewart & Strong.

@joinmaa.bsky.social members always have access to PRIMUS through the member library.

www.tandfonline.com/toc/upri20/3...

Humanizing Defining in Mathematics with Sandwiches This paper discusses multiple versions of an activity in which participants create, discuss, and analyze possible definitions of the term “sandwich.” This activity has helped us humanize mathematic...

New Release: "Humanizing Defining in Mathematics with Sandwiches" by @thewordninjabk.bsky.social @drew-lewis.com @sbagley.bsky.social Bockting-Conrad, Ho, Libertini, Owens, Pilgrim, @matthematics.com & @solidangles.bsky.social about students writing definitions.

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Improving Collegiate Mathematics Teaching and Learning Through SoTL Published in PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies (Ahead of Print, 2025)

My (first!) new paper published in PRIMUS is joint work with Jackie Dewar of Loyola Marymount and Megan Breit-Goodwin of Anoka-Ramsey CC. We provide results and analysis of a survey of SOTL practitioners in mathematics. #MetaMath
doi.org/10.1080/1051...

Volume 35.8 was initially listed inaccurately as a special issue on Linear Algebra. That special issue is coming soon.

Painting the In-Betweenness and Squishing Circles: Learning Linear Algebra In this paper, we share two activities: one focused on the ideas of linear independence, basis, and span; and a second focused on eigenvalues and eigenvectors. These activities engaged students wit...

"Painting the In-Betweenness and Squishing Circles: Learning Linear Algebra" by Soto & Armbruster about two activities: one focused on the ideas of linear independence, basis, and span; and a second focused on eigenvalues and eigenvectors.

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Uplifting Students’ Stories: Meaningful Implementation of Mathematics Autobiographies in College Mathematics Courses Mathematics autobiographies have been implemented as assignments for students to write about their previous mathematical experiences. This paper explores a meaningful and more advanced implementati...

"Uplifting Students’ Stories: Meaningful Implementation of Mathematics Autobiographies in College Mathematics Courses" by Raygoza & Cawley about an advanced implementation of the mathematics autobiography assignment.

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Investigating Grade Distributions in the Calculus Sequence This study examines grade distributions and factors related to student performance in the calculus sequence at the University of Hartford, a private, liberal arts institution. Using data collected ...

"Investigating Grade Distributions in the Calculus Sequence" by Kmail & Rabideau about factors related to student performance in the calculus sequence.

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From Guided to Guiding: Optimizing Note-Taking Scaffolds with Universal Design for Learning Improving learning in postsecondary mathematics courses is of significant importance to reduce barriers to undergraduate degree completion. This article shares development work identifying ways tha...

"From Guided to Guiding: Optimizing Note-Taking Scaffolds with Universal Design for Learning" by Bertrand, Keazer & Phaiah about improving learner agency by transforming guided notes into an enhanced, UDL-aligned version called guiding notes.

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Supporting Student Appreciation of Inquiry-Based Calculus Active learning can contribute to greater student performance in undergraduate STEM. However, students sometimes resist active learning techniques when classroom norms do not align with their learn...

"Supporting Student Appreciation of Inquiry-Based Calculus" by Heacock, Bubp & Hallman-Thrasher about four assignments used in an undergraduate inquiry-based calculus course designed to foster student buy-in.

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Real Analysis 2nd Chance – Support Project to Overcome the Transition to Advanced Mathematics The transition from school to university mathematics is challenging for students in many ways. The project Real Analysis 2nd Chance is based on Just-in-Time-Teaching (JiTT) principles and aims at s...

"Real Analysis 2nd Chance – Support Project to Overcome the Transition to Advanced Mathematics" by Bertram, Rolka & Geisler about Just-in-Time-Teaching (JiTT) principles and student experiences with them.

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