Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

Students' use of problem posing is an assessment tool for evaluating mathematical creativity, and it plays a substantial role in creative tasks. Integrating problem-posing tasks into a curriculum is beneficial for teaching and learning mathematics. The Photo-Math Project is an example of problem posing in terms of generating new problems. This…

We study the augmented reality sandbox (ARSB) as an embodied learning environment to foster meaning making in the context of bivariable calculus. We present the case of Tiago, a first-year bachelor chemistry student, performing a series of tasks based on embodied design, including perception-based, action-based and incorporation-based tasks.…

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…

The learning of calculus concepts is considered challenging for students. This claim is actual for calculus in general and for specific concepts in particular. In this paper, we focus on the concept of the inflection point. We argue that one of the roots of this problem is the lack of a useful and productive meaning of the concept--the…

The current study aims to explore the impact of the two-column format in writing simple mathematical arguments. That is to say, a structured method of presenting a mathematical proof or argument by using a tabular layout with two columns. The underlying goal of the research reported in this paper is to inform understanding of how to effectively…

In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model…

Common student errors and misconceptions can be addressed through the method of classroom voting, in which the instructor presents a multiple-choice question to the class, and after a few minutes for consideration and small-group discussion, each student votes on the correct answer, using a clicker or a phone. If a large number of students have…

The paper presents results of two case studies with undergraduate students majoring in applied mathematics and engineering. The first case study deals with students' preferences for and difficulties with application problems and pure mathematics questions in their courses. The students were majoring in applied mathematics and taking a second-year…

Previous studies have explored students' understanding of the relationship between definite integrals and areas under curves, but not their metacognitive experiences and skills while solving such problems. This paper explores students' mathematical performance, metacognitive experiences and metacognitive skills when solving integral-area tasks by…

The goal of our study is to take what previous research has reported as the benefit of pairing mathematics courses with writing across the curriculum initiatives and the inclusion of writing to learn activities, specifically journaling in calculus courses, and expand upon notions of student perceptions of the benefits of writing in math. Thus, the…

A set of weekly optional online quizzes was used with 104 students on a Multivariable Calculus course (MC), via the Moodle online system. These quizzes contributed a maximum of two extra points, and this was awarded if the student scored more than 9 points (out of 20) on the exam. All the students got the same questions and could resubmit the…

Classroom flipping is the practice of moving new content instruction out of class time, usually packaging it as online videos and reading assignments for students to cover on their own, and devoting in-class time to interactive engagement activities. Flipping has garnered a large amount of hype from the popular education media and has been adopted…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…

This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…