Background/purpose: This research is motivated by the difficulties often experienced by students in adapting to their first year of college, especially related to learning calculus. To address these difficulties, a solution needs to be found so that these problems can be resolved. One solution that is expected to yield optimal results in…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

In most mathematics textbooks, each lesson is followed by a set of homework problems in one of two ways -- blocked practice and mixed practice. Additionally, most mathematics textbooks rely on a common learning strategy called overlearning, that is, mastering a skill and continuing to practice this same skill. This study investigated the effects…

In an online asynchronous vector calculus course, we observed exam answers solved with a formula from online homework instead of the formula from lecture. Our exploratory study investigated (1) why students learned from homework instead of lecture for this topic and (2) their epistemological frames (e-frames) for lecture and homework. Per (1),…

There is a growing interest in using comparative judgement as a peer assessment tool involving students choosing the 'better' of two pieces of work. However, it has not been shown whether peer assessment through comparative judgement is effective for students' learning. To gain a better understanding of the comparative judgement process, we…

Many researchers have stressed the embodied nature of mathematical understanding. Here we explore how embodied knowledge may evolve as students learn a basic calculus concept: the rate of change. We examined undergraduate students with different levels of calculus knowledge working in pairs to model the rate of change in an everyday phenomenon.…

Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables.Motivated by the work of…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

Simon Fraser University in Vancouver, Canada offers two introductory calculus courses designed for students enrolled in science and engineering programs. Students identified as needing additional support based on their admission grades take the version of the course where students meet weekly for four hours instead of three. A new approach for the…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which…

It remains difficult to foster problem-solving and mathematical-reasoning capabilities in classrooms where students and teachers are accustomed to the more traditional forms of education. Several studies suggest that this difficulty might be related to the kind of knowledge students acquire in such environments, which could be fragmented and…

This paper presents preliminary hypotheses about the relationship between faculty goals for the introductory calculus-based physics course and their beliefs about student learning of problem solving. All faculties have problem solving as a major goal for their courses. There appears to be however, an instructional paradox. When discussing how…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…