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…

Transforming an observable phenomenon into a tractable model is a challenging process, from determining the appropriate modeling scale to making realistic simplifying assumptions. However, many modeling texts are anchored around problems that have already been synthesized into a digestible format, which inhibits an opportunity to engage students…

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced…

Background: Implementing research-based teaching practices has been repeatedly cited as an important factor for student success in university mathematics courses. Many research-based practices increase the amount of student-student and/or student-instructor interaction. However, some instructors are hesitant to implement such practices because…

Introductory courses in biology often lack sufficient emphasis on quantitative skills and interdisciplinary problem solving, leaving many students unprepared for more advanced biology coursework and hampering their ability to pursue biology research careers. MathBench Biology Modules were created to enhance the quantitative skills of biology…

Worked-examples have been established as an effective instructional format in problem-solving practices. However, less is known about variations in the use of worked examples across individuals at different stages in their learning process in student-centred learning contexts. This study investigates different profiles of students' learning…

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…

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…

Statistical modeling is a core component of statistical thinking and has been identified by several countries as a curricular goal for secondary education. However, many secondary teachers have minimal preparation for teaching this topic. The goal of this research study is to learn about teachers' perceptions of the role statistical models play in…

Learning by invention is an alternative approach to teaching statistics where students are tasked with attempting to solve a problem before being taught the canonical formula for solving it, often resulting in increased understanding of material compared with traditional instruction. The first study, conducted in a college statistics classroom…

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…

The purpose of this three study dissertation is to investigate why students are enrolled in introductory physics courses experience difficulties in being successful; one possible source of their difficulties is related to their epistemology. In order to investigate students' epistemologies about mathematics and physics, students were observed…

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random. We assume only a basic understanding of probability.

We report on a study investigating the influence of context, direction of translation, and function type on undergraduate students' ability to translate between graphical and symbolic representations of mathematical relations. Students from an algebra-based and a calculus-based physics course were asked to solve multiple-choice items in which they…