Research-Informed Methodology

Did you know that there is an entire field of research devoted to helping students learn undergraduate mathematics well? In the United States, for instance, the Mathematical Association of America has a Special Interest Group, Research in Undergraduate Mathematics Education (RUME), with hundreds of researchers devoted to this very area. More generally, worldwide many researchers have developed, and continue to actively develop, effective approaches to help students learn Calculus well. At the same time, few students actually benefit from this research, which is particularly unfortunate given how many students struggle with various aspects of learning Calculus deeply.

Part of the reason we created Matheno was to rectify this, and directly integrate the results of such excellent research into materials anyone anywhere in the world can easily find and use. While we are just getting started, this page summarizes how we currently use, and aim to further use, educational research to design, test, and improve our materials.

How We Use Research

To start we have reviewed findings from focused research on specific topics and used them to shape lesson sequencing, activity design, and common-misconception checks. For example, many studies show that students do not typically develop a deep understanding of the concept of "limit," which is problematic since this concept is the foundation of Calculus on which derivatives and integrals are built. Hence in our beginning section Limits Concepts, we use various proven approaches to help students build a solid baseline understanding.

We begin with an intuitive and conceptual understanding of limits, and then move to a proven approach in the Pancake Story to illustrate the concepts needed for the formal definition of the limit of a function. To understand limits at infinity, we use a research-based tool called the Epsilon Strip. We conclude the section with a proven lab activity in the Lab: Find a Limit By Using Approximations to allow students to explore the formal definition of the limit of a function, and to see how the definition works in practice.

We are in the process of extending this same approach to develop the derivative and the integral, grounded in that existing understanding of limits.

We also generally use research results regarding how to present material in ways that minimize cognitive load. For example, we draw on research presented in Richard Mayer's book Multimedia Learning that "takes an evidence-based approach to improving education using well-designed multimedia instruction" (reference below). Overall, we want our users to focus their energy on learning new key ideas and developing strong problem-solving skills, rather than wasting valuable cognitive resources on things like "gaming the system" to score points on some meaningless activity.

We're Just Getting Started

While Matheno has been around for a while, only recently (as of 2026) is it becoming what we've long envisioned, fully making use of research in the ways we describe here. If you have a resource to share, something you think we've missed, a suggestion to make, or would like to develop research-based materials for us to host — or even to use our platform to test a new activity or approach — please get in touch! We've made everything free to the world given our stated goal:

"Provide high-quality, interactive materials to dedicated learners everywhere in the world,
regardless of ability to pay,
so they (you!) can learn well and excel."

We'd love to build a community of learners and educators who are dedicated to learning and teaching well. Please join us.