Project Overview


Coherent Labs to Enhance Accessible and Rigorous Calculus Instruction

The Challenge

Attrition among even the most talented students presents one of the main barriers to significantly increasing the number of graduates from colleges and universities with degrees in science, technology, engineering, and mathematics (STEM) fields. The nature of instruction in freshman courses is a primary factor determining whether students leave the STEM pipeline, and introductory calculus sequences are an important part of this pivotal early undergraduate experience. In particular, students in calculus often find their course to be an overwhelming collection of isolated procedures, conceptually inaccessible, and not relevant to their academic interests and goals.

Our Response

Project CLEAR Calculus is a research-based effort to make calculus conceptually accessible to more students while simultaneously increasing the coherence, applicability, and rigor of the content learned in the courses.

The principal investigators of Project CLEAR Calculus have conducted more than two decades of basic and design research on the teaching and learning of calculus, culminating in an instructional framework which leverages students’ intuitive reasoning to develop robust understandings that support modeling and problem-solving in novel situations. Research-based resources for CLEAR Calculus have expanded from the original active-learning labs to also include virtual manipulatives, conceptual videos, formative assessments, and interactive lecture resources. 

Guiding Definitions

Coherence: Instructional activities are coherent to the extent that they leverage consistent meanings across different representations and contexts. The coherence of CLEAR Calculus resources supports students generalizing and abstracting a small number of powerful ideas at the core of the field. 

Labs: Cooperative labs engage students in challenging problems requiring them to select, perform, and evaluate actions that support their construction of powerful mathematical ideas.

Applicability: Instructional activities effectively incorporate applications to the extent that they support students in identifying mathematical relationships, making and justifying claims, and generalizing across contexts to extract common mathematical structure. The applicability of CLEAR Calculus resources not only ensures that students develop useful tools, but provide a foundation of meaning for reasoning about the abstract foundations of those tools.

Rigor: Instructional activities are rigorous to the extent that they require students to engage in problem-solving activity whose structure reflects that of the underlying mathematics to be learned. The rigor of CLEAR Calculus resources supports students in developing productive understandings that can serve as a strong foundation for further study in math and science.