Discovery Learning Assessments

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Overview:

Motivated by a talk given by Eric Mazur, a team of mathematics instructors at the United States Military Academy set out to determine if there was a better way to assess students in Mathematical Modeling and Introduction to Calculus. The result of this work was the creation of Discovery Learning Assessments (DLAs).

Discovery Learning Assessments are a way of re-claiming assessment time as learning time during which students are assessed on skills that are most relevant for success in today's world. They take the place of traditional quizzes and exams to make assessment time more relevant for students and instructors alike. DLAs do this by requiring students to investigate a real-world scenario before coming to class to participate in a three-part assessment flowing from an individual component to a team component to an individual reflection component which is followed up with constructive instructor feedback soon thereafter.

DLAs were first introduced in Mathematical Modeling and Introduction to Calculus at the United States Military Academy during the Fall 2017 semester. That semester we conducted a pilot study which quantitatively showed a positive impact on student grades in Single Variable Calculus (taken the following semester) for students who had never had a calculus course before. Otherwise quantitatively, there were no statistically significant differences observed in either a positive or a negative direction. However, the qualitative observations of the instructors teaching the pilot sections and the post-survey feedback from students were decidedly positive. Consequently, the overall conclusion from the pilot semester was that DLAs were a beneficial alternative to traditional assessments.

Since the pilot, not only have DLAs been implemented course-wide in Mathematical Modeling and Introduction to Calculus, they have also been introduced as quizzes in several other classes as well. I have written and administered DLAs in Linear Algebra, Discrete Mathematics, and Multi-Variable Calculus and Introduction to Differential Equations. Additionally, other instructors have implemented DLAs in a Mathematical Modeling course for majors and a Pre-Calculus course.

Samples:

• Flight Planning
In this DLA, students explore vectors and vector equations of lines through the application of flying a drone. The first page is the read ahead which contains a link to the Practice Simulator. The second page is the map to be used on the read ahead. The third and fourth pages are the individual component. The fifth and sixth pages are the team component which references the Team Simulator. The seventh page is the map for the team component. The last page is the individual reflection component.
• Eigen
In this DLA, students discover the eigenvalues and eignevectors for a matrix. The first page of the document is a guide for instructors, the second is the Read Ahead, and the remaining pages are the three-part assessment.
• Cyber
In this DLA, students are introduced to a cryptography applciation of the material they have been learning in class. The first page of the document is a guide for instructors, the second is the Read Ahead, and the remaining pages are the three-part assessment.

Tools for Writing Your Own DLAs:

• Checklist
• Team Roles

Publications:

• Chapter 27: Developing the Cutting Edge of Assessments - Discovery Learning Assessments in Teaching and Learning the West Point Way - Educating the Next Generation of Leaders (May 2021)
In this peer-reviewed book chapter, we discuss the motivation to develop a new kind of assessment, the inital development of DLAs, and their evolution.
• Going Beyond Promoting: Preparing Students to Creatively Solve Future Problems (July 2020)
In this peer-reviewed article, DLAs are described within the larger context of the Mathematical Modeling and Introduction to Calculus course at the United States Military Academy at West Point.
• A research paper about the full results of the pilot study is in progress.

Future Directions:

• Work towards adapting DLAs to various student accommodations is underway.
• Studying the effectiveness of DLAs at other institutions and in other courses.
• Building a robust library of DLAs for many undergraduate mathematics courses.
• Adapting the WeBWorK platform to support DLAs.