About the Program
The Mathematics Department at the University of Michigan has a commitment to making our Introductory Program courses (Math 105, 115, and 116: Data, Functions, and Graphs, Calculus I, and Calculus II) a vital part of our undergraduate students' education. This started in the 1990s when we instituted what was then called “Calculus Reform,” adopting smaller classes, a conceptual focus, and active learning. Over the years, we’ve updated and improved both the content of the courses and the ways we teach them as the research on mathematics education has become clearer and more definitive, and our understanding of what we can and should do in these courses has become clearer. Below, we highlight different aspects of this work, and what students in our courses may expect.
Our texts, with their fresh approach to calculus, give us the opportunity to strengthen students' grasp of the underlying concepts. Students are taught to read the textbook and write full essay answers to many of the interesting problems. In our classes students work together actively, and outside the class they meet frequently to solve their team homework problems.
Curriculum
Our Introductory Program courses are concerned with what we need to know, not the mechanical procedures that are powered by the mathematics that we are teaching and learning. They focus on deep, conceptual understanding, real-world applications, and problem solving. We learn procedures as well, of course, but those are not the primary focus of our courses: we want to understand the mathematics in the courses from many viewpoints, including numerical, graphical, and English descriptions, as well as from a symbolic or algebraic perspective.
Instruction centered around interactive learning and student responsibility
It is unambiguous that the way we learn mathematics is by doing it: by being actively engaged with the material and our understanding. Our classrooms are centered on this: students work together in class to develop their understanding of the course material. We teach these courses in small sections, so that students in the course have direct access to their instructor and to the other students in their section. Instructors in these courses have significant training in the use of active learning instructional techniques, and are supported by the Department as they teach these courses. They are part of a team with the students in their section, working together to help students learn the course material.
Restructured Assessment
Our goals in these courses are for all students to learn the material: University of Michigan students are strong and capable, and we believe that everyone in our courses can succeed. Our assessment model in these courses reflects this: we have added significant repeatable, mastery assessment that allows students to review and retake until they have demonstrated mastery of the material being evaluated. Other work in the courses includes homework, work in class, and (now much lower stakes!) exams.
Comprehensive faculty & graduate student instructor development program
We start every fall term with an intensive training week for all new instructors in the Introductory Program. This is followed by weekly teaching meetings and periodic classroom observations with feedback, and instructors have access to a set of fully developed classroom activities to assist them in formulating their classes.
Below are some materials that you may find useful in learning more about our program's professional development schedule. Please note that these are historical: the information will be representative of the structure of and activities in the week, but are not a description of what necessarily will happen this year.
