Doug Corey and Steven Jones recently edited a book titled “Sharing and Storing Knowledge about Teaching Undergraduate Mathematics: An Introduction to a Written Genre for Sharing Lesson-specific Instructional Knowledge” They have answered a few questions about this publication below.
What was the genesis of this book?
We had done a study to see what kind of materials were available to university mathematics instructors. It was lacking in resources to help teach specific content, and in sharing reasoning of experts through instructional decisions. In order to address these needs, we developed a written genre for instructors to share their instructional knowledge on teaching specifics content. We call the genre “Lesson Analysis” and a written example of a Lesson Analysis, a “Lesson Analysis Manuscript”, or LAM for short. LAMs give instructors a space to share lessons in which they have had great success and to explain the reasoning behind the instructional choices in the lesson.
Who would you say is the target audience for this chapter?
University mathematics instructors and mathematics educators. We believe that there are a lot of reflective teachers out there that have valuable knowledge about teaching mathematics at the university level. This opens up one way for them to share their knowledge and to learn from their peers.
How did you select or identify contributors to the book?
We reached out to many college mathematics teachers that we knew from conferences. Many from the RUME (Research in Undergraduate Mathematics Education) community. We thought those in the RUME community might have insight about representing instructional knowledge in written form. We also had representatives from key mathematics organizations like MAA and AMATYC.
What are some of the key ideas in the book?
One of the key ideas is that we don’t currently have good ways to share what we learn from the years of experimentation by instructors in their day-to-day classes. When we talk about instruction, it is usually about generalities (methods or instructional principles), and not about the myriad of nitty-gritty decisions that are involved in each lesson, or the subtle moves/practices that make a difference in student learning. We are trying to open up the space to share this detailed knowledge, and do it in the context of a specific lesson. Now teachers can support others by capturing detailed practice that has not been accessible in print.
Another key idea is that every LAM is built around solving an “instructional challenge”. An instructional challenge is a problem the lesson is created to solve. It could be about improving the learning of students, or developing a certain mathematical practice like modeling or proving, or how to build effective classroom norms, etc. These are practical problems that teachers face, and that some teachers have tried hard at solving.