Doug Corey recently published a paper in the conference proceedings for the Research in Undergraduate Mathematics Education (RUME) conference. The paper was titled “Exploring the Knowledge Base for College Mathematics.” Doug has answered a few questions about this paper below:
Who were your co-authors on this paper?
Linlea West, a graduate student who has since graduated and Kamalani Kaluhiokalani, an undergraduate student who has since become a graduate student.
Who would you say is the target audience for this paper?
Researchers in undergraduate mathematics education, and secondly, instructors of undergraduate mathematics.
What is the big problem you hoped to address with this paper?
We wanted to see how well current materials available to undergraduate mathematics instructors fit with our framework on the kind of information fundamental to build a knowledge base for teaching. We adapted a framework from others (Hiebert and Morris, 2009) to apply a broad sample of materials that might have elements of a knowledge base for teaching undergraduate mathematics.
What are some of the key ideas in the paper?
We found that a few key elements of a knowledge base for teaching undergraduate mathematics are hard to find in the currently available materials. Specifically, knowledge of student mathematical thinking and rationale behind instructional decisions were both quite rare. What was common was a lot about the mathematics that we teach (or that we could teach). There was a little about how to possibly teach a particular topic, but very little on why those instructional decisions were warranted. The best examples (we found three fairly good examples out of more than 150 studied) had a very clear understanding of student mathematical thinking around specific topics/concepts and were able to engineer activities/problems/questions/instructional environments, etc. based on the student thinking AND IN SO DOING help the reader understand why these choices seemed preferable above others. Undergraduate mathematics instructors seem to have few resources to improve their craft by building upon the knowledge of others, especially the reasoning of teachers on how to weigh possible instructional decisions.
What are some of the main ideas you hope your audience will take from the paper?
We argued that we need a different focus in the knowledge we are sharing about teaching undergraduate mathematics. It should be based on teaching specific mathematical content, grounded in understanding student thinking of that content, and understanding the reasoning behind the instructional decisions, not just sharing the instructional decisions themselves. Because teaching happens in different contexts (administrative, curricular, demographic, etc.) it is more important to understand why certain choices are made so that teachers can learn what might be best (or better) in their context.
The abstract for the paper is below.
In this paper we explore a wide sample of currently available instructional materials intended for college mathematics instructors (textbooks, magazines, teacher editions, lesson plans, teaching articles, classroom notes for flipped classrooms, books, etc.) in order to assess how available materials are building a knowledge base for teaching. We modify a framework from Hiebert & Morris (2009) to look for key categories of knowledge that are fundamental for a knowledge base for teaching mathematics. We found that few articles contained meaningful amounts of multiple categories. We use the categories to describe the nature of current available materials and argue that a new genre of instructional material and scholarly work to create the missing knowledge is needed.