A major issue facing undergraduate mathematics teaching is that much accumulated knowledge and wisdom about teaching specific lessons is lost as experienced instructors retire or leave for other reasons. While methods for sharing teaching knowledge do exist, most either speak to broader generalities in teaching or miss crucial details that would make the materials easier for others to try out in their own classes. Discussions of quality instruction rarely reach the level of decision-making necessary for planning and implementing a single lesson. For example, a shared lesson plan might suggest that an instructor use a certain activity, or hold a 5 minute discussion on a certain idea, but without explaining how such an activity or discussion might actually play out with real students. It is rare to find materials that detail explicit rationales and purposes behind each part of the activity or discussion. These are vital pieces in understanding the craft of teaching and in helping others effectively implement and adapt pieces of the lesson to their instructional context. In response to this need, recent work has proposed an improved method for sharing instructional knowledge at the individual-lesson level, called “Lesson Analysis Manuscripts” (LAMs) (Corey & Jones, 2023a; 2023b).
For this special issue, we solicit undergraduate math instructors to identify a single lesson (or potentially two very closely related lessons) with an important instructional challenge in their own teaching, for which they feel they have developed a successful lesson that addresses the challenge. This special issue will consist of a collection of these high-quality LAMs that can serve as exemplars to the undergraduate mathematics teaching community for how to share lesson-specific accumulated instructional knowledge with one another. Not only can these LAMs be used by others, but we hope they will spur undergraduate instructors to consider writing their own LAMs for future publication and use. In this way, we can work together toward building a strong “knowledge base” for teaching undergraduate mathematics.
To provide guidance for potential authors in this special issue, the following are key requirements that a LAM submission should contain. A detailed description of the purpose and nature of each of these items can be found in Chapter 2 of the MAA book edited by Corey and Jones (2023a – see reference below).
- The manuscript should focus on a single lesson (or a pair of closely related lessons) that addresses an important instructional challenge. Examples of important instructional challenges could be: (a) How can this major topic be motivated so the students see a real need for it? (b) How can students develop a particularly important meaning for a certain mathematical concept? (c) How can I begin to help students toward developing a certain mathematical practice, such as argumentation or justifying? (d) How can I overcome a well-known student difficulty in understanding a concept or idea?
- The manuscript should make explicit the instructional decisions made, both about the lesson activities as a whole and about actions taken during the lesson, and explain why these instructional decisions are effective in achieving the lesson goals. The reasoning about instructional decisions reveals insights about the craft of teaching, and such reasoning is important knowledge that readers of LAMs can use to improve their own instruction. Understanding the reasoning behind instructional decisions in a lesson also helps others better modify the lesson to their instructional context and for their instructional goals, while keeping the key effective elements of the lesson. Questions to consider here could be: (a) Why did you use this particular activity or approach, as opposed to others? (b) Why did you ask that question? (c) What were you planning on getting out of a certain discussion? (d) Why did you sequence the activities as you did?
- The manuscript should make explicit the actual student thinking that happens during the lesson, and how certain key moments actually play out during the lesson. Knowledge of student mathematical thinking provides valuable insight and is often the justification for key instructional decisions. Examples of such thinking are: how students tend to think about prior concepts that the lesson will build on, the nature of student thinking during the lesson, and the kind of mathematical thinking the lesson is intended to achieve. Including examples of student responses and dialogue is extremely helpful, either as summaries of how the dialogue unfolds, or perhaps even as snippets of literal classroom excerpts/transcripts. Important items to include here could be: (a) How do students tend to think of certain ideas coming into the lesson? (b) What different responses do students usually give to a question or to part of an activity? (c) What do you, as the instructor, do with those responses? (d) How do your classroom discussions actually play out? We note that the synthesis of student thinking typical in LAMs usually does not meet the definition of “research” by IRB boards, so IRB approval often may not be needed. However, prospective authors should check with their IRB board to ensure this is the case for their particular LAM.
- To make the LAM interpretable and usable, the manuscript should adequately describe the background and context in which the lesson happens (school type, class type, typical student demographics); how sound teaching practices were used (equitable instruction, soliciting student thinking); what the lesson actually consisted of (tasks/activities, questions); and a few post-lesson reflections on how the lesson addressed the instructional challenge and how it could be further refined, or adapted to different instructional goals and contexts.
- We strongly recommend prospective authors look at a recent book that describes LAMs in detail and contains many LAM examples (Corey & Jones, 2023a). We also recommend a shorter summary article that recaps the main points of a LAM and includes a single example (Corey & Jones, 2023b). We invite those with questions about writing a LAM to email the lead guest editor directly: Doug Corey, email@example.com.
Because of the specific nature of LAMs, for this special issue we are requiring prospective authors to submit a 1-page extended abstract about their proposed LAM directly to the lead guest editor Doug Corey: firstname.lastname@example.org. This 1-page extended abstract will enable us to provide feedback early in the process that will make for stronger LAMs that can serve as exemplars. The extended abstract should contain (a) a clear statement of the instructional challenge being addressed, (b) a few brief highlights of the lesson that addresses the instructional challenge, and (c) a description of how the author will include the required instructional decisions, student thinking, and appropriate background.
Extended abstracts will be accepted by email to the lead guest editor until October 31, 2023. For those invited to submit a full LAM based on their extended abstract (invitations will be sent no later than December 31, 2023), full submissions will be due by May 31, 2024. These full LAM submissions will then go through the usual journal referee process. Because of the detail required in a LAM, papers for this Special Issue might be longer than a typical PRIMUS article. To give some rough guidance, we would expect a LAM to be between 5,000 and 9,000 words, not counting figures, references, or supplemental materials. Supplementary materials, such as color illustrations or entire activity handouts, may be published in the online version.
Corey, D.L., & Jones, S.R. (Eds.) (2023a). Sharing and storing knowledge about teaching undergraduate mathematics: An introduction to a written genre for sharing lesson-specific instructional knowledge. Washington, DC: Mathematical Association of America.
Corey, D.L. & Jones, S.R. (2023b). Sharing instructional knowledge via lesson analysis. International Journal of Mathematical Education in Science and Technology. DOI: 10.1080/0020739X.2022.2121775