A Menu for Making a Math Lesson Story

Lee Shulman
CC BY-NC Flickr
In my last post I talked about different types of lesson plans and suggested that one type, a lesson plan as a story, might have some benefit as a shareable unit of teaching.

When I think of teaching and what makes (or can make) it a profession, I think of attributes of professions described by Shulman (1998):
  • the obligation of a service to others, as in a "calling";
  • understanding of a scholarly or theoretical kind;
  • a domain of skilled performance or practice;
  • the exercise of judgment under conditions of unavoidable uncertainty;
  • the need for learning from experience as theory and practice intersect; and
  • a professional community to monitor quality and aggregate knowledge.
To support teaching as a profession, I value public displays of teaching that reflect Shulman's list of attributes. For the sharing of lesson plans, we can do better than over-templated, step-by-step, anyone-can-follow scripts. We can also do better than brief, make-of-it-what-you-will ideas that lack sufficient implementation guidance. In the stories we tell about teaching, we should seek some middle ground between an over-designed lesson template and an unstructured narrative. Since lesson stories are arguably more about the planning than the plan, they should focus on teacher decision-making and teacher practice, so that other teachers may learn from them. The minimal amount of structure to a lesson story probably starts with these four parts:
  1. A description of the context (grade level, class size, demographics, features of your school environment, etc.)
  2. The rationales behind your lesson planning (not just the choices you made, but why you made them)
  3. A description of the implementation (a low-inference description, mindful of the students' perspectives as participants, of the classroom activity, discussion, and work produced by students)
  4. A reflection (now with more inference, with a focus on how the decisions you made in planning played out in implementation and what that might mean for a lesson revision)

A Menu of Math Lesson Planning Resources

So far this is subject-neutral. In some subjects, rationales in lesson planning might have to be developed and explained from first principles. In mathematics education, however, we're fortunate to have an established body of knowledge related to planning and teaching. To plan a math lesson and then tell its story, I see four categories of resources that form a menu of options.

Planning Guide

For planning and describing the reasons for choices made in the lesson, choose one of the following:

Instructional Model

To structure the delivery of the lesson, choose one of the following:
Lecture and "I do, we do, you do" are also instructional models. They have their place but should probably be used somewhat sparingly. Besides, there probably isn't much demand for lesson plans that consist of a lecture.

Teaching Practice

Teaching is complex and teachers are engaged in many practices at once. However, for improving one's practice and communicating that in a story, it's best to focus on only one or two teaching practices described in NCTM's Principles to Actions:
  • Establish mathematics goals to focus learning.
  • Implement tasks that promote reasoning and problem solving.
  • Use and connect mathematical representations.
  • Facilitate meaningful discourse.
  • Pose purposeful questions.
  • Build procedural fluency from conceptual understanding.
  • Support productive struggle in learning mathematics.
  • Elicit and use evidence of student thinking.
For a different list of teaching practices, you could also consider the TeachingWorks high-leverage practices.

Reflection

In addition to using student work/activity in your reflection, choose from:

What We Gain

Suppose we choose resources from the menu above and tell our lesson story. What have we gained? We've built upon a body of knowledge that can help readers. To some extent, we already do this. When I hear a teacher say they taught a 3-Act Task, I immediately have some knowledge about the instructional model they used. When I hear a teacher say they planned a lesson using the 5 Practices, I know that means they took time to (among other things) anticipate student strategies. With a piece from each of these four categories there is still a lot of freedom to tell a lesson story, but the shared pieces communicate a lot about your lesson and provide a foundation for a common understanding across teachers.

Now, to refer back to my last post, let's think about the usefulness of lesson plan repositories again. Generally, lesson plan repositories are arranged by grade level, topic, and content standard. Instead, what if a repository allowed you to search based on the items in the menu? Imagine being able to search or filter by teaching practice, such as "Show me lessons in which the teacher focused on building procedural fluency from conceptual understanding." Or perhaps you're working with a new instructional coach, and you search for lessons in which the teacher had an observer use the SERP 5x8 Card. We stand to improve our signal-to-noise ratio considerably when teachers can look for lesson plans based on more than just lesson content, and the lessons they find are more likely to be a better "fit" if they are known to have a preferred planning guide, instructional model, teacher practice, or reflection tool.

Next post: I attempt to write a lesson story.

References

Shulman, L. S. (1998). Theory, practice, and the education of professionals. The Elementary School Journal, 98(5), 511–526.
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