Teaching to Learn, Learning to Teach

II.a. Ingredients for a Developmental Lesson

Aim: a question that a particular lesson is designed to answer or a statement or phrase in-

troducing the topic of a lesson. Usually it is written on the board at the start of the lesson.

Sometimes it is elicited from students during the early stages of a lesson.

Performance objectives (standards): specific content and skills students are expected to

master by the end of the lesson. Lessons usually have between three and five objectives.

Preparation: prior classroom instruction or homework that prepares student for this les-

son.

Development: outline of the actual lesson.

Motivation: an introductory question that reviews prior preparation and establishes the

topic that will be examined.

Questions: prepared in advance and narrowly focused. Designed to elicit information from

students based on prior preparation.

Notes: information obtained from students is translated into a detailed outline that is

placed on the board.

Medial summary questions: promote deeper probing and classroom dialogue. Used to

monitor student progress toward achieving objectives during the lesson.

Final summary question(s): Based on the aim question, it integrates material from the en-

tire lesson and allows teacher to assess student understanding and achievement of objec-

tives.

Application: extra optional question(s) that draws on and broadens what students are

learning in the unit. These can be used as review, additional assessment, or as transitions

to future lessons.

Homework: independent work that scaffolds on the lesson to prepare students for the next

lesson.

II.b. Sample Developmental Mathematics Lesson

(developed by Rhonda Eisenberg)

AIM QUESTION/STATEMENT: How can we use similar triangles to solve problems?

PERFORMANCE OBJECTIVES (STANDARDS):

1. Review the relationship between corresponding sides and angles of similar triangles


2. Apply the properties of similar triangles to find the heights of various figures


3. Solve the problems involving indirect measure using similar triangles
   PREPARATION:


4. PREVIOUS HOMEWORK: Problems from textbook on properties of similar triangles


5. PREVIOUS LESSON: What are the properties of similar triangles?
   DEVELOPMENT:


6. MOTIVATION QUESTION: In a summer camp a dead tree had to be cut down. The tree
   stood 16 yards from the recreation hall. Since the tree was leaning in the direction of
   the recreation hall, it seemed best to let it fall in that direction. Would it hit the build-
   ing? What do you think? How would you figure out if the tree would hit the recreation
   hall?


7. QUESTIONS/NOTES/MEDIAL QUESTIONS:

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