Currently I am writing a short book based on my very popular iae-pedia page Good Math Lesson Plans (http://iae-pedia.org/Good_Math_Lesson_Plans). I started to think about the role of Advance Organizers in a good lesson. The idea of an advance organizer is attributed to David Ausubel. See http://en.wikipedia.org/wiki/David_Ausubel. Quoting from this Wikipedia document:

An advance organizer is information presented by an instructor that helps the student organize new incoming information. This is achieved by directing attention to what is important in the coming material, highlighting relationships, and providing a reminder about relevant prior knowledge.

Advance organizers are helpful in the way that they help the process of learning when difficult and complex materials are introduced. This is satisfied through two conditions:

1. The student must process and understand the information presented in the organizer—this increases the effectiveness of the organizer itself.
2. The organizer must indicate the relations among the basic concepts and terms that will be used.

Some Web browsing led me to the book:

Joyce, Bruce and Weil, Marsha (1996). Models of teaching (fifth edition). Retrieved 2/1/2012 from: http://www.nimhindia.org/MODELS OF TEACHING.pdf. (The eighth edition can be purchased from Allyn & Bacon).

I knew Bruce Joyce when he was teaching at the University of Oregon, and I have previously read some of his publications. I have always considered them to be quite insightful. Quoting from the book:

Most teaching episodes have both content and process objectives. The content objectives include the information, concepts, theories, ways of thinking, values, and other substance that the students can be expected to learn from the experience that results. The process objectives are the ways of learning—the conduct of the social and intellectual tasks that increase the power to learn. In the case of a model of teaching, the process objectives are those that enable the students to engage effectively in the tasks presented when the model is being used. A good lesson plan considers both.

One of the key ideas covered in the book is that a typical teacher makes use of very few lesson plan models or designs. The authors have observed that a typical teacher will adjust the material to be taught so it fits the lesson plan and teaching model that the teacher typically uses. The authors suggest that increasing the repertoire of models a teacher is comfortable in using will lead to better learning on the part of students.

I was educated by a “stand and deliver” style of math teaching. In high school and college this model of math teaching still dominates. In my career as I transitioned from being a math teacher to being a computer science teacher to being a teacher of teachers, I gradually learned models that fit the various teaching situations. For example, in my math teaching I had never see small group discussions, but I eventually learned to make routine use of this in my teaching of teachers. In my math teaching I had never seen use of math manipulatives. Now, I am a strong supporter of math manipulatives as an aid to teaching and learning math. I encountered project-based learning only once in my math education, and I eventually came to make PBL a routine component of my teacher education courses.

Here is a list (arranged in alphabetical order) of some of the types of lesson plan models that Joyce and others have identified as particularly useful:

• Cause and Effect (Inference, hypotheses, generalization).  See http://en.wikipedia.org/wiki/Causality.
• Concept Attainment (Comprehension, comparison, discrimination, and recall). See http://en.wikipedia.org/wiki/Concept_learning.
• Concept Development (Categorization).See http://people.selkirk.bc.ca/akosling/Study_Skills_Webpages/Memorization.html. 
• Cooperative Learning, including Peer Instruction and Team-based Project-based Learning. See http://i-a-e.org/iae-blog/peer-instruction-fostering-learning-for-understanding.html and http://iae-pedia.org/Good_PBL_Lesson_Plans.
• Direct Instruction. See http://www.nifdi.org/15/.
• Discussion (Essential questions).
• Inquiry (Problem-solving, Problem-based learning). See http://iae-pedia.org/Problem_Solving and http://iae-pedia.org/Math_Problem-based_Learning.
• Learning from Simulations (including Computer Simulations).
• Mastery Learning. See http://en.wikipedia.org/wiki/Mastery_learning.
• Memorization (Aids, such as Mnemonics). See http://people.selkirk.bc.ca/akosling/Study_Skills_Webpages/Memorization.html.
• Resolution of Conflict.
• Synectics (Use of group interaction to stimulate creative thought through analogical thinking). See  http://en.wikipedia.org/wiki/Synectics.
• Values Development (Ethics, civility, cultural understanding).

Final Remarks

Take a look at the models of teaching that you routinely use. Do you have a repertoire of a half-dozen or more models? If not, think about adding one new model to your repertoire. Select one that you and/or your colleagues are confident is an effective model for use with the students and subject matter that you teach. If you use a teaching model that you find particularly effective but that few of you colleagues use, give yourself the task of helping your colleagues add this teaching model to their repertoire. .