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Lesson Critique

                                               ©1995-2008  Mahesh C. Sharma  All rights reserved.

A. Instructional Activity
Are the lesson plan and flow of instructional activities guided by these principles of mathematics teaching?
o Socratic questioning 
o Direct instruction (didactic) 
o Guided discovery 
o Coaching 
o Individualization 
o Assessment 
o Planned reinforcement and meaningful homework 

B. Lesson Content

Does the instructional lesson clearly shows that every mathematical idea reflects the these three components?*
o Linguistic component2 
o Conceptual component 
o Procedural component 
   *The content of the lesson must integrate the development of the language of mathematics, conceptual models and the procedure/algorithm related to that concept.

C. 6 Levels of Knowing

Does the lesson show that the mastery of a mathematical concept is developmental? Does the lesson reflect the six levels of knowing in its execution?
o Intuitive level (knowing and showing the mastery by connecting and extending the new oconcept with prior knowledge, skills and procedures) 
o Concrete level (knowing and showing the mastery through concrete models) 
o Pictorial (knowing and showing the mastery through pictures, diagrams, context and representation) 
o Abstract level (knowing and showing mastery through symbolic representation, manipulation and abstractions) 
o Applications level (knowing and showing the mastery by applying the knowledge in intra-mathematical, interdisciplinary and extracurricular applications) 
o Communication level (the ability to explain, describe, teach other person, defend argument or method, write about it, etc) 

D. Lesson Structure and Organization

Do the instructional activities aim at developing a structure that is predictable, and at the same time has novelty?  Each lesson should have:
o Mental mathematics4 
o Conceptual development 
o Development of prerequisite skills5 (Sequencing, spatial orientation and space organization, visualization, pattern recognition, deductive and inductive reasoning)6 
o Writing number stories and problem solving 
o Planned activities for mastery and automaticity

©1995-2008  Mahesh C. Sharma  All rights reserved.