From the same place that brought you Fractions: You're Teaching Them Wrong
, this is another resource to up your teaching to the highest reaches of the universe....
You're a novice teacher, you're an experienced teacher. You think you've been teaching concepts, but you're not sure. You know why? BECAUSE YOU DON'T KNOW WHAT A CONCEPT IS!
This is the definitive 60 page fully detailed explanation that explains everything EVERYTHING you need to know about teaching mathematical concepts. EVERYTHING! After reading this, you will be the "concept expert" among your colleagues and will be schooling your supervisors and their supervisors in no time, because they are probably clueless when it comes to concepts as well.
More than a "good read," this is almost a college course on concept development which will change how you think about your own teaching, as well as help you evaluate whether the materials you are given or those that you purchase are doing a good job on concept development.
Actually, after reading and understanding this manuscript, you will once and for all understand the importance of conceptual understanding, revise your teaching so that it includes concept development, and learn how to design and administer assessments that truly show what level of concept development your students have attained.
This is written in 10 chapters, with many, many examples included about how it would affect your teaching. It will help you understand the errors your students make and how to rectify the underlying concepts that led to these errors.
Table of Contents
Prologue: Why Should You Be Teaching Concepts?
Chapter 1: What is a Concept?
Chapter 2: Critical Features and Superficial Features
Chapter 3: Types of Concepts
Chapter 4: All About Prototypes
Chapter 5: Stated Versus Developed Concepts
Chapter 6: Misconceptions and Missed Conceptions
Chapter 7: Levels of Conceptual Understanding
Chapter 8: Assessing Conceptual Understanding
Chapter 9: Innovative Understanding
Chapter 10: You Better Be Teaching Concepts
A Bonus Overgeneralization
The Roots of a Popular Misconception
Addendum 1: The Top Ten Concepts That Teachers Miss
Addendum 2: Conceptual Understanding vs. Functional Understanding
Addendum 3: Language and Conceptual Understanding
Yes, I know this is an expensive item, but believe me, it is more than worth it. You'll save hundreds of dollars on cruddy products that don't actually teach or assess concepts, and hopefully you'll learn how to make concept building materials of your own (and not just in mathematics; many of these principles apply to science, social studies and language arts education.)