My client, Sacramento math teacher Edric Cane, recently published a book for teachers’ continuing education on a concept he calls Teaching to Intuition. Teaching to intuition means, broadly, making sure students can tell the story of what is happening behind a numerical operation before they learn an algorithm for it. He also refers to this as entrusting knowledge to the creative use of the mind rather than solely to memorized theorems. In his November 2011 article in Mathematics Teaching in the Middle School Cane illustrates teaching to intuition this way:
First, I ask my students three important questions: What is 5 dogs and 3 dogs? What is 5 cats and 3 cats? What is 5 dogs and 3 cats? This last question elicits some initial confusion and a variety of answers. One student always suggests “3 pets.” We make it our common answer and discuss what went on in their minds as they answered the question….My hope is for that experience to substitute for memorized rules.
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The book describes the author’s philosophy and gives many easy-to-emulate examples for putting it in practice in the classroom. Many examples draw from upper elementary and middle school math but can also apply to high school topics. Throughout, Cane makes reference to the Common Core standards and how to implement them within the “intuition” framework. For more information about Common Core standards, click here.