Tuesday, December 31, 2013

What's 13-4? Don't Ask Common Core

It is easy to miss exactly what the Common Core standards are requiring without careful examination and visual demonstration. For example, one headline under "Operations and Algebraic Thinking" in Grade 1 reads simply "Add and Subtract within 20." No problems there. But CCSS.Math.Content.1.OA.C.6 gives a much more complete picture of what Common Core means by "going deeper" into a given subject matter:

"Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13)."

Must a first grader be taught how subtract through "decomposing" a number? Here's how this is presented in my son's first grade Common Core stamped textbook:

Rather than teach simple arithmetic to six and seven year olds, Common Core is subordinating subtraction to the concept of place value. A simple calculation has thus been morphed into a two step process that is not at all intuitive to a first grade mind, viz., 13-4 is really 13-3=10-1=9. And students are expected to be able to do this on their own. Witness the companion workbook exercise that puts this model into practice:

And if we are to believe the book, students will have to "decompose" on their state assessments such as in this "Test Prep" section:

Is a beyond the pale standard like this what American Federation of Teachers President Randi Weingarten had in mind when she wrote that Common Core exists to give our children "higher-order capabilities like critical thinking and problem solving, mastery of essential knowledge, and the skill and will to persist"?

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