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"?

4 Corners and a Diamond

This is the graphic organizer that my sons' parochial school has implemented in all grade levels, beginning in first grade. It is called "Four Corners and a Diamond," and its most prominent feature--the fourth corner where students have to explain in multiple sentences every step of the mathematical process--is designed to prepare students for the written component of the new state tests inspired by the Common Core Standards. The explanations are extremely tedious, very time consuming (especially for my oldest son, a third grader), and utterly unnecessary. Once math on the elementary level in Catholic School was about computation and memorizing facts. Now, thanks to the diocese's decision to implement Common Core, math is about "understanding the process," even though elementary school students do not possess the cognitive abilities to understand mathematical processes in the way Common Core dreams.

Here is my third grade son's "critical thinking word problem." Educators are obsessed with "critical thinking," believing that they can turn any kid into Socrates or Descartes. The trouble is that they skip the basic memorization of the foundational elements--too boring for kids, they tell us--and jump to the more difficult problems that they are not equipped to handle. This is why we have generations of poorly educated Americans.


The "Critical Thinking" word problem


 

A third grader solves the problem on the "Four Corners of a Diamond" graphic organizer



 

The teacher's typed comments, along with a model for what the response should say