Write Math?

By far Common Core's most distinctive feature, as articulated in CCSS.Math.Practice.MP3, is its emphasis that students be able to explain verbally what they are solving. In principle, there is nothing wrong with that. But in practice, "writing math" is putting traditional computation on the back burner. Why? Because we are told that students will have to write out their rationales on state tests in some capacity--and, admit it or not, teachers are forced to tune their instruction tightly so students will do well on the state tests. The fact that we have not yet seen the state tests and their implementation of this writing principle has not stopped Common Core stamped math books from shifting their focus.

Witness, for example, this photo from a third grade Common Core math book and its "Write Math" section. Notice it is labeled "H.O.T.," implying that this type of problem is "in."

Notice the last word--"Explain." No longer is it enough to just solve and check your work mathematically. Now it must also be explained verbally. Here's another third grade problem.

How well will students who struggle with reading, or students whose native language is not English, fare in this methodology? Yet American Federation of Teachers President Randi Weingarten tells us that "civil rights groups that see public education as an anchor of democracy and a great equalizer have embraced these standards." Perhaps these groups have not done their homework on what Common Core actually entails.



This writing methodology not only emphasizes student explanations, but is also gives pride of place to word problems. Have a look at the first grade book from the same textbook series. Notice the "Test Prep" label in the upper right hand corner.

There is nothing wrong with word problems per se, yet here we find the underlying issue: if word problems will be the focus of the state assessments (two of the three "Test Prep" pages in this section are entirely given to word problems), then teachers will be forced to give the bulk of their precious few classroom minutes to practicing word problems. This gives far less time for drilling the basic facts that are essential to mathematics, and without knowledge of the basics, the students will fall farther behind year after year.

This excessive verbiage will cause Common Core to fail, as a generation of students will know neither mathematical computation nor mathematical concepts. So much for Common Core's Mission Statement that promises to prepare students "to compete successfully in the global economy" in the future.

Instead these students will not even be able to make change from a $5 bill.

How to Obfuscate Two-Digit Multiplication

Once upon a time, two-digit multiplication was an exercise in computation: multiply one digit through, add a zero, then multiply the second digit through, and finally add the two together. But Common Core, despite its promise, has reinvented and obfuscated this simple process. True to its emphasis of having all levels of mathematics explained in words (more on this in the "Four Corners and a Diamond" post), Common Core offers a verbose explanation of how to solve 43 X 25. This is a photograph of a math workbook of a fourth grader whose Long Island parochial school has adopted the Common Core. The book has the Common Core stamp on the cover. The teacher is required to teach the students according to the outline on this page, not according to the traditional method. Have a look:

Just as with the Common Core method for subtracting 13-4 (see post "What's 13-4? Don't Ask Common Core"), in this example the concept of place value has been elevated over the ability to solve the problem in the most straightforward manner possible. This place value method is articulated in standard CCSS.Math.Content.4.NBT.B.5. Rather than add two sets of numbers in the end, students now need to add four, keeping track all the way, as the fourth grader did in this photograph.

It is worth noting that the fourth grader is required by his teacher to solve two-digit multiplication in this manner. He understands the traditional way of multiplying but not the Common Core way, and he has therefore performed poorly--and been reduced to tears more than once--on his math tests that require the obfuscated method.

And the worst part: this boy scored in the 97th percentile on his Iowa Test of Basic Skills in mathematics, yet he cannot handle the Common Core methodology. His mother and father each sit with him to complete his homework every night. If this boy is struggling this much, how will the children of average or below-average intelligence fare? How will students who do not have parents to help them with their homework fare?

Yet American Federation of Teachers President Randi Weingarten somehow believes that Common Core standards "have the potential to disrupt the cycle of increasing poverty and economic and social stratification by making essential skills and knowledge available to all children, not just some."

It seems to me that Common Core will push these students farther behind.

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