A return to mathematical ignorance
["Common Core" represents an attempt by the powers-that-be to standardise (and thereby control) schooling in the United States. We have seen all of this before. Certainly in New Zealand where the State holds a virtual monopoly on education. The outcome, if Common Core is successful is therefore predictable: a burgeoning ignorance of the general population.
The following sentences from the New York Times could have been written today in homage to the Common Core Standards Initiative, the recently adopted national standards for the teaching of mathematics and English-language arts in grades K–12.
“Instead of this old method, the educators would stress from the earliest grades the new concept of the unity of mathematics and an understanding of its structure, using techniques that have been developed since the turn of the century. . . . The new concepts must be taught in high school to prepare the students for the type of mathematics that they will find when they reach college.”
But the century in question here is the 20th, not the 21st. This article, written in 1961, is not about today’s Common Core, but about New Math, the program that was supposed to transform mathematics education by emphasizing concepts and theories rather than traditional computation. Instead, after a few short years of propagating ignorance of all things mathematical, New Math became the butt of jokes nationwide (the Peanuts comic strip took aim more than once) before it was unceremoniously abandoned.
Flash forward 50 years, and Common Core is today making the same promises: “The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.”
But what makes us think Common Core will live up to its hype? And how is it substantially different from New Math, as well as subsequent math programs such as Sequential Math, Math A/B, and the National Council of Teachers of Mathematics Standards? These have all failed America’s children — even though each program promised to transform them into young Einsteins and Aristotles.
The problem with Common Core is not that it provides standards, but that, despite its claims, there is a particular pedagogy that accompanies the standards. And this pedagogy is flawed, for, just as in New Math, from the youngest ages Common Core buries students in concepts at the expense of content.
Take, for example, my first-grade son’s Common Core math lesson in basic subtraction. Six- and seven-year-olds do not yet possess the ability to think abstractly; their mathematics instruction, therefore, must employ concrete methodologies, explanations, and examples. But rather than, say, count on a number line or use objects, Common Core’s standards mandate teaching first-graders to “decompose” two-digit numbers in an effort to emphasize the concept of place value. Thus 13 – 4 is warped into 13 – 3 = 10 – 1 = 9.
Decomposition is a useful skill for older children, but my first-grade son has no clue what it is about or how to do it. He can, however, memorize the answer to 13 – 4 – but Common Core does not advocate that tried-and-true technique.
Common Core’s elevation of concept over computation continues in its place-value method for multiplying two-digit numbers, which is taught in fourth grade. Rather than multiply each digit of the number from right to left, Common Core requires students to multiply each place value so that they have to add four numbers, rather than two, as the final step in finding the product.
Common Core’s most distinctive feature is its insistence that “mathematically proficient students” express understanding of the underlying concepts behind math problems through verbal and written expression. No longer is it sufficient to solve a word problem or algebraic equation and “show your work”; now the work is to be explained by way of written sentences.
I have seen this “writing imperative” first-hand in my sons’ first- and third-grade Common Core math classes. There is certainly space in their respective books for traditional computation, but the books devote enormous space to word problems that have to be answered verbally as well as numerically, some in sections called Write Math. The reason, we are told, is that the Common Core–driven state assessments will contain large numbers of word problems and spaces for students to explain their answers verbally. This prescription immediately dooms grammar-school students who have reading difficulties or are not fluent in English: The mathematical numbers that they could have grasped are now locked into sentences they cannot understand.
The most egregious manifestation of the “writing imperative” is the Four Corners and a Diamond graphic organizer that my sons’ school has implemented to help prepare for the writing portion of the state assessments. The “fourth corner” requires students to explain the problem and solution in multiple sentences. How all this writing helps them with math is yet to be demonstrated.
Hence Common Core looks terribly similar to the failed New Math program, which also emphasized “the why rather than the how, the fundamental concepts that unify the various specialties, from arithmetic to the calculus and beyond, rather than the mechanical manipulations and rule memorizations.” Common Core may not completely eschew the “how,” and it may not be obsessed with binary sets and matrices as New Math was, but it is likely to lose the “how” — the content — in its efforts to move the “why” — the concepts — into the foreground.
The problem is not that students, including those in the primary grades, should not be presented the basic concepts of mathematics — they should be. But there is a difference between learning basic concepts and expressing the intricacies of true mathematical proofs that Common Core desires. Mathematical concepts require a high aptitude for abstract thinking — a skill not possessed by young children and never attained by many. What will happen to students who already struggle with math when they not only are forced to explain what they do not understand, but are presented new material in abstract conceptual formats?
All students must learn to perform the basic mathematical operations of addition, subtraction, multiplication, and division in order to function well in society. Knowing why these operations work as they do is a great benefit, but it is not essential. And in mathematics, concepts are often grasped long after students have mastered content — not before.
In trying to learn both the “why” and the “how” in order to prepare for the state assessments, students will not fully grasp either: They will not receive the instructional time needed to learn how to do the operations because teachers will be forced to devote their precious few classroom minutes to explaining concepts, as the assessments require. The “how” of the basic operations, which need to be memorized and practiced over and over, will be insufficiently learned, since Common Core orders teachers to serve two masters.
The result is simple arithmetic: Instead of developing college- and career-ready students, we will have another generation of students who cannot even make change from a $5 bill, all courtesy of the latest set of bureaucrat-promoted standards that promise to save American education.
By giving concept priority over content, Common Core has failed to learn the history lesson from New Math. Students instructed according to Common Core standards will ultimately know neither the “why” nor the “how,” and we will eventually consign these standards to the ever-expanding dustbin of failed educational initiatives, until the next messianic program is unveiled.
And, of course, this doomed educational experiment, like its predecessors, has a high cost: our children’s ability to do math.
— David G. Bonagura Jr. is a teacher and writer in New York. He has written about education for Crisis, The Catholic Thing, The University Bookman, and the Wall Street Journal.
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