The Education Invasion. Joy Pullmann
a column (or stick) to represent ten. The sticks lined up in a row of ten would form a large square, which represents one hundred.
Russell’s first-grade daughter gasps when she notices him in her classroom and trots over to hug him. Then, slightly embarrassed, she quickly returns to one of several irregular trapezoidal tables that take the place of desks. The children wear collared shirts, mostly polos, and no jeans — a loosely defined uniform the Warren district requires.
Latdrik gathers all the children in front of the smartboard. “I’m ready to teach,” she announces. “I’m ready to learn,” the kids chorus.
She walks them through several ways to write the day’s date on a smartboard-projected calendar, writing directly on the screen. Then they clap and slap their legs, chanting in unison as they move through a series of simple addition problems: “Three plus three is six — kicks! Four plus four is eight — great!”
Latdrik switches over to a large paper pad on an easel, with more ten-stick and one-cube groupings, and calls on kids to tell her what number each represents. A girl gives a correct answer, and Latdrik asks her, “Raven, what strategy did you use to find out what number that is?” Raven responds, “First I counted by tens, then by ones.”
The teacher then discusses two good answers to the previous day’s homework problem. Finally she says: “If you want to help me solve my math problem, give me a wink.”
Liberty Elementary has four first-grade classes. The smartboard displays the names of each class’s teachers, and below each the number of students in that class: 22, 22, 21, and 23. Latdrik wants to bring a treat to school for all the first graders next week, she says. So how many should she make? This is a “real-world problem” of the kind that many teachers are emphasizing thanks to Common Core, whose math benchmarks use the term “real-world” fifty-one times.9 She tells the children to return to their desks and take out their math manipulatives — foam versions of the ten-sticks and one-cubes on the screen. The children cluster in twos and threes, pulling out their “math journals” to help solve the problem. Latdrik moves among the tables, giving suggestions and answering questions.
Two little girls sitting at a table nearby are working independently. One with pigtails gathered all over her head by colorful plastic bobbles draws on her paper a stick-and-cube diagram that matches her manipulatives, which in turn correspond to the numbers on the board:
She counts up the sticks and writes down the results: 10 + 10 + 10 + 10 + 10 + 10 + 10 = 70. She missed one. Finally, she counts the cubes, and writes her answer to the problem: 78.
Her partner, a girl in a yellow polo shirt, with hair in thin braids, writes in her math journal:
Instead of proceeding to add these numbers in the traditional way, beginning with the right-hand column, the girl counts up the tens from the left column and takes out eight ten-sticks. She does the same for the ones column using the little cubes, and then counts up all the manipulatives. On her paper she writes “86.” She has counted the one-cubes incorrectly. But she doesn’t know it yet, so she plays with the remaining foam blocks until Latdrik tells the children to put away the manipulatives and discuss their answers. It has taken the group approximately eight minutes to work this problem. To answer it the traditional way would take an average first grader about fifteen seconds.
On the wall are two posters suggesting different ways to add and subtract. They include tally marks, drawing a picture, a number line, and a number sentence: 7 +4 =11. What’s missing is the standard algorithms for addition and subtraction: stacking the numbers and computing them by columns, starting with the ones column. Common Core doesn’t call for this procedure until the fourth grade. For first graders, it prescribes exactly what Latdrik has done: using “a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths,) to model add-to, take-from, put-together, take-apart”; teaching children to compare “a variety of solution strategies”; and the like.10
Activities like those practiced in Sarah Latdrik’s class have appeared in stories about Common Core’s “new way of school” in newspapers across the country. These methods have actually been around for decades, variously dubbed “new math,” “reform math,” and even “fuzzy math.” As critics point out, multiplying the things that children must keep track of leads to simple errors like those made by the two girls trying to add up two-digit numbers with a detour through sticks and cubes. Moreover, the amount of time eaten up by such convoluted methods means less time for calculating practice. Children are then hampered when they reach algebra, where success requires having routine math procedures down cold.
Most high-achieving countries call for fluency in three-digit addition and subtraction in third grade, says Ze’ev Wurman, a former U.S. Department of Education official who helped write California’s well-regarded math standards. Those countries also typically introduce standard algorithms immediately, the way many of today’s parents learned math. In Wurman’s view, “The rubbish that fills [Common Core] in earlier grades about ‘strategies’ ‘relationships’ and ‘properties’ . . . is not truly ‘rubbish’ — and one can find some good explanation for a little bit of need of them — but it is repeated ad nauseam.” Thus the curriculum “opens itself up for easy interpretation of fuzz and invented algorithms, which most implementations and textbooks gleefully (or ignorantly) proceed to make.”
Parents have raised many complaints about the time-devouring Common Core math processes and the incomprehensible problems their young children are assigned. Many examples of confusing math homework have gone viral.
Jeff Sevart, an electrical engineer who lives in Indiana, posted his second-grade son’s Common Core math homework on Facebook. The instruction for the assignment read: “Jack used the number line below to solve 427 –326. Find his error. Then write a letter to Jack telling him what he did right, and what he should do to fix his mistake.” After spending two hours trying to help his son figure out the answer, Sevart himself wrote the letter:
Dear Jack,
Don’t feel bad. I have a Bachelor of Science Degree in Electronics Engineering which included extensive study in differential equations and other higher math applications. Even I cannot explain the Common Core Mathematics approach, nor get the answer correct. In the real world, simplification is valued over complication.
Sevart then demonstrated the traditional, straightforward method of subtraction. “The answer is solved in under 5 seconds,” he wrote, whereas the process that “Jack” used was “ridiculous and would result in termination” in the workplace. He signed his letter “Frustrated Parent” and put it online. Sevart’s outraged post soon appeared on Yahoo! News, Glenn Beck’s radio program, the Huffington Post, and Time online, among other media outlets.
Another angry dad was the comedian Louis C.K., who took to Twitter to express his vexation over his daughter’s third-grade math homework.
My kids used to love math. Now it makes them cry. Thanks standardized testing and common core!
— Louis C.K. (@louisck) April 28, 201411
He then repeated his complaints on the Late Show with David Letterman.
The usual response from Common Core supporters to such complaints is: Common Core is not a curriculum; it’s only a set of standards for curriculum and testing, which publishers and teachers then use as the basis for writing math problems and other assignments. Imagine a recipe book that lists ingredients but doesn’t specify quantities or processes; the cook can figure that out. So if the dish isn’t tasty, blame the cook, not the recipe book.
But if all the cooks are turning out similarly unpalatable dishes, that means the recipes deserve some criticism. Tom Loveless of the Brookings Institution observed