Common Core has come under attack. Critics say the standards enlarge federal control of education — and do a lousy job teaching math.

Those attacks, however, rely on gross distortions and misunderstandings, say defenders of the standards.

Joseph Almeida has taught math for a decade, first in New York and currently in Massachusetts. In 2008, his students had the second-highest math test scores among charter school children in Manhattan. While he taught successfully even before Common Core came along, Almeida describes the standards as a positive development, primarily due to a winnowing in what teachers are expected to cover in a given year.

“They give the teacher a way to teach in-depth, and give a limit to what the teaching is,” Almeida told The Daily Caller News Foundation.

Students previously would cover a wide range of topics every year, he said, but knowledge retention was poor and students failed to acquire the internal mastery essential for easily learning more advanced concepts in later years. More focused standards, he said, limit the number of concepts taught in a particular year. For example, students in grades 1 and 2 focus very heavily on addition and subtraction, before moving on to a similarly precise focus on division and multiplication in grades 3 through 5. The upshot is that students wind up with more mastered concepts after many years, Almeida said, even if they appear to learn less in a particular year.

“We’re doing students a disservice if we advance them faster than they’re ready,” he said.

Bill McCallum, a mathematics professor at the University of Arizona who chaired the writing committee for the math standards, says Almeida’s assessment is exactly what his group intended of the standards.

“The biggest problem [with old math standards] was mile-wide, inch-deep curricula,” McCallum told TheDCNF. He objected strongly to the sentiment that more constrained standards constituted any kind of “dumbing down” in math.

“I don’t know where that comes from,” he said. A tighter, more aggressive focus on particular topics, he argued, helps prevent the same lessons, such as basic division, from being retaught every year for years on end and allows more steady advances that will leave students well-prepared for algebra and geometry when the time comes. This principle of focusing on fewer topics is not original to Common Core, he said, but is borrowed from the standards used by other countries which routinely trounce the United States international math tests, such as South Korea and Singapore.

Despite borrowing several ideas from abroad, McCallum said that Common Core is ultimately a “conservative” approach to standards reform, building atop previous methods used in the United States rather than launching a wholesale remaking of math education on par with the “New Math” fad in the 1960s. In comparison to that, McCallum claims that Common Core was really a “consensus-based” approach to updating math education.

McCallum said he is frustrated by what he views as a wide array of other misinterpretations of the standards.

A textbook distortion of the standards, he says, occurs when individuals complain that the standards lower the bar by excluding calculus and other mathematics disciplines essential to succeeding in STEM disciplines in college.

Such critics, McCallum argues, are forgetting that Common Core establishes goals targeted at all students, not merely those going on to math-centered fields. Just because future engineers will need extra math is no reason to set an “unreasonably high” bar for everybody, McCallum argued.

“Kids who want STEM careers will always need calculus and that’s still true,” said McCallum. “[But] to require calculus of everybody is not reasonable to me.”

Examples of baffling math problems taken from Common Core-aligned curricula, frequently deployed by critics of the standards, earned little more than derision from McCallum.

“Kids have been bringing back silly math problems for years,” well before Common Core was even conceived, McCallum said. Baffling problems and worksheets should be blamed on poor proofreading by textbook companies, not the standards.

Almeida agreed, saying that in his schools “Common Core” textbooks were often virtually identical to those he used before.

“They change them a bit and then slap on a sticker,” he said.

Almeida added that hostile reactions to various Common Core lessons may also be rooted in confusion over how lessons are being taught. Schools are not abandoning traditional ways of doing addition, multiplication, and more, he said, but rather are using the tighter focus on particular subjects to teach them in additional ways.

“We need to imagine we’re learning as children are, ” Almeida said. Adults can comprehend basic math in a straightforward, abstract way, he said, but younger children need more, he argued.

“So much of our math doesn’t focus on place value,” he said, a concept he said is critical to students gaining a greater, lifelong understanding of math. “Place value is so important, and embedded into everything in math, and students don’t understand it well enough.”

While emphasizing place value when teaching students basic addition may seem excessive when simple tools are available may seem excessive, he said, such emphasis pays off years later when students learn about more complex concepts such as decimals and fractions, he said. The broader benefit, he said, is a “seamless thread” running through years of mathematics instruction that did not exist under earlier standards, said Almeida.

However, additional points of emphases only supplement traditional ways of learning material, said McCallum.

“People ask me, ‘Why did you get rid of the old-fashioned way [of solving problems like multiplication]. Well, actually, Common Core does say your student should do that the old-fashioned way.”

Despite his firm defense of Common Core, McCallum told TheDCNF that if the standards die, the damage may not be great, since he says they have still helped to entrench the idea nationwide that school standards must be higher than they were before. While the “common” component of Common Core helps for comparing states, the other aspects of the standards can be closely replicated by states working alone.

“If a state decides to go it alone, and they choose focused standards, all they’ve lost is a bit of time,” said McCallum.