Sydney Young is a confident, vivacious 10-year-old who was comfortable recently showing a classroom full of parents at Fuquay-Varina Elementary School how fifth-graders learned to solve math word problems requiring multiplication and division with decimals.
But Sydney admitted later that she occasionally cries in frustration over her math homework.
Her aunt, Jean Rodgers, helps Sydney with math at home. And Rodgers gets frustrated, too. Many elementary math lessons today don’t look much like they did few years ago.
Rodgers has turned to YouTube videos for help and scoured bookstores for math texts. She attended the fifth-grade math night for families to learn how to help her niece, a conscientious student who aspires to go to Harvard.
“She doesn’t like to not understand,” Rodgers said of her niece. “Even though she’s fine now, the last thing we want is for her to get behind and not be able to catch up.”
Sydney was in second grade when North Carolina adopted national goals for student achievement in math and reading called Common Core standards. Four years later, the standards continue to be controversial with some parents and students. Math in particular – what students should know, when they should learn it, and how to teach it – is a flashpoint in the debate.
A state group established by the legislature called the Academic Standards Review Commission has before it a recommendation – written by one of its work groups – to dump Common Core math. The commission is set to vote on its final report in December.
The proposal would have the state replace Common Core math in the lower grades with the math standards used in Minnesota. John Scheick, a former university math professor who led the commission’s math review, criticized the teaching methods being used with Common Core math.
“Excessive use of so-called models or visual methods of calculation is detrimental to the attainment of speed and accuracy in standard calculations since they are inherently inefficient,” the draft states.
“They are useful to get the concepts across or for easy mental calculations. It appears from numerous published examples and complaints from parents that some teachers are making the computations with models into monstrously complex exercises.”
In the upper grades, algebra, geometry, statistics and other disciplines are combined and taught in an integrated fashion over three courses. The commission is considering separating them again. Students would go back to taking two algebra courses and one geometry course.
Rodgers, Sydney’s aunt, is like many adults who share Common Core math pains. Their frustration comes up in casual talks with friends, in online exchanges and at public meetings.
Elementary math problems that students were once taught to solve in one or two steps today may look like a collection of multilayered and sometimes confusing tasks involving grids, drawings and models.
For example, fifth-graders are taught to multiply whole numbers with decimals using 100-block grids. Finding the product of 1.45 x 2 involves shading two full grids then shading 45 of the smaller blocks twice, with each of those representing .45. The two .45 drawings are combined to get .9.
Common Core supporters say these new math lessons are part of what will help improve U.S. students’ standing on international math tests, where peers from around the world consistently outperform them.
The aim, supporters say, is to have students understand how math works through visualization and conversations. Students eventually learn the traditional ways of solving math problems. But the idea is that they will first develop a deeper understanding of numbers and concepts that will smooth the transition to algebra and higher-level math topics.
The standards describe what students should learn each year from kindergarten through eighth grade and what math courses should cover in high school.
At all levels, the standards list eight “mathematical practices” that students should develop. They include reasoning abstractly and quantitatively, modeling with mathematics, and constructing viable arguments and critiquing the reasoning of others.
“There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b) (x + y) and a student who can explain where the mnemonic comes from,” says the introduction to the math standards. “The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c) (x + y).”
The need for the standards and the new approaches to learning math are obvious not just because the U.S. isn’t doing as well as other countries but because employers say workers lack needed skills. Jobs require workers to know math and collaborate to solve practical problems, said Ron Preston, an associate professor at East Carolina University and president of the North Carolina Council of Teachers of Mathematics.
“The answers won’t be in the back of the book when you’re out there in the workplace,” Preston said.
First year the hardest
Dana Snapp, a fifth-grade teacher at Fuquay-Varina Elementary School, has students sit in groups of four to talk about multiplying with decimals. The students talk to each other and write out their answers to a problem that demonstrates that multiplying by one-tenth is the same as dividing by 10.
Before, what we had was algorithms, formulas, ways of computing numbers but not necessarily understanding what you are doing with the numbers.
Dana Snapp, a fifth-grade teacher at Fuquay-Varina Elementary School
Snapp, who has taught fifth-grade math using the old standards and Common Core, said the first year of Common Core was the hardest. The lack of continuity between the new and old standards meant that students hadn’t learned all they needed in fourth grade to be able to move smoothly to fifth-grade topics.
Now well beyond that inaugural year, Snapp said she supports the standards and appreciates their value.
“Before, what we had was algorithms, formulas, ways of computing numbers but not necessarily understanding what you are doing with the numbers,” she said. “I think that made it really difficult when they got to higher-level math, like algebra, for instance, when they had to do abstract math but didn’t understand how the numbers worked.
“It was difficult for me to learn at first, too,” she said. “I can see now that the kids get it. When they get it, it’s more solid, and they don’t lose it.”
Teachers at Fuquay-Varina and the school’s math coach, Rene Herrick, devised strategies for teaching each of the academic goals.
To help parents know what’s being taught, Wake filled its YouTube channel with hundreds of math demonstration videos. Fuquay-Varina and some other schools in Wake invite parents to family math nights like the one Jean Rodgers attended with her niece.
Herrick said parents will see the benefits of Common Core.
At the family math night at Fuquay-Varina, fifth-graders demonstrated techniques for solving problems and explained the steps.
“If you were to stand up and do a direct instruction lesson for 45 minutes, showing them how to do it over and over, they would continue to practice something they don’t understand,” Herrick told the adults.
Supporters speak up
Common Core critics have dominated the debate for months, but now supporters have started to speak up.
The board of the state math teachers council has asked the standards commission to keep Common Core.
Separately, Ladnor Geissinger, a retired UNC-Chapel Hill math professor, called the standards commission’s math recommendations “a hack job.”
The math review group makes a poor case for choosing Minnesota standards over Common Core, Geissinger said. And it’s apparent that the reviewers were not familiar with research on how students “progress from one stage to another,” he said.
“They pay no attention to such things,” Geissinger said. “It’s quite clear they were set on changing things. It’s not an unbiased review.”
Diane Briars, president of the National Council of Teachers of Mathematics, criticized the commission’s math review for what she said were its inconsistencies.
“What they recommend is inconsistent both with best practice and the research evidence – even the reports they cited themselves,” she said.
Scheick, who led the Common Core math review, has refused twice since this summer to talk about how the recommendations were developed. Commission members decided earlier this year to refer questions to the two commission chairmen. Scheick declined to answer questions about the math recommendations after the commission’s public meeting in November, and after the chairmen said he could talk.
“The News & Observer is harassing us with these public records requests,” Scheick said. “This conversation is over.”
The News & Observer has made three public records requests since July but has received no documents.
Scheick’s work group decided to go with the Minnesota standards because it found that they are clearer and meet guidelines in a 2008 national report on math education by the National Mathematics Advisory Panel. Minnesota students do better on national assessments, the state commission’s draft report noted.
This year, 53 percent of Minnesota fourth-graders scored at or above “proficient” on the National Assessment of Educational Progress math test, while 44 percent of North Carolina’s fourth-grade students reached that mark.
On the eighth-grade NAEP math test, 48 percent of Minnesota’s students were at or above proficient, while 33 percent of North Carolina’s were.
NAEP scores, which are considered the nation’s report card, dropped nationally this year compared with 2013. There seems to be no connection between Common Core and student performance on this year’s test. Minnesota’s fourth-grade scores dropped four points, while North Carolina’s dropped one point, which NAEP considered an insignificant change from 2013. Virginia’s fourth-grade scores were unchanged while Texas saw fourth-grade scores go up two points. Neither state uses Common Core standards.
Eighth-grade math scores were unchanged in Minnesota and Virginia but declined four points in North Carolina and Texas.
The North Carolina Council of Teachers of Mathematics, in its critique of the state commission’s work on the math goals, said the group misrepresented the national math advisory panel’s 2008 recommendations, made inaccurate claims that Common Core omitted topics that are actually included, and makes untrue statements about what students are expected to know about geometry.
“It is unclear whether the ASRC (Academic Standards Review Commission) analysis simply misunderstood the inclusions in the Common Core or neglected them in their review,” the council’s board wrote. “Regardless, it again calls into question the quality and thoroughness of the review and the validity of resulting recommendations.”
The commission is set to adopt its final report in December. The State Board of Education has the final say over academic standards.
André Peek, the commission’s co-chairman, said it’s possible the commission may not vote to suggest that the state adopt Minnesota’s math plan but may instead use it as an example of how North Carolina’s math goals should be written.
“I don’t think that there’s a big debate that we’re not the people to decide the content of math standards, this commission,” Peek said. “Our point is that these standards are not clear.”