Amping up math standards has been a key piece of the campaign to get American high school students "college and career ready," but some critics say the math skills now demanded of many high school students are simply harder than they need to be, even for the majority of college-bound students.
Nearly 20 states now require high school students to take Algebra II, although Texas, which started the trend back in 2006, dropped the requirement last year.
Meanwhile, a number of Algebra II concepts have worked their way down into Algebra I exit exams. This summer, New York revised its test to align it with Common Core expectations, adding tougher material traditionally taught in Algebra II or trigonometry.
"It's a nice challenging test for an honors student," says Geri Ganzekaufer, a 29-year veteran math teacher at Schreiber High School in Port Washington, New York. "I think the people writing the test haven't been in the classroom for a while."
New York is not alone, argues Bob Schaeffer, public education director for the National Center on Fair and Open Testing, a Washington-based education advocacy group. He argues that the eighth- and 10th-grade Common Core standards "feel like curriculum designed by folks who want everyone to become math professors.
The dilemma teachers and policymakers face is that people now want to produce more college ready high school graduates with advanced math under their belts. But the result is many students struggle with complex math that, critics argue, they will not need for most college majors or even high-level careers.
How much math do college-bound students really need? Its a conversation many consider overdue.
The Whirlpool
A recent report by the Center for New York City Affairs at The New School found that 30 percent of New York City high school students in the prospective class of 2014 flunked the Algebra I exam on their first try. Those who failed averaged two more attempts, and the pass rate for repeats fell to 20 percent, and 2,500 took the exam more than five times. The authors of the study call this the Algebra Whirlpool.
"The test is simply too hard and verbally confusing for the average student," argues Ganzekaufer. Skewing the scoring doesnt solve the problem and, doubling up on math doesnt make them better at it or like it more. Not every child needs to tackle quadratic equations and exponentiation, she argues.
Ganzekaufer argues that excess time spent on challenging math that many students don't need and can't learn squeezes out not just arts and language but even basic numeracy, which, she says, gets lost in the pursuit of higher math.
Students who are endlessly drilled on math they will never use, she says, draw a blank, she says, when they are asked to say what 20 percent of 200 is.
How much, how early?
Ouida Newton, a math teacher currently on sabbatical as the Arkansas Teacher of the Year, says she was initially worried about some of the complex math now required of eighth-graders. But she says her fears proved groundless.
"I've learned over the past 30 years that students will do what you expect them to do, Newton said. If you set the bar high, they'll reach it. But it requires support."
Newton defends the Common Core math. While it does push some difficult concepts into lower grades, she says, the way it teaches them with applied problems helps students grasp them more easily.
"The big thing about Common Core is that we don't just teach them how to do rote mathematical processes," Newton said. "We now aim at conceptual understanding, and we do a lot of modeling and hands-on work."
Her eighth-graders, Newton says, now have a better understanding of some of the algebra principles than her Algebra I students in years past. For instance, systems of equations had traditionally been taught in high school, Newton said, and when the concept was pushed down to eighth grade under Common Core, she was nervous.
But the kids got it, she said, because we didnt teach it rote. Instead, they taught systems of equations using a real-world problem. They set up a problem involving creatures they called blobs, which were multiplying at different rates. The challenge was to use math to determine at what point one population of blobs would catch and surpass the other.
When you go about it with a real-world angle, when it has meaning to the kids, they get it, Newton said.
But should all high school students be taught esoteric skills such as polynomial functions and parametric equations? Newton says yes.
If we want our kids to be successful, theyve got to have a strong foundation, she says.
A broader pushback
On one level, it seems that any debate over rigorous high school math has long been answered. In recent years, the notion that all students should leave high school college or career ready, has become an axiom, although there is little actual discussion of the common readiness denominator for widely disparate college majors or careers.
But scratch beneath the surface, and you find percolating doubts.
Its true that mathematics requires mental exertion, writes political scientist Andrew Hacker in The New York Times. But theres no evidence that being able to prove (x + y) = (x - y) + (2xy) leads to more credible political opinions or social analysis.
Hacker argues that required algebra should be replaced with an alternative he calls citizen statistics, which would help students understand the data around them, such as how unemployment or inflation rates are calculated.
Joseph Rosenstein, a math professor at Rutgers University, argues any student who is not going on to calculus does not need complex numbers, rational exponents and cube roots. If you think about it, he tells the Hechinger Report, a class in statistics would be more important than Algebra II, in reading charts and determining probability.
And Gary Rubenstein, an award-winning math teacher at New York City's prestigious Stuyvesant High School, writes on his blog that he would gleefully chop at least 40 percent of the topics that are currently taught from K to 12.
The real world
Nebraska is not a Common Core state and has a strong history of local control, says Shelby Aaberg, chair of the math department at Scottsbluff High School and Nebraska's 2014 Teacher of the Year. But the math standards, Aaberg said, are just as rigorous.
To make math curriculum more applied to real life, Aaberg says, Nebraska invited 40 major businesses in the state to find authentic tasks that require workers to use high-level math skills to solve real problems. These real-world problems then form the basis for the curriculum, so at every stage students know how they might use what they are learning.
One company has been asked to build monorails for Disney and needs workers to use trigonometry to figure out the proper curvature of the rails for a turn. Another company wants to know how much steel will be required to build a light pole base, which Aaberg says could be solved using polynomials.
Polynomials could also be used to understand how antibiotics work in the body. What happens if you stop taking the antibiotic course before it finishes? Aaberg, whose wife is a clinical pharmacist, has his students create a graph on how the concentration of antibiotics in the bloodstream falls until it dips below the threshold of effectiveness.
Biologists trying to weigh an alligator, he says, would use similar tools, choosing from a variety of models to extrapolate weight based on previous experience. Higher math skills, Aaberg says, help you analyze the data you would uncover in a variety of fields.
Is more always better? Aaberg does not think so, but he is also not completely certain where and how those lines ought to be drawn.
This conversation expanding, Aaberg says, and thats a good thing. We cant conceptualize the future world, so what should we be teaching kids?"
Nearly 20 states now require high school students to take Algebra II, although Texas, which started the trend back in 2006, dropped the requirement last year.
Meanwhile, a number of Algebra II concepts have worked their way down into Algebra I exit exams. This summer, New York revised its test to align it with Common Core expectations, adding tougher material traditionally taught in Algebra II or trigonometry.
"It's a nice challenging test for an honors student," says Geri Ganzekaufer, a 29-year veteran math teacher at Schreiber High School in Port Washington, New York. "I think the people writing the test haven't been in the classroom for a while."
New York is not alone, argues Bob Schaeffer, public education director for the National Center on Fair and Open Testing, a Washington-based education advocacy group. He argues that the eighth- and 10th-grade Common Core standards "feel like curriculum designed by folks who want everyone to become math professors.
The dilemma teachers and policymakers face is that people now want to produce more college ready high school graduates with advanced math under their belts. But the result is many students struggle with complex math that, critics argue, they will not need for most college majors or even high-level careers.
How much math do college-bound students really need? Its a conversation many consider overdue.
The Whirlpool
A recent report by the Center for New York City Affairs at The New School found that 30 percent of New York City high school students in the prospective class of 2014 flunked the Algebra I exam on their first try. Those who failed averaged two more attempts, and the pass rate for repeats fell to 20 percent, and 2,500 took the exam more than five times. The authors of the study call this the Algebra Whirlpool.
"The test is simply too hard and verbally confusing for the average student," argues Ganzekaufer. Skewing the scoring doesnt solve the problem and, doubling up on math doesnt make them better at it or like it more. Not every child needs to tackle quadratic equations and exponentiation, she argues.
Ganzekaufer argues that excess time spent on challenging math that many students don't need and can't learn squeezes out not just arts and language but even basic numeracy, which, she says, gets lost in the pursuit of higher math.
Students who are endlessly drilled on math they will never use, she says, draw a blank, she says, when they are asked to say what 20 percent of 200 is.
How much, how early?
Ouida Newton, a math teacher currently on sabbatical as the Arkansas Teacher of the Year, says she was initially worried about some of the complex math now required of eighth-graders. But she says her fears proved groundless.
"I've learned over the past 30 years that students will do what you expect them to do, Newton said. If you set the bar high, they'll reach it. But it requires support."
Newton defends the Common Core math. While it does push some difficult concepts into lower grades, she says, the way it teaches them with applied problems helps students grasp them more easily.
"The big thing about Common Core is that we don't just teach them how to do rote mathematical processes," Newton said. "We now aim at conceptual understanding, and we do a lot of modeling and hands-on work."
Her eighth-graders, Newton says, now have a better understanding of some of the algebra principles than her Algebra I students in years past. For instance, systems of equations had traditionally been taught in high school, Newton said, and when the concept was pushed down to eighth grade under Common Core, she was nervous.
But the kids got it, she said, because we didnt teach it rote. Instead, they taught systems of equations using a real-world problem. They set up a problem involving creatures they called blobs, which were multiplying at different rates. The challenge was to use math to determine at what point one population of blobs would catch and surpass the other.
When you go about it with a real-world angle, when it has meaning to the kids, they get it, Newton said.
But should all high school students be taught esoteric skills such as polynomial functions and parametric equations? Newton says yes.
If we want our kids to be successful, theyve got to have a strong foundation, she says.
A broader pushback
On one level, it seems that any debate over rigorous high school math has long been answered. In recent years, the notion that all students should leave high school college or career ready, has become an axiom, although there is little actual discussion of the common readiness denominator for widely disparate college majors or careers.
But scratch beneath the surface, and you find percolating doubts.
Its true that mathematics requires mental exertion, writes political scientist Andrew Hacker in The New York Times. But theres no evidence that being able to prove (x + y) = (x - y) + (2xy) leads to more credible political opinions or social analysis.
Hacker argues that required algebra should be replaced with an alternative he calls citizen statistics, which would help students understand the data around them, such as how unemployment or inflation rates are calculated.
Joseph Rosenstein, a math professor at Rutgers University, argues any student who is not going on to calculus does not need complex numbers, rational exponents and cube roots. If you think about it, he tells the Hechinger Report, a class in statistics would be more important than Algebra II, in reading charts and determining probability.
And Gary Rubenstein, an award-winning math teacher at New York City's prestigious Stuyvesant High School, writes on his blog that he would gleefully chop at least 40 percent of the topics that are currently taught from K to 12.
The real world
Nebraska is not a Common Core state and has a strong history of local control, says Shelby Aaberg, chair of the math department at Scottsbluff High School and Nebraska's 2014 Teacher of the Year. But the math standards, Aaberg said, are just as rigorous.
To make math curriculum more applied to real life, Aaberg says, Nebraska invited 40 major businesses in the state to find authentic tasks that require workers to use high-level math skills to solve real problems. These real-world problems then form the basis for the curriculum, so at every stage students know how they might use what they are learning.
One company has been asked to build monorails for Disney and needs workers to use trigonometry to figure out the proper curvature of the rails for a turn. Another company wants to know how much steel will be required to build a light pole base, which Aaberg says could be solved using polynomials.
Polynomials could also be used to understand how antibiotics work in the body. What happens if you stop taking the antibiotic course before it finishes? Aaberg, whose wife is a clinical pharmacist, has his students create a graph on how the concentration of antibiotics in the bloodstream falls until it dips below the threshold of effectiveness.
Biologists trying to weigh an alligator, he says, would use similar tools, choosing from a variety of models to extrapolate weight based on previous experience. Higher math skills, Aaberg says, help you analyze the data you would uncover in a variety of fields.
Is more always better? Aaberg does not think so, but he is also not completely certain where and how those lines ought to be drawn.
This conversation expanding, Aaberg says, and thats a good thing. We cant conceptualize the future world, so what should we be teaching kids?"