U.S. teens learn advanced math — after school


BEAM recruits low-income middle schoolers in New York City and prepares them for high-level math in high school and college. Photo: Erin Patrice O’Brien, Atlantic

“Online and in the country’s rich coastal cities and tech meccas . . . accelerated students are learning” more complex math than ever before, writes Peg Tyre in The Atlantic. A “new pedagogical ecosystem” — math enrichment camps, after-school and weekend classes, “math circles” and online sites — is growing rapidly.

“More than 10,000 middle- and high-school students haunt chat rooms, buy textbooks, and take classes on the advanced-math learners’ Web site the Art of Problem Solving,” she writes.  Richard Rusczyk, a former Math Olympian who founded the site, is opening two brick-and-mortar centers to teach advanced math and plans an online program for elementary students.

The Proof School, a small independent secondary school in San Francisco, also teaches “amped-up math” — often to the children of high-tech parents.

The Russian School of Mathematics offers classes in 31 locations nationwide.

The Russian School of Mathematics offers classes in 31 locations nationwide.

STEM parents hope to “supplement or replace what they see as the shallow and often confused math instruction offered by public schools, especially during the late-elementary and middle-school years,” writes Tyre.

U.S. elementary teachers often are uncomfortable with math says, Inessa Rifkin, a co-founder of the Russian School of Mathematics, which enrolls 17,500 students in after-school and weekend math academies in 31 U.S.
locations. She thinks kids start to go astray in second or third grade.

Teachers at the Russian School help students achieve fluency in arithmetic, the fundamentals of algebra and geometry, and later, higher-order math. At every level, and with increasing intensity as they get older, students are required to think their way through logic problems that can be resolved only with creative use of the math they’ve learned.

“Students quickly learn their math facts and formulas,” then use that to explore the world, writes Tyre.

From the math-and-science site Expii.com:

Imagine a rope that runs completely around the Earth’s equator, flat against the ground (assume the Earth is a perfect sphere, without any mountains or valleys). You cut the rope and tie in another piece of rope that is 710 inches long, or just under 60 feet. That increases the total length of the rope by a bit more than the length of a bus, or the height of a 5-story building. Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could fit underneath the rope?

The options given are bacteria, a ladybug, a dog, Einstein, a giraffe, or a space shuttle. The instructor then coaches all the students as they reason their way through.

Einstein is the right answer. But the point is get students to “execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy,” writes Tyre.

Bridge to Enter Advanced Mathematics (BEAM), a New York City nonprofit, looks for joyful problem solvers in low-income middle schools. They’re offered “a three-week residential math camp the summer before eighth grade, enhanced instruction after school, help with applying to math circles, and coaching for math competitions, as well as basic advice on high-school selection and college applications.”

Singing an aria from Tosca requires years of training in music. Credit: Metropolitan Opera

Singing an aria from Tosca requires years of training in music. Credit: Metropolitan Opera

Tyre implies that conceptual understanding and “problem solving” can be learned without foundational skills, responds Barry Garelick, author of Confessions of a 21st Century Math Teacher.

She compares a regular ninth-grade algebra class to a lecture “on the basics of musical notation” versus a middle-school problem-solving students singing “an aria from Tosca.”

 

Singing an aria from Tosca requires “years and years of training in basic vocal skills,” writes Garelick. “Musicality is built up from mastery of the basics.”  Similarly, students learn to solve complex math problems by learning how to solve basic problems, then harder problems and so on.

Here’s a profile of the Los Angeles math teacher whose student earned a perfect score in AP Calculus — and whose students all pass the AP exam.

Teachers “should always think of the next level,” said Anthony Yom, who was born in Korea. “Where are they going in the next level, what are they learning in the next class? Then, you can do some backward planning, and that will help you do a good job at explaining things.”

AP lessons are online, free

Free Advanced Placement courses in calculus, physics and macroeconomics are available on edX, reports Nick Anderson for the Washington Post.

Davidson, a private college in North Carolina, worked with high school teachers and the College Board, which oversees AP, to develop online lessons.

“Perhaps it is best to think of them not as MOOCs, but as massive open online lessons, or MOOLs,” writes Anderson. They’re meant to “supplement live teaching, not replace it.” However, the courses could help a motivated student with a weak teacher — or none at all.

Other MOOCs by edX partner universities target AP biology, computer science and chemistry, writes Anderson.

Philanthropist Steven B. Klinsky, is funding an MIT-Harvard venture to create a MOOC pathway to earning a year of college credit for free.

Nancy Moss, an edX spokeswoman, said some of the high school offerings have drawn 10,000 or more students. “The enrollment has been phenomenal,” she said.

Klinsky envisions “a freshman-year catalog of more than 30 introductory courses from top colleges in an array of subjects as diverse as calculus and Western civilization,” writes Anderson. “The MOOCs would include quizzes, tests and online discussion groups, with texts and other materials provided free online,” and a nonprofit partner could provide mentoring and tutoring.

From ‘algebra for all’ to ‘algebra for none’

Thanks to the “algebra for all” movement, nearly half of eighth-graders were taking algebra or geometry in 2013, writes Brookings researcher Tom Loveless in High Achievers, Tracking, and the Common Core. In the Common Core era, only advanced — and advantaged — students will be accelerated.

California pushed 59 percent of students into eighth-grade algebra, though not everyone passed. Now districts have no incentive to offer algebra (or geometry) in middle school. In well-to-do Silicon Valley districts, parents are demanding eighth-grade algebra so their kids will be prepared for AP Calculus by 12th grade.

But urban middle schools with low-income, minority students usually place all students in the same math classes, writes Loveless. Smarter students can’t get ahead.

Accelerated math will survive in affluent school districts, reports the San Jose Mercury News. Parent pressure has been fierce. But students in lower-income districts won’t be on track for AP Calculus, unless they catch up in summer school or double up in math in high school.

Hector Flores, of San Jose, tried to ensure his son was on track to take calculus in high school — even sending him to a summer math institute. But the Evergreen School District placed him in an “integrated” Common Core eighth-grade math class, where he’s reviewing much of what he already learned. “He’s literally caught in the crack” of the Common Core transition, said Flores, a former math teacher. Now, to take calculus, his son will have to take an extra class in high school.

Low-income, black and Latino students who excel in math should have the chance to take the algebra-to-calculus track, writes Loveless. It’s not elitism. It’s equity.

Because of their animus toward tracking, some critics seem to support a severe policy swing from Algebra for All, which was pursued for equity, to Algebra for None, which will be pursued for equity.  It’s as if either everyone or no one should be allowed to take algebra in eighth grade.

Barry Garelick taught in a middle school that lets very few students take algebra in eighth grade, he writes in Out in Left Field.  A student asked him if she’d qualified for Algebra I. “I don’t want to be with the stupid people,” she said.

“In the name of egalitarianism and the greater common good,” the vast majority of students will take a watered-down Core version of algebra in ninth grade, he writes. They’ll end up as “stupid people.”

Teach programming, statistics — not calculus

Get rid of high school calculus to make way for computer programming and statistics, writes Steven Salzberg in Forbes.

With computers controlling so much of their lives, from their phones to their cars to the online existence, we ought to teach our kids what’s going on under the hood. And programming will teach them a form of logical reasoning that is missing from the standard math curriculum.

With data science emerging as one of the hottest new scientific areas, a basic understanding of statistics will provide the foundation for a wide range of 21st century career paths.

Most students won’t need calculus, Salzberg writes. Those who do can take it in college.

If a few top universities announced they value programming and statistics as highly as calculus,  “our high schools would sit up and take notice,” he writes.

I’m not sure everyone needs computer science, but I would like to see non-calculus alternatives for non-STEM students.

When my daughter was entering 12th grade, I suggested she take AP Statistics, which I thought she might be able to use in the future.  The college counselor said AP Statistics was considered second rate. Elite colleges demanded AP Calculus.

My daughter earned a C in calculus her first semester. The counselor said she’d doomed her college chances. So Allison dropped the course to do an independent study on American poetry, was rejected by Yale, Brown, Penn, etc. and went to UCLA, where she earned an A+ in statistics. After two years, she transferred to Stanford, where she dabbled in programming. (“Everyone knows Java,” she said.)

Two math pathways in high school?

Most community college students don’t need Algebra II, but do need mastery of middle-school math, concludes What Does It Really Mean To Be College and Work Ready?, a recent report by the National Center on Education and the Economy. In his Top Performers blog, NCEE’s Marc Tucker explains why he supports Common Core Standards, which require Algebra II content, but doesn’t think Algebra II should be  graduation requirement.

Algebra II prepares students to take calculus, which fewer than five percent of U.S. workers will use on the job, writes Tucker. Why require it of everyone?

Some students, including many who will go on to STEM careers, should study Algebra II and beyond, including, if possible, calculus.  But many others, going on to other sorts of careers, should study the advanced mathematics that is appropriate for the kind of work they will do.  Homebuilders, surveyors and navigators might need geometry and trigonometry, whereas those going into industrial production or public health might want to pursue statistics and probability.  We argued not for lowering the standards but for creating pathways through advanced mathematics in high school that make sense in terms of the kind of mathematics that may be most useful to students when they leave school and enter the workforce.

Phil Daro, who headed the team that wrote the Common Core State Standards (CCSS) for mathematics, also co-chaired the NCEE study’s math panel. Daro writes that the Common Core math standards include “college ready” and STEM goals. The lower “college ready” standards are not as rigorous as a traditional Algebra II course, though they are “more demanding than the NCEE study found was necessary for success” in community college.

 In writing the CCSS, we were charged with articulating one set of standards for all students that would be sufficient preparation for 4-year college programs.  . . . we could not customize different standards for different students with different destinations.  The principle behind this is social justice, but it has a cost.  One could argue that it would be better to have the common standards end earlier, and specialized standards start sooner.

Indeed, my own view is that there should be two mathematics pathways to college readiness that split after grade 9: one for students with STEM ambitions and one for students with other ambitions.

To avoid “social justice risks associated with different pathways,” Daro suggests making both pathways qualify for college admission without remediation.

By 10th grade, students would have to decide whether to take the easier non-STEM path or tackle college-prep math courses that keep the door open to a career in engineering, math and hard sciences.

Now, many students wander through years of middle-school and college-prep math without understanding what they’re doing. If they’re assigned to remedial math in college, the odds are they won’t earn a degree or a job credential. Is that social justice?

NCEE: Only 5% need calculus

Only 5 percent of students will use calculus in college or the workplace, concludes a new report on college and career readiness by the National Center on Education and the Economy. Most community college students could succeed in college courses if they’ve mastered “middle school mathematics, especially arithmetic, ratio, proportion, expressions and simple equations.” Many have not.

The report calls for providing an alternative track — less algebra, more statistics — for high school students who aren’t aiming at university STEM degrees.

In a few years, high school diplomas in North Carolina will show whether a graduate is prepared for a four-year university, a community college and/or a career.

Honors Track

In Honors Track, fiction in the new Atlantic, ambitious students form a cheating ring.

WE WERE SEDULOUS. We were driven. Our vocabularies were formidable and constantly expanding. We knew the chemical elements by number and properties, the names and dates of battles in the world’s greatest wars.

We arrived at school early and put in twelve-hour days. Exhaustion was routine. Most of us repelled it with Pepsi or Mountain Dew. Others took a more holistic approach. Neil Casey did a series of deep-breathing exercises; May Wang sipped from a thermos of ginseng tea. Dale Gilman, the vice principal’s son, whom none of the rest of us could stand, rolled his ankles and wrists around while he sat through each class. “It really gets the blood flowing,” he said in his high-pitched voice, even though we never asked him to explain.

. . .  The pamphlets we took home from the Guidance Office showed photographs of trees in a perpetual state of October, and students’ faces laughing under jaunty knit caps.

I liked the story — but it made no sense to have the top students taking “honors calculus” in their junior year.  They’d take AP Calculus as seniors.

Discipline stats: What’s fair?

Black students are suspended, expelled and arrested at higher rates than whites, concludes a new report by the U.S. Education Department’s Office of Civil Rights. “The everyday educational experience for many students of color violates the principle of equity at the heart of the American promise,” Education Secretary Arne Duncan said.

What About the Kids Who Behave? asks Jason Riley in the Wall Street Journal. Though Duncan said the discipline statistics don’t prove discrimination, inevitably schools will be pressured to ease up on black kids who act up. That will be hard on their classmates, most of whom will be “students of color,” and their teachers.

The Obama administration’s sympathies are with the knuckleheads who are disrupting class, not with the kids who are trying to get an education. But is racial parity in disciplinary outcomes more important than school safety?

The report also found that high-minority high schools are half as likely to teach calculus as low-minority schools. That probably reflects fewer students who are prepared to take college-level math.

In addition, teachers in high-minority schools have less experience and therefore earn less. If these schools have more first- and second-year teachers — which I’d bet they do — that’s a real problem.

Boys dominate AP physics, computer science

Most STEM fields are likely to remain predominantly male. Boys take more AP physics and computer science exams, while girls now dominate AP biology (59 percent), notes Curriculum Matters, who’s been reading the AP Report to the Nation. While Calculus AB exam-takers are evenly split, 59 percent of those who tackle the more advanced Calculus BC are male.

Males make up 58 percent of AP music theory exam-takers, 74 to 77 percent in physics and 80 to 86 percent in computer science.

Gender differences were minor for Chemistry, European History, Latin, Statistics and U.S. Government and Politics.

In The Big Bang Theory, three males are physicists (theoretical, experimental and astro) and one is an engineer, while the female scientists are biologists.

 

Who needs calculus?

Calculus is the wrong goal for 90 percent of students, argued Harvey Mudd Professor Arthur T. Benjamin at the Ciudad de las Ideas in Puebla, Mexico.

“For the last 200 years, the mathematics that we’ve learned starts with arithmetic and algebra, and everything we do after that is taking us toward one subject, calculus. I think that is the wrong mathematical goal for 90 percent of our students,” he says. “We’re now living in an age of information and data, and the mathematics that will be most relevant to our daily lives is probability and statistics.” Only some professions require calculus. Everyone reads—and many misunderstand—media reports about health, science, and the environment that contain statistics. Better literacy in probability and stats would benefit everyone.

Most students don’t make it to calculus — or statistics. I didn’t. As a journalist — a notoriously innumerate trade — I frequently had to struggle with statistics to understand reports. I found my arithmetic skills very useful.

The Carnegie Foundation‘s redesign of community college math curricula stresses statistics and quantitative reasoning for students who aren’t headed for STEM careers.

I wonder how high school math would change if students could choose between a STEM-prep or math-for-citizenship track. Would we let students opt out of the calculus track in ninth or tenth grade? How about the kids who keep flunking algebra?