Failing remedial algebra, passing statistics

Michigan State will drop its algebra requirement in favor of “quantitative literacy,”  reports Inside Higher Ed.

“We’re trying to present mathematics in a way that makes it more accessible and understandable,” said Vince Melfi, associate professor of statistics and probability. For example, students will study how probability applies to health and risk, Melfi said.

. . . students could be informed that a hypothetical person’s test came back positive for breast cancer. Based on that information, they would be asked to determine the likelihood that the person had the disease.

After arriving at answers, students would be encouraged to discuss the value of screening for diseases such as breast cancer or prostate cancer — a topic that has fostered debate among medical professionals, Melfi said. “An important part of these courses is to go beyond just manipulating symbols on a page and coming up with the right answer, and to reflect on what those answers mean in a specific context,” he said.

Statistics probably is more useful to non-STEM students than the algebra. But, I wonder about college students who can’t figure out 2x + 4 = 14. It’s not rocket science.

Wayne State University in Detroit decided to drop its general-education math requirement, but plans to introduce “math experience” courses for students whose majors don’t require math.

Remedial math — basic algebra — is a huge stumbling block for many students, especially at the community college level, reports Science DailyPoorly prepared students are more likely to be able to pass statistics, City University of New York researchers have found.

New community college students assessed as needing remedial algebra were placed randomly in a remedial algebra course, remedial algebra with weekly workshops providing extra support or in a college-level statistics class with weekly workshops.

Fifty-six percent of statistics students passed compared to 39 percent in remedial algebra. By the middle of their second year in college, 57 percent of statistics students had met their college’s math requirement, compared to only 16 percent of remedial algebra students.

SF: No child gets ahead in math

San Francisco public schools don’t teach Algebra I or Geometry to even the brightest, most math-loving eighth graders writes Ben Christopher on Priceonomics. Why? he asks.

The new mathematical course sequence “ensures that all students enter high school with the same mathematical foundation,” say SFUSD officials. No child gets ahead.

Common Core recommends that only the strongest math students take algebra in middle school. Nearly all districts let some middle schoolers take algebra. But not San Francisco.

California’s old math standards called for all eighth-graders to take algebra. Some districts placed nearly all or most students in algebra, while others only let well-prepared students take algebra.

Early algebra was linked to a significant decrease in average math scores within a given district, a University of North Carolina study found.

However, individual students almost always are “better off in a more challenging class,” says researcher Thurston Domina. The problem is that schools changed the curriculum and staffing to push all or most kids into algebra.

“Now, when you . . .  put a lot of kids in algebra, you change the peer environment, you have teachers who have never taught algebra teaching algebra, and you’ve got this problem in the classroom where you’ve got to figure out whether you’re going to teach algebra at all, because a bunch of the students don’t know fractions.” 

SFUSD isn’t dumbing down math, STEM director Jim Ryan tells Christopher. Common Core’s Math 8 includes algebra topics such as linear equations, roots, exponents, and an introduction to functions. 

Likewise, the course called “Algebra I” that students will now take in their first year of high school introduces a number of the concepts we all associate with introductory algebra (quadratic equations, say), but also delves deeper into modeling with functions and quantitative analysis.

Advanced students will be encouraged to “delve deeper” rather than accelerate, says Ryan.

However, those who want to get to AP Calculus in 12th grade will have to catch up in summer school or take a “compressed” course that combines Algebra 2/trig with pre-calculus.

Gifted classes almost always are “disproportionately white and Asian and relatively affluent,” writes Christopher. But it’s hard to teach “one-size-fits-all” math “without boring the math nerds to tears.” 

Ambitious parents demand 8th-grade algebra

Educated parents want their kids to take algebra in eighth grade, so they’ll be ready for calculus in 12th grade, writes Jay Mathews in the Washington PostCommon Core is doing a lousy job of explaining why bright students should wait till high school to take algebra.

A student works in an eighth-grade algebra class at Holy Spirit School in East Greenbush, N.Y. Photo: Mike Groll, AP

A student works in an eighth-grade algebra class at Holy Spirit School in East Greenbush, N.Y. Photo: Mike Groll, AP

Private schools aren’t cutting back on eighth-grade algebra, Mathews writes.

“Ambitious parents . . . are unlikely to tolerate delaying algebra, no matter what the experts say.”

Schools are dropping eighth-grade algebra or restricting access, according to Tom Loveless of Brookings. “The portion of eighth-graders in advanced math has declined from 48 percent in 2013 to 43 percent in 2015.”

Students who get an early start on algebra earn higher scores on AP exams, his research shows. Yet that opportunity is “more open to white and Asian students in suburban schools than to disadvantaged youngsters in schools serving students of color.”

Tracking is linked to higher AP scores

Tracking in eighth grade — usually in math — correlates with higher scores on AP tests at the end of high school, concludes the 2016 Brown Center Report on American Education.

In eighth grade, the tracking question currently boils down to whether high achieving students who are ready for a formal algebra course will get one—or whether all students will take the same general math course.

States with larger percentages of tracked eighth graders produce larger percentages of high-scoring AP test takers, the study found. “The heightened AP performance held across racial subgroups—white, black, and Hispanic.”

There was no relationship between tracking and and the number of students taking AP tests — just to the number who earned a 3, 4 or 5.

Another section looks at how Common Core State Standards (CCSS) are changing instruction in math and reading.

Teachers are teaching more nonfiction in fourth and eighth grade, NAEP data show.

In addition, “data and geometry are receding in importance in fourth grade math, and course enrollments in eighth grade math are shifting away from advanced courses toward a single, general math course,” the report notes.

Eighth graders study algebra at San Francisco's Presidio Middle School in 2011. Photo: Lenny Gonzalez, MindShift

Eighth graders study algebra at San Francisco’s Presidio Middle School in 2011. Photo: Lenny Gonzalez, MindShift

That suggests fewer achievers will start on the path to passing AP Calculus.

San Francisco Unified middle schools no longer teach algebra, as part of the shift to Common Core standards, reported Ana Tintocalis for KQED last year.

For years, all eighth graders took algebra and many failed, said Lizzy Hull Barnes.  Now no one will take algebra till ninth grade.

This “is a social justice issue for SFUSD,” writes Tintocalis. “District officials say the controversial practice of tracking students — or separating them based on talent and ability — is simply wrong.”

Algebra II vs. ‘numeracy’

Teach “numeracy” for 21st-century citizens instead of Algebra II, argues political scientist Andrew Hacker in The Math Myth: And Other STEM Delusions. The algebra-to-calculus track is a waste of time for everyone but future mathematicians and a few engineers, he argues in a New York Times op-ed.

Calculus and higher math have a place, of course, but it’s not in most people’s everyday lives. What citizens do need is to be comfortable reading graphs and charts and adept at calculating simple figures in their heads.

Teacher Wars‘ author Dana Goldstein, hated math in high school, she writes in Slate. She’s sympathetic to Hacker’s argument that requiring students to learn abstract math is driving up dropout rates, especially at colleges that serve disadvantaged students.

“We are really destroying a tremendous amount of talent—people who could be talented in sports writing or being an emergency medical technician, but can’t even get a community college degree,” Hacker told her.

He teaches at Queens College, part of the City University of New York system, which enrolls many students from low-income families. Fifty-seven percent of CUNY students fail the required algebra course, according to a 2009 faculty report. The failure rate fell to 44 percent (still very  high), when students were allowed to substitute statistics, a later study showed.

For two years, (Hacker) taught what is essentially a course in civic numeracy. Hacker asked students to investigate the gerrymandering of Pennsylvania congressional districts by calculating the number of actual votes Democrats and Republicans received in 2012. The students discovered that it took an average of 181,474 votes to win a Republican seat, but 271,970 votes to win a Democratic seat.

Goldstein found Hacker’s argument “pretty convincing.” However, her math-loving husband, a computer programmer, wasn’t sold. “Math helps us understand the world around us!” he said.

Daniel Willingham, a cognitive psychologist at the University of Virginia, also was dubious “about any call to make math—or any other subject — less abstract.”

Some community colleges are using Carnegie’s Statways and Quantways courses — statistics and numeracy — to move more remedial students to college-level  math. I think it makes sense for students who aren’t pursuing STEM careers. But I’d hate to give up on algebra in high school. That shuts the door early.

New math, old math: Who needs math?

Common Core math isn’t really new math, writes A.K. Whitney in The Atlantic. One hundred years ago, reformers argued for teaching all students — not just the smartest — to understand and apply math. In The Reorganization of Mathematics in Secondary Education, they backed algebra for all to teach “habits of thought and of action.”

However, progressive educators, followers of Dewey, pushed back, arguing that most Americans don’t need to understand math.

William Heard Kilpatrick, a very influential professor at Columbia University Teachers College, “set his sights on reforming math education, making it less about building the intellect and more about whether it was needed for everyday living,” writes Whitney.

Advanced math should be offered only to students with interest, talent and plans for engineering or science careers, Kilpatrick’s committee argued in a 1920 report, The Problem of Mathematics in Secondary EducationMost students could make do with arithmetic.

In 1922, 40 percent of U.S. students took algebra; that dropped to 30 percent by 1934. Twenty-three percent took geometry in 1922, but only 17 percent in 1934.

When progressive ideas about math fell out of favor, “deeper understanding didn’t quite catch on either,” writes Whitney.

Math was taught for understanding before the Common Core, responds Barry Garelick in a comment. Parents who object to how Common Core is being implemented have valid concerns, he writes.

I was in kindergarten when Sputnik went up and U.S. complacency crashed. We heard a lot about what “Ivan” could do that we kids couldn’t. That led to “new math” in the ’60s, which was all about understanding. It confused people too.

NY asks more on algebra test — and more fail

“If the percentage of students passing the Algebra I exam falls to 63 percent from 72 percent, and the passing grade is scheduled to increase by 9 points in coming years, should the test be made easier?” That’s the question facing New York state education officials, according to the New York Times.

In 2013, the State Board of Regents decided too many high school graduates were unprepared for college. They revamped English and Algebra I exams required for graduation and made plans to raise the passing score to a “college-ready” level.

Pass rates have fallen on new Core-aligned exams. Statewide, less than a quarter of students met the “college-ready” level in Algebra I. Here are sample questions, which seem easy to me.

It’s even worse in New York City, where “only 52 percent of students passed the 2015 exam, down from 65 percent the previous year on the old exam,” reports the Times. “Just 16 percent reached the ‘college-ready’ level.”

Among the ideas the city is considering: having fifth graders take math with a specialized instructor instead of one teacher for all subjects; teaming up with local universities to get more sixth- and seventh-grade math teachers certified in math instruction; creating summer programs for middle- and high-school students who are struggling in math; and training middle-school and algebra teachers in how to address students’ “math anxiety.”

Mayor Bill de Blasio has pledged that all students will have access to algebra in eighth grade by 2022, and all students will complete algebra by the end of ninth grade.

At Park East High School in Manhattan, most students enter doing math below grade level, yet 91 percent of students who took the Algebra I Regents this year passed it.

Ninth graders have two periods of algebra each day, which crowds out art, music and health.

Can 4-year-olds play their way to algebra?

Greg Toppo’s The Game Believes in You argues that digital gaming can “make our kids smarter.” But Toppo hopes gaming “is not the Next Big Thing” in education,, he said at a Fordham event. “Because the Next Big Thing in education always sucks. It always fails. I hope it’s the Next Small Thing, and it just keeps going under the radar. Keep it away from the real rule-makers.”

“Many educational fads start out as compelling insights, then collapse beneath the weight of enthusiasts’ cheers and the hucksters’ attempts to cash in,” adds Robert Pondiscio.

Preschooler can learn algebra by playing a game called DragonBox, writes Toppo on the Hechinger Report.

But inventor Jean-Baptiste Huynh, a Vietnamese Frenchman living in Oslo (who taught math in Spain), says the game is about “speed and imagination,” not algebra.

“Mathematics is creativity. It’s play,” says Huynh. It’s asking “what if?”

In his game, a box arrives with a baby dragon inside. The dragon must be alone before it will eat. Players must figure out what to do.

The game board is divided into two sides, with your little dragon-in-a-box on one side. On both sides are “cards”—random images of lizards, horned beetles, deep-sea fish, and angry tomatoes. . . . To win each level, you must touch and tap and drag the cards to get rid of all of those on the dragon’s side. Once you do, he noisily eats everything that remains on the other side and the level is done.

. . . On level 12, one of the animal cards has mysteriously been replaced by a little black “a.” Five levels later, there’s a “c.” Finally, on level 18, the little wooden dragon box is momentarily replaced by a floating letter “x.” You’re doing proto-algebra. It’s been about three minutes since you downloaded the game.

. . . Addition, multiplication, division, fractions—all of them appear, without fanfare or explanation. By game’s end, at level 100, you’ve moved seamlessly, baby step by baby step, from a cute baby dragon eating a spiky two-headed lizard, to this: “2 over x plus d over e equals b over x,” which you solve, fearlessly and perhaps even a bit impatiently, in exactly 14 steps. You are 4 years old.

Here’s a video:

Liz Kolb has advice for teachers on how to “gamify” the classroom.

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.”

‘Integrated’ math is hodge-podge math

To force math teachers to change their teaching to fit the Common Core, Darren’s school district is switching to “integrated math,” he writes on Right on the Left Coast.

The new books mix algebra and geometry, but don’t integrate the concepts, he complains. It’s just a “hodge-podge.”

Instead of Algebra, Geometry and Advanced Algebra, his high school will offer Integrated Math 1, Integrated 2 and Integrated 3, then the option of Pre-calculus, Stats and Calculus.

While Common Core opposes acceleration in middle school, his district will allow the best students to take Integrated 1 in eighth grade.

So if we want kids to be able to take AP Calculus AB and/or BC in high school, we need to accelerate them in high school.  . . . so in addition to Integrated 2 and 3 we’ll now have Integrated 2+ and Integrated 3+.  And if a student isn’t quite ready for Integrated 3 we’ll offer Transition to Integrated 3.  Of course that means we’ll also have to offer Transition to Integrated 1 (which would in effect be an 8th grade math course, or the pre-algebra course we haven’t been allowed to have in years) and a Transition to Integrated 2 course.

Integrated math has been around for a long time. I remember when San Jose Unified tried it. And then abandoned it. Common Core standards don’t require integrated math, but some think it’s a better fit than the traditional math sequence.