Algebra or statistics?

Most new students place into remedial math at California community colleges. Eighty percent will never pass a college-level math course. Some colleges have boosted success rates by teaching statistics and quantitative reasoning, rather than algebra, to non-STEM students.

Florida colleges will let students opt for college-level courses, even if they’ve done poorly on a placement exam. Instead of letting students ignore the placement results, let them try the test again, a graduate student suggests.

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.

Will this boy graduate high school?

subwayThe other day, on the subway in NYC, I saw this ad. It turns out there has been some commotion over it. (Approved and defended by Mayor Bloomberg, it is part of New York City’s recent campaign to raise awareness about teen pregnancy.)  I would like to add my own two or three objections to the mix.

First, this is an example of the “precision fallacy” in statistics. (That’s the best term I could find; there may be better.) Specifically, the ad confuses the individual’s probabilities with those of the group. It may be that “kids of teen moms are twice as likely not to graduate than [sic] kids whose moms were over age 22,” but this probability doesn’t hold for individuals.

Second, adults put words in this child’s mouth (and banal words at that). A baby or toddler would not say anything remotely close to this, unless someone had prepped him to do so.

That brings up a larger problem: from a young age, children are trained to describe themselves in statistical terms, at school and elsewhere. They learn to say, “My growth in such-and-such a skill is 30 percent,” or “I was one of the sixty percent who had the right answer.” In measure, in the right context, this may be fine–but when it’s the dominant lingo and mode of thought, it crowds out substance and meaning. (I wrote a satirical piece about this tendency.)

Beyond that, I did not bear this child as a teen, nor did 99.999999 percent of NYC subway riders, in all likelihood. (For all we know, this kid’s mom might have a chauffeur.) The “you” is not a real you, nor the “I” a real I. Yet here’s a tear-streaked face bringing sadness to a passenger’s day–and to what end?

What good does it do even for the target audience, teens who might get pregnant or father a child? If I were a teen looking at the picture, I’d want to wipe the little boy’s cheeks. I’d want to take out a book and read to him. Yet I wouldn’t be able to do so. I might dream of being a parent one day–and, if I were foolhardy enough, I’d want that day to come soon.

Worst of all, this ad gives the impression that the boy’s existence is a mistake and his fate sealed (or at least tipped in a direction). This is wrong. Once a child comes into the world, he or she is no mistake. Nor do we know what that child’s life will be.

Of course teen pregnancy is no light matter, no matter how it’s handled. I imagine many involved with the ad had good intentions. Still, it  fails to inform, enlighten, or persuade. And what a sad-looking kid.

No room in class? Earn credits online

California college students could bypass wait lists and earn credits online under a bill introduced by a Democratic legislative leader. State colleges and universities would be required to accept credits from faculty-approved online courses for about 50 high-demand, lower-level classes with long wait lists.

Nearly two-thirds of community college students place into remedial math. Half of students in Statway — Carnegie’s intensive, yearlong developmental math pilot  –passed a college statistics course in the second semester. By contrast, only 5.9 percent of non-Statway remedial students at the same community colleges earned college math credit in their first year; that rose to 15.1 percent in two years.

Study: Hybrid class works for college students

College statistics students in a hybrid class — online instruction plus a one-hour face-to-face session — performed slightly better than the control group and spent 1.7 fewer hours per week on the course, write William G. Bowen, Matthew M. Chingos, Kelly A. Lack and Thomas I. Nygren in Education Next.

“The effect of the hybrid-format course did not vary when controlling for race/ethnicity, gender, parental education, primary language spoken, score at the standardized pretest, hours worked for pay, or college GPA,” the authors report.

Half the students who participated come from families with incomes less than $50,000 and half are first-generation college students. Less than half are white, and the group is about evenly divided between students with college GPAs above and below 3.0.

Carnegie Mellon designed the hybrid course, which was taught at public universities in New York and Maryland.

Students in the control group received three to four hours of face-to-face instruction each week.

Moving to the hybrid model could cut the costs by 19 percent to 57 percent, depending on whether professors do all the teaching or assign sections to teaching assistants, the authors estimate.

Teaching the quantified student

 “I am a bad teacher” wrote Sujata G. Bhatt in Valerie Strauss’ Washington Post blog in the school test-taking season of 2011.  Education reformers want to use data to drive instruction, reform and accountability, wrote Bhatt. “At what cost? Does this data really represent learning and knowledge?”

Since then, she’s embraced data, Bhatt writes in The Quantified Student.

She teaches in a high-poverty Los Angeles school. Many of her students aren’t fluent in English. In the fall of 2010, her fourth graders were particularly unprepared.

Since California’s standardized test for fourth graders measured skills almost all my students needed, I analyzed its requirements, broke them down into core concepts, and then worked and reworked these concepts with the students until they felt a sense of mastery over them. My daily job consisted of finding different, creative ways of approaching, teaching, and reteaching the same core skills so that most all students could incorporate them into their cognitive toolkits.

It worked. The students succeeded wildly. They returned to me for fifth grade with heightened confidence. They saw something new in themselves: the reward of effort and the joy of success.

They also came back with questions about “how many more points it would take to get to the next level, how many more problems they’d need to get right to get those points.”  They saw the test as a game they wanted to win.

Teaching the same cohort in fifth grade, she looked for ways for her students to explore their interest in data. 

We used math websites like TenMarks that enable students to learn about their own learning even as they practice new skills. We analyzed information graphics and dove into ways of presenting numerical information. We explored how numbers shape our understanding of ourselves and the world. And much of their enthusiasm and curiosity for these tasks came out of their interest in numbers from standardized testing.

She now believes standardized testing can help teachers understand how well they’ve taught and help students become “agents in their own learning.”

Testing — and evaluation systems built on test scores — need to get a lot better, Bhatt writes. But it makes more sense “to work to create better data than to fight data.”

Data analysis is an increasingly significant and empowering way of making sense of the world. All sorts of professions use data to interpret their work and decide upon courses of action. Why shouldn’t we in education?

In the high tech world there’s a growing movement called “The Quantified Self.” With quantified self models, adults use data to change habits and behaviors–to lose weight, exercise more, to calm themselves.

“Why not help our students become makers and masters of their own data, and help them use it to propel their own learning forward?” Bhatt asks.

The Measured Man is a fascinating — and somewhat alarming — Atlantic profile of Larry Smarr, an astrophysicist, computer scientist and highly quantified human.

Teachers feel poorly prepared in math

Many teachers say they’re not well-prepared to teach math, according to an excerpt from a new book, Inequality for All, by William H. Schmidt and Curtis C. McKnight.

In first through third grade, teachers feel prepared to teach only grade-level math topics, a survey of Michigan and Ohio teachers found. In some districts, only half said they were ready for grade-level math. (My first husband said his sister became a second-grade teacher because she couldn’t do third-grade math. This, apparently, is not a joke.)

Upper elementary teachers were more confident, though only one fourth of teachers in one district said they were well prepared to teach decimals.

Only 50 to 60 percent of middle school teachers felt well prepared to teach math topics in Michigan and Ohio standards. Both states plan to introduce algebra topics in eighth grade, but only half the teachers are ready.

At the high school level, at least 75 percent of math teachers feel confident about teaching 60 percent of math topics. But they’re not ready to expand into new areas.

. . .  there is an increasingly strong push for the inclusion of probability and statistics in high school, as is found in the Common Core State Standards, yet less than half of the surveyed mathematics teachers felt well prepared to teach it. Teachers’ self-perceptions of their preparedness seem likely, if anything, to overestimate what they know and how well prepared they are rather than to underestimate it.

Elementary and middle school teachers typically didn’t study much math in college. Even in middle school, three out of four math teachers didn’t major or minor in math.

. . .  a very large percentage of middle school students were being taught increasingly more complex mathematics, as called for in the Michigan and Ohio state standards, by teachers who lacked a strong background in mathematics.

High school math teachers have a stronger math background, but almost a third didn’t major or minor in math.

When teachers were tested on math knowledge, those who’d studied less math in college did worse. Results confirmed “what the teachers told us when they said that they were not well prepared,” Schmidt and McKnight write.

 

Everyone needs statistics

Everyone Should Learn Statistics writes Ed Sector’s Kevin Carey, after serving on a jury. The defense attorney tried to confuse the jury with bad statistics — or didn’t understand statistics himself.

Which is not surprising, given that statistics isn’t part of the standard curriculum schools require students to complete in order to get a high-school or college diploma. Math education is still largely interpreted as a progression through algebra and geometry to calculus. And I’m not against working harder to improve math education. But in terms of things you really need in order to make your way in modern society, statistics is way, way up there, above a lot of things that are currently lodged in the curriculum.

Carey provides a video of Donald Duck in Mathmagicland. I vividly remember watching this in seventh grade.

‘A’ students don’t belong in remedial ed

More ‘A’ students are being placed in remedial college classes. It’s not grade inflation, says a researcher.

Carnegie’s math pathways for remedial students are showing signs of success. Students learn statistics or “quantitative reasoning.”

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?