‘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.

Algebra or statistics?

Poorly prepared college students were more likely to pass college-level statistics than remedial algebra, in a controlled experiment at three New York City community colleges. Statistics is more useful to students in non-STEM majors, some believe.

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.)

Beware of statistics

From Spurious Correlations, which has other examples, including a correlation between U.S. spending on science, space and technology and suicides by hanging, strangulation and suffocation.

Per capita consumption of mozzarella cheese (US)
correlates with
Civil engineering doctorates awarded (US)

Upload this chart to imgur

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Per capita consumption of mozzarella cheese (US) Pounds (USDA) 9.3 9.7 9.7 9.7 9.9 10.2 10.5 11 10.6 10.6
Civil engineering doctorates awarded (US) Degrees awarded (National Science Foundation) 480 501 540 552 547 622 655 701 712 708
Correlation: 0.958648

A new path to college math

A Los Angeles-area community college is trying the Carnegie Foundation’s alternative path to math success, an algebra-and-statistics mix called Statway. Success rates for remedial students — normally very low — are rising.

A Denver university is taking back remedial education from community colleges in hopes of boosting success rates.

No silver bullet for remedial woes

Reformers are transforming — sometimes eliminating — remedial education at community colleges, but fixing remedial ed will be “vastly more complex” than they think, argues Hunter R. Boylan, who runs the National Center for Developmental Education.

Virginia’s community college system raised success rates for unprepared students by lowering math demands for non-STEM majors. Carnegie’s Pathways reforms focus on statistics and quantitative reasoning rather than advanced algebra.

Success paths for all

How can high schools ensure graduates are college- and career-ready, asks an Education Next forum.

Students need multiple pathways, writes Robert Schwartz, a Harvard professor emeritus who coleads the Pathways to Prosperity Network. “We have allowed a very important idea—that all students need a solid foundation of core academic knowledge and skills—to morph into a not-so-good idea: that all students need to be prepared to attend a four-year college,” he writes.

If we follow a cohort of 8th graders, roughly 2 in 10 will drop out before high school graduation, and another 3 will graduate high school but choose not to enroll in postsecondary education. Of those who do go on and enroll in four-year institutions, nearly 4 in 10 will drop out before attaining a degree. Of those who enroll in community colleges, roughly 7 in 10 will drop out. The bottom line: by age 25, only 33 percent of the cohort will have attained a four-year degree, and another 10 percent will have earned a two-year degree.

Many good jobs require some education beyond high school but not a four-year degree, Schwartz writes. He likes the northern European model: “All students pursue a common curriculum up through grade 9 or 10, and then choose between an academics-only pathway leading to university and a more applied-learning pathway leading to a vocational qualification.”

Instead of letting students choose their path, we “force march all students” through a math sequence leading to calculus, a goal few will achieve and even fewer will need, he writes.

Yet most community college students and many university students aren’t prepared for college algebra. “In my view, the vast majority of students in two- and four-year institutions would be much better served by getting a solid grounding in data, statistics, and probability in high school,” he writes.

Common foundational skills are essential, writes Cynthia G. Brown, senior fellow at the Center for American Progress. All students should take a college-prep curriculum, but high school students could choose “curricular options that fit their interests, skills, and plans for the future.”

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.