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.

Baseball lessons

Juan Lagares scored twice in game 1 of the National League playoffs to help the Mets win. Photo: David J. Phillips, Associated Press

Edutopia links to baseball-themed activities for the World Series.

Statistics is a natural. The National Council of Teachers of Mathematics (NCTM) offers Baseball Statistics Lesson Plans for grades 6-8,  a baseball statistics lesson for grades 3-5 and a geometry lesson for students in grades 6-8.

A star pitcher in the Negro Leagues, Satchel Paige was 43 when he started in the Major Leagues.

A star pitcher in the Negro Leagues, Satchel Paige was 43 when he started for the Cleveland Indians.

There are baseball-linked lessons in other subjects too. The Negro League eMuseum features primary sources, including a timeline and history modules covering various Negro League teams, as well as lesson plans for teachers.

Other lessons include: Narrative, Argumentative, and Informative Writing About BaseballBaseball Economics and The Physics of Baseball.

When I was in school, kids would sneak in transistor radios to follow the World Series, catching each other up during passing periods. Without weeks of playoffs first, the Series was more exciting.

Colleges asks: How much math?

Math is the largest barrier to high school and college graduation for Washington students, reports Katherine Long for the Seattle Times. Now community colleges are lowering math requirements and redesigning remedial math to help more student earn a degree.

Students who are studying to become nurses, social workers, early-childhood educators or carpenters may never use intermediate algebra, much less calculus. Yet for years, community colleges have used a one-size-fits-all math approach that’s heavy on algebra and preps students for calculus.

. . . Some colleges . . .  have started to offer a math sequence that focuses on statistics, and persuaded the state’s four-year colleges to accept it as a college math credit. Others are offering a learn-at-your-own-pace approach.

Seattle Central is using Statway, a remedial math alternative developed by the Carnegie Foundation. By the third year, 84 percent of students passed the three-course series, which includes college credit in statistics. That year, only 15 percent of remedial students completed one quarter of college math by the end of one year.

Statway credits transfer to all of the state’s public four-year universities, though only on a trial basis at University of Washington. Janice DeCosmo, a UW associate dean,  warns Statway “can limit students’ career choices because it doesn’t prepare them to take calculus,” writes Long.

Learning statistics enables students to “interpret the world around them,” argues Paul Verschueren, a Statway instructor.

Other community colleges are using the “emporium” approach to remedial math. At Big Bend Community College, instructors record short video mini-lessons on math topics. “Students watch the videos, then test their understanding, entering answers in a computer program that gives them immediate feedback,” writes Long.

Students progress at their own pace.

‘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.”