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.

Against Algebra II

Advanced algebra should be an elective for motivated math students, not a requirement, argues novelist Nicholson Baker in a Harper’s cover story (subscribers only), Wrong Answer.
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Baker isn’t the first to question whether future arts majors need advanced math, notes Popular Science.

In 1950, only 25 percent of students in the U.S. were taking algebra, while the Soviet Union was churning out mathematicians, writes Baker. The National Defense Education Act, passed in 1958, raised math requirements, “creating a lot of unhappy students who, as they struggle through required math course after required math course, become discouraged and learn to hate school.”

The Common Core won’t help, Baker argues.

Algebra 2 Common Core is “a highly efficient engineer for the creation of math rage: a dead scrap of repellant terminology, a collection of spiky, decontextualized, multistep mathematical black-box techniques that you must practice over and over and get by heart in order to be ready to do something interesting later on, when the time comes,” he writes.

Education Secretary Arne Duncan sees Algebra II as “the mystic portal to prosperity,” Baker complains.

Baker proposes “a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus.”

After that, advanced math would be reserved for those who really want to learn it.

Algebra II isn’t what it used to be

Passing Algebra II no longer shows mastery of algebra or preparation for college math, concludes a new Brown Center report, The Algebra Imperative.

“Pushing students to take more advanced coursework has been a mainstay of American school reform for several decades,” writes researcher Tom Loveless.

In 1986, less than half of white 17 year-olds and less than a third of blacks and Hispanics had completed Algebra II. That’s up to 79 percent for whites and 69 percent of black and Hispanic students.

But “getting more students to take higher level math courses may be a hollow victory,” Loveless writes.  ”As enrollments boomed, test scores went down.”  

Figure 1. NAEP Math, 17 Year-Olds who have Completed Second Year Algebra (1986-2012)

“More and more unprepared students are being pushed into advanced math in middle school,” Loveless writes. In some cases, eighth graders with second- and third-grade math skills are placed in algebra classes.

A study out of California found that marginal math students who spent one more year before tackling Algebra I were 69% more likely to pass the algebra end of course exam in 9th grade than ninth grade peers who were taking the course for the second time after failing the algebra test in 8th grade.

. . . A study of Charlotte-Mecklenburg students by Clotfelter, Ladd, and Vigdor found that low achievers who took 8th grade algebra experienced negative long term effects, including lower pass rates in Geometry and Algebra II.

It’s not just algebra either. “There is very little truth in labeling for high school Algebra I and Geometry courses,” Jack Buckley, commissioner of the National Center for Education Statistics, told Education Week.

Study: Blended math boosts learning

Students learned significantly more when they used Carnegie Learning’s hybrid algebra program — a blend of online and classroom instruction — reports a two-year Education Department study, which used a randomized control group.

There were no significant results in the first year, reports Ed Week‘s Inside School Research.In the second year, students who used Cognitive Tutor Algebra I improved by 8 percentile points.  That’s double the amount of math learning most high school students achieve in a year, said Steve Ritter, a founder and the chief scientist of Carnegie Learning, in Pittsburgh.

The improvements were similar across students of different ethnic and socioeconomic background, and high, regular, and low initial math ability, Ritter said. The researchers found similar improvements among participating middle school students—higher-performing math students typically take algebra in 8th grade rather than in high school—though the middle school sample was not large enough to show significant effects in the same way as the high school students.

Usually students worked with the individualized tutorial program for two days a week and spent three days learning in the classroom.

42 minutes to learn algebra?

It Only Takes About 42 Minutes To Learn Algebra With Video Games, writes Jordan Shapiro on Forbes, citing the Washington State Algebra Challenge, which used DragonBox App. According to Washington University’s Center for Game Science and the Technology Alliance, 4,192 K-12 students solved 390,935 equations over the course of five days in early June.

What’s even more impressive, “of those students who played at least 1.5 hours, 92.9% achieved mastery. Of those students who played at least 1 hour, 83.8% achieved mastery. Of those students who played at least 45 minutes, 73.4% achieved mastery.”

Shapiro downloaded DragonBox “and was astonished to see how quickly my son (then 7) learned to do complex algebraic equations.” Now his five-year-old is playing. “I watched him breeze through the first two chapters in about 20 minutes.”

Creator Jean-Baptise Huynh tells Shapiro that DragonBox teaches “the mechanics of algebra processes and abstraction,” but students will need teachers or parents to “transfer the knowledge to pencil and paper.”

Dragonbox2 screenshot

Darren, a high school math teacher, is skeptical that normal kindergarteners and first graders can learn algebra. “My experience is that there is often a huge gap between the game or manipulative and the transference of what’s learned there to actual algebra,” he writes on Right on the Left Coast.

I can’t pass algebra

Javier Cabral wants to study the humanities at a university, but he can’t pass algebra. After failing algebra in high school, he failed seven times in 4 1/2 years at a community college before dropping out. Diagnosis with a math disability got him more time on tests, but that didn’t help. Should algebra-less students be barred from pursuing a university degree?

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.

Brookings: Ability grouping is back

Elementary teachers are using ability grouping once again, according to the 2013 Brown Center Report on American Education by Tom Loveless.

Ability grouping was very popular from the 1960′s through the 1980s, but came under attack as inequitable in the 1990′s. In 1961, 80 percent divided children into robins, bluebirds and sparrows, or the like. (I was a bluebird in 1958.) By 1998, only 28 percent of fourth graders were being placed in reading groups by ability. That shot up to 71 percent by 2009, Brookings finds.

Math ability grouping rose from 40 percent of fourth graders in 1996 and 42 percent in 2003 to 61 percent in 2011.

With more computers in elementary classrooms, teachers may be “more comfortable with students in the same classroom studying different materials and progressing at different rates through curriculum,” writes Loveless.

Although ability grouping is coming back, efforts to de-track middle school math are continuing. However, pushing more eighth graders into algebra isn’t raising achievement, the report finds.

States with rising percentages of eighth graders taking Algebra I, Geometry, and other advanced math classes were no more likely to raise their NAEP scores from 2005-2011 than states with declining percentages of eighth graders in those courses.

When more students take pre-algebra and algebra, the courses appear to be watered down, writes Loveless. However, there’s no watering-down effect for geometry.

The U.S. is often exhorted to emulate the high-scoring  “A+ countries” — Belgium (Flemish), Czech Republic, Hong Kong, Japan, Korea, and Singapore – in math instruction. However, “the average A+ country made no more progress in math achievement than any other country in TIMSS” since 1995, the report finds.

And the Finns may do well on PISA but they’re nothing special on TIMSS.

Algebra 1 for all — but it’s not always algebra

Nearly all high graduates in the class of ’05 passed Algebra I — or a course labeled Algebra I, concludes a new federal study. But fewer than one in four studied the challenging algebra topics needed to prepare for college-level math, the National Assessment of Educational Progress study found. Most geometry and “integrated math” also were watered down. From Education Week.

Education watchers hoping to close persistent achievement gaps among students of different racial and ethnic groups long have pushed for all students to take “college-ready” class schedules, including at least four years of high school math, including Algebra I and II, Geometry, and Calculus. Here, at least, the transcript study shows this push has paid off: Graduates in 2005 earned on average 3.8 credits in math, significantly more than the average of 3.2 credits earned by graduates in 1990. Moreover, from 1990 to 2005, black graduates closed a six-percentage-point gap with white graduates in the percentages of students earning at least three math credits, including in algebra and geometry.

Two thirds of Algebra I and Geometry courses covered core content topics. However, the quality of courses varied widely. Only a third of algebra students spent 60 percent of their time on challenging topics such as functions and advanced number theory. Only a fifth of geometry students primarily studied rigorous material.

“We found that there is very little truth-in-labeling for high school Algebra I and Geometry courses,” said Sean P. “Jack” Buckley, the NCES commissioner, in a statement on the study.

“Honors” meant nothing in algebra:  ”Regular” Algebra I classes were more likely to be rigorous than “honors” classes. Geometry honors classes were more likely to be rigorous, but only a third of honors geometry classes contained challenging material, compared with 19 percent of regular geometry classes.

Researchers analyzed the textbooks used; it’s possible teachers added more challenging supplemental material. However, “students who took classes that covered more rigorous topics in algebra and geometry scored significantly higher on the NAEP than those who studied beginner topics, regardless of the course’s title,” Ed Week reports.

It’s no wonder so many high school graduates are placed in remedial math in college, despite passing high school math courses, often with B’s and C’s.