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.

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.

Geometry without proofs

These days, high school geometry is light on proofs, writes Barry Garelick on Education News. Students may know the sum of the measures of angles in a triangle equals 180 degrees, but most can’t prove the proposition.

If done right, the study of geometry offers students a first-rate and very accessible introduction to the nature and techniques of logical argument and proof which is central to the spirit of mathematics itself.  As such, a proof-based geometry course offers to students—for the first time—an idea of what mathematics means to mathematicians, and how it is used.  Also, unlike algebra and pre-calculus, since geometry deals with shapes, it is easier for students to visualize what it is that must be proven, as opposed to more abstract concepts in algebra.

Most geometry textbooks give students “one or two proofs that are not very challenging in a set of problems devoted to the application of theorems rather than the proving of propositions,” he writes. Many problems indicate missing angles or segments as algebraic expressions. It is, to quote Mr. Spock, “illogical.”

Chocolate geometry

As a Los Angeles teacher, Nigel Nisbet turned Toblerone chocolate bars into geometry problems to motivate math-hating students, he said at a TEDx conference in southern California. He asked students: ”Why make a chocolate bar in the shape of a triangular prism?”

A vote for new math standards

Common Core math standards are as good as the best state standards and correct common math misperceptions, writes Hung-Hsi Wu, a Berkeley math professor emeritus,  in the cover story in American Educator.

Dr. Wu, who helped write California’s math framework, praises the ”mathematical integrity” and logical progression of topics in an interview with Rick Hess.

The standards teach fractions over grades three to five, giving students enough time to learn and internalize the material, says Wu. He also likes the standards approach to learning negative numbers and moving from middle school geometry to algebra and high school geometry. Delaying algebra instruction till high school is not a problem, he argues.

However, he’s not confident teachers will be able to teach the standards.

. . .  we need better teacher preparation and improved professional development in order to stay educationally afloat no matter what the standards may be. If we cannot get better teacher preparation or improved professional development, then we would be better off with a set of standards that is at least mathematically sound.

Wu is wrong, responds Ze’ev Wurman, another veteran of California’s battle for math standards and a fierce defender of eighth-grade algebra.  Wu changed sides because he concluded “American elementary and middle school teachers are incompetent to teach algebra or prepare for it,” Wurman writes.

“School mathematics in this country is a sad joke,”, comments Michael Goldenberg, a math coach. “Knowing procedures and manipulations and calculations is great for standardized tests (which drive just about every contemporary education deform scheme) but say very little about mathematical reasoning, thinking, and or understanding.”