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Against core standards

August 2, 2010 By

Today, California’s board of education is expected to adopt the Common Core Standards already approved by 30-odd states.

Dissenters Bill Evers and Ze’ev Wurman believe California will trade eighth-grade algebra for an “obese, unteachable” math course. Despite the state standards, many eighth graders can’t handle algebra.  Yet Evers and Wurman argue that setting the bar high has helped students.

Over the past decade and a half, California’s Latino student population has almost doubled from 30 percent to over 50 percent, many of them facing special learning challenges. Yet the number of students taking algebra by eighth grade has jumped from 16 percent to 60 percent, while the success rate has jumped from 39 percent to 48 percent since 2002. In 2002, only a third of high school students took Algebra 2 by grade 11; now more than half take it, and with increasing success rates.

More importantly, between 2003 and 2009 the number of African American students successfully taking Algebra 1 by grade 8 more than tripled from 1,700 to 5,400; the jump among Hispanic students was from 10,000 to 45,000; and for students from low-income households, from 12,000 to 49,000. Algebra 2 in high school shows similar results. Finally, since 1997, California State University freshman enrollment has doubled from 25,000 to 50,000, while remediation rates in mathematics have dropped from 54 percent to 37 percent.

San Francisco Chronicle columnist Debra Saunders, a veteran of the “math wars,” warns that going from “fuzzy crap” math — as the state education secretary called it — to eighth-grade algebra was a tough fight: “Once you’ve captured turf, you have to hold it.”

Massachusetts, another state with high standards, already has adopted the common core. Sandra Stotsky, who helped create the state’s standards, protests the decision.

In a New York Times’ Room for Debate last year, Stotsky said English teachers aren’t prepared to teach the common core English Language Arts standards, which call for students to learn to read scientific and historical texts as part of English class.

Go here to read Common Core’s Standards Still Don’t Make the Grade: Why California and Massachusetts Must Retain Control Over Their Academic Destinies by Stosky and Wurman.

Pushed hard by Arne Duncan, all but a few states seem certain to adopt the new standards. How will they implement them? That’s another question.

Update: Minnesota will not adopt Common Core Standards; they think the math standards are unclear and want to retain local control.

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Unteachable

July 24, 2010 By

If California adopts common core standards in math with an algebra supplemnt, the result will be unteachable, argue Bill Evers and Ze’ev Wurman, both dissenting members of the standards commission, in the Sacramento Bee.

Because of the distortions the proposed standards will cause, the Algebra I course in eighth grade will be burdened with an unteachable and unlearnable number of topics (about 70 standards in one year). Topics like the Pythagorean theorem and scientific notation (how scientists write large numbers in a simplified form using exponents) will now be taught in Algebra I. Yet these and many other algebra-prep topics have been part of pre-algebra courses both in California traditionally and in high-performing countries.

Currently 60 percent of California students take algebra in eighth grade.  Under the new stndards, only the best students will be prepared to pass eighth-grade algebra, they write.

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Music students excel in algebra

June 17, 2010 By

Middle school students who study music do better in algebra, concludes a study by Barbara Helmrich of Baltimore’s College of Notre Dame. From Miller-McCune Online:

Students who studied a musical instrument did the best, followed by students who sang in a choir. Those who didn’t study music had the lowest algebra scores.  The effect was especially strong for black students.

Middle-school music instruction “takes place during a time (age 10-12) in which a proliferation of new synapses occurs in the developing brain,” Helmrich writes. She thinks music helps form and strengthen new synapses.

The particularly robust results for African-American students suggests “offering music education in middle school might present an alternative strategy for narrowing the achievement gap” between students of different races, Helmrich writes in the Journal of Adolescent Research.

Of course, there could be correlation-causation issues lurking.

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Why cosines?

June 14, 2010 By

Why Do We Learn About Cosine Functions? asks Forrest Hinton on The Quick and the Ed. I’ve waited more than 40 years for the answer — which he has not got.

Hinton flashes back to his Algebra III classroom in a Raleigh suburb. A girl asks why she has to learn about cosines. What’s the point?

He asks her what she wants to be when she grow up. She answers: a beautician.

I went on to describe how the business cycle oscillated between recession and expansion, much like a cosine function, and how she would have to follow this trend as a small business owner. The young woman was unimpressed.

He continues with “a vague, cop-out” answer:

On the whole, mathematics is a useful subject because it teaches you how to think logically, problem solve, and justify the things you do. It also stretches your mind as you deal with abstract complexities and forces you to be concerned with small, but important, details. Now, let’s take a look at example three…

There’s a lot that high school juniors might learn, Hinton writes. Teachers should understand why they’re teaching certain pieces of knowledge and skills, so they can motivate students to learn.

Are they learning it merely because it’s tradition? Will 10% of the Algebra III class eventually use this in their professional lives? Are students, in reality, learning to generally solve problems and confront complexities?

I took Algebra II/Trig because I needed it to apply to selective colleges. (In those days, only math-science types took AP Calculus.) Algebra was fine, but I hated trig. I was running out of enthusiasm for jumping through hoops and trig seemed more like a strategy for torturing 16-year-olds than an essential subject. I repeatedly asked my teacher why those of us with no aspirations for math, science or engineering majors had to learn sines, cosines, logarithms and so on. What was the point? He couldn’t answer the question. At the end of the year, he gave me a higher grade than I deserved. I was so surprised that I asked him if he’d made a mistake. He said he’d factored in my classroom participation. I guess he liked being asked, even though he had no answer suitable for a future English major.

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'Algebra for all' flunks the test

February 10, 2010 By

Pushing algebra for all students has failed to prepare low-achieving students for college,  reports Education Week.

• An analysis using longitudinal statewide data on students in Arkansas and Texas found that, for the lowest-scoring 8th graders, even making it one course past Algebra 2 might not be enough to help them become “college and career ready” by the end of high school.

• An evaluation of the Chicago public schools’ efforts to boost algebra coursetaking found that, although more students completed the course by 9th grade as a result of the policy, failure rates increased, grades dropped slightly, test scores did not improve, and students were no more likely to attend college when they left the system.

Students with very poor math skills are “misplaced” in algebra classes, concluded Tom Loveless in a 2008 Brookings Institution paper.

“No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,” said Mr. Loveless, who favors interventions for struggling students at even earlier ages.

Algebra-for-all policies were a reaction to research showing that remedial math is a dead end, especially for low-income and minority students, while algebra is a “gateway” to advanced math classes and then to college.

But putting all students in the same math class seems to have held back the high achievers without doing much for the low achievers, says Elaine M. Allensworth of the Consortium on Chicago School Research.

“Meanwhile, the kids who weren’t taking advanced classes before are taking them now,” she said, “but they’re not very engaged in them. They have high absence rates and low levels of learning.”

Some districts now are double-dosing, requiring low-scoring students to take a math “readiness” class at the same time they take algebra. In many schools, algebra teachers “spend a very large portion of that year on basic arithmetic,” said William Schmidt, a Michigan State education professor.

It seems obvious that schools should teach arithmetic in elementary school to give students a shot at learning algebra in eighth or ninth grade. Why isn’t this happening? And if detracking holds back the good students, frustrates the poor students and exhausts the teacher, why keep doing it?

Update: Students who worked in a computer lab on a pre-algebra and algebra learning program outscored similar students taught in a classroom, reports What Works Clearinghouse.

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CUNY's got a math problem

November 14, 2009 By

Basic algebra stumps most first-year students at City University of New York freshmen, according to a CUNY report. 

“These results are shocking,” said City College Prof. Stanley Ocken, who co-wrote the report on CUNY kids’ skills. “They show that a disturbing proportion of New York City high school graduates lack basic skills.”

During their first math class at one of CUNY’s four-year colleges, 90% of 200 students tested couldn’t solve a simple algebra problem, the report by the CUNY Council of Math Chairs found. Only a third could convert a fraction into a decimal.

Seventy percent of CUNY students were graduated from New York City public schools, where they say standards are low.

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Algebra = ‘most failed’ college class

April 24, 2009 By

Math 111 –  intermediate algebra — is the “most failed” class at Oregon State.  Students aren’t prepared, says an instructor.

“If you never had to memorize your times tables, how do you factor a number with a calculator?” (Peter) Argyres said. “I see people fail Math 111 for arithmetic issues all the time.”

When students never learned the basic information appropriately in high school, or earlier, it is significantly more difficult for them to succeed when they get to college algebra.

Only half of incoming students place into college math.

OSU Frosh Gettin’ Suspicious They Ain’t Learnin’ Much in High School, summarizes the Two Million Minutes Blog.

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Are American students learning?

March 3, 2009 By

How Well Are American Students Learning?, the Brown Center report, criticizes proposals to model a national U.S. exam on Europe’s PISA (Programme for International Student Assessment). Some PISA questions are ideologically biased, the report argues.

PISA wants to assess whether students are capable of applying science to public policy. Fair enough. That capacity can be evaluated, however, without making a judgment about students’ political beliefs. PISA asks students whether they support several environmental policies and then creates an index of “responsibility for sustainable development” from the responses. Responses in favor of the policies are responsible; those opposed are not. That kind of questioning is inappropriate on a science assessment. Without serious reform, PISA is inappropriate for benchmarking.

The report also argues against requiring all eighth graders to take algebra, as California and Minnesota plan to do.  Too many students already are “misplaced” in math courses they can’t handle, the report concludes:  Until they’ve learned to deal with fractions, decimals or percentages, they can’t do algebra.

Via Education Gadfly.

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II Doesn’t Always = II

January 26, 2009 By

Algebra II Doesn’t Always = II, reports the Washington Post.  To prepare students for college and for technical careers, 20 states and the District of Columbia now require students to take advanced algebra. But the course content and standards vary significantly from school to school:  One school’s Algebra II is another school’s Remedial Math.

“I want to make sure that if a student takes a course, it’s really a significant course, not a watered-down version,” said Ronald A. Peiffer, Maryland deputy state superintendent for academic policy.

Peiffer said that when the state made Algebra I a graduation requirement in the early 1990s, many schools began offering two versions, the traditional course and one some teachers called “baby algebra.” The state tried to rectify the disparity later, mandating an end-of-course graduation test for Algebra I that students are expected to pass to receive a diploma.

Ninety percent of Virginia’s Algebra II students passed the end-of-course Standards of Learning exam. Students need the course for an advanced diploma, but skip it if they’re content with a regular diploma.

Achieve worked with a group of states to design a national end-of-course Algebra II exam with both open-ended and multiple-choice questions.  It was tried last year in a dozen states. “In some states, only one in five students passed,” the Post reports.

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