Can QAMA end the math wars?

The Quick, Approximate, Mental Arithmetic (QAMA) calculator could end the math wars, writes Sanjoy Mahajan on Freakonomics.

I typed “25 x 37? and pressed “=”. A short underline cursor flashed away on the bottom left of the screen, without offering an answer. Instead, it demanded an estimate. Like a skilled tutor, it answered my question with its own.

When I entered 100, it asked again. For how could two numbers, each around 30, multiply only to 100? When I tried 400 and even 800, I still got no answer. Only when I tried 900 did the calculator answer my original question and tell me the exact answer (925). By experimenting, I found that, in order to get the exact answer, the estimate must be at least as close as 814–an error of 12 percent.

Useful? Good enough to enable The Treaty of QAMA?

Why our kids hate math

“Our kids hate math” because they’re pushed to learn higher math before they’ve mastered the basics, writes Patrick Welsh, who teaches at T.C. Williams High in Virginia, in USA Today.

The experience of T.C. Williams teacher Gary Thomas, a West Point graduate who retired from the Army Corps of Engineers as a colonel, is emblematic of the problem. This year, Thomas had many students placed in his Algebra II class who slid by with D’s in Algebra I, failed the state’s Algebra I exam and were clueless when it came to the most basic pre-requisites for his course. “They get overwhelmed. Eventually they give up,” Thomas says.

Thirty-one percent of eighth-graders took algebra in 2007, nearly double the percentage compared to 1990, reports the National Center for Education Statistics. In California, 54 percent take algebra in eighth grade. But many repeat it in ninth grade — and still do poorly.

My colleague Sally Miller . . . is the first to warn that too much math too soon is counterproductive. When Miller asked one of her geometry classes what 8 x 4 was, no one could come up with the answer without going to a calculator. “In the lower grades, more time has to be devoted to practicing basic computational skills so that they are internalized and eventually come naturally.”

Charlotte-Mecklenburg’s eighth-grade algebra classes have a “negative effect on most students, especially those students who weren’t stellar in math background,” says Charles Clotfelter, a Duke professor who studied the effects. Doing poorly “knocked them back on their heels.”

“It is time to ensure that all kids absorb the fundamentals of math — computation, fractions, percentages and decimals — first before moving on to the next level,” Welsh concludes.

A frightening number of students never learn math fundamentals. It’s the single greatest barrier to success in community colleges, which attract the un-stellar students. Students who’ve passed high school math classes — including a class called algebra — don’t understand fractions, percentages or decimals and can’t multiply 8 x 4 without a calculator.

NYC tracks grads’ college progress

New York City is telling high schools how well their graduates are doing at public colleges, including how many need remedial classes and how many drop out after the first semester, reports the New York Times. High schools are judged on graduation rates, in part, but not on graduates’ skills.

Illinois, Denver and Philadelphia also are tracking high school graduates to see how they do in college, reports the Times. Studies show many high school graduates falter in college because they lack basic reading, writing and math skills.

New York, like other cities, has made a considerable effort to improve its high school graduation rate — now 59 percent, up from 47 percent in 2005 — and push more of its students to enroll in college. But many of those students are stumbling in basic math and writing: 46 percent of New York City public school graduates who enrolled in one of the City University of New York two-year or four-year colleges in 2007 needed at least one remedial course, and 40 percent of them dropped out within two years.

At a third of the city’s 250 high schools, at least 70 percent of the graduates who went on to CUNY needed remedial help.

This is nothing new, community college instructors told the Times.

Elizabeth Clark teaches remedial writing at LaGuardia Community College to high school graduates who are unprepared to write a college essay.

“They don’t know how long it should be; they don’t know how to develop an argument,” Ms. Clark said. “They have very little ability to get past rhetoric and critically analyze what is motivating the writer, and you have to push them past simple binaries.”

There are also more basic problems, Ms. Clark said, such as students not knowing that each sentence must begin with a capital letter or using “u” instead of “you.”

. . . Susan L. Forman said that many of the issues have remained the same for the four decades she has taught remedial math at Bronx Community College, including students easily confused by fractions and negative numbers and becoming paralyzed when they are told they cannot use calculators.

What has changed, she said, is that students are often overly confident.

They don’t understand how much they don’t understand, she said.

Update: Chicago City Colleges can’t afford remedial classes, said Mayor Richard Daley, who called for limiting admissions to students prepared to do college-level work. Daley envisions offering remedial classes at alternative high schools. This would be a dramatic change, if it happens.

Innumerate, unemployable

A British haberdashery hires only applicants who can do mental math, reports the Daily Mail,  Most fail.

Colin Bamberger, 82, whose parents founded the Remnant Shop in 1944, said that less than one in ten applicants are now able to solve basic maths problems without turning to a calculator or till.

In the past, around eight in ten made the grade.

. . . He said: ‘Most of the youngsters who come to us for jobs are unemployable because they are not numerate.

. . . ‘It is all very well using calculators but if you have not got some idea what the answer is, how do you know if you have pushed the right button? It’s so easy to make a mistake.

Bamberger blames poor teaching and over-reliance on calculators.