The math problem: All rote, no reasoning




Warhol’s fractions: Teaching through the arts

A Maryland middle school integrates arts with the standard curricula, reports Edutopia on Bates Middle School in Annapolis.

For example, in a science classroom you might see students choreographing a dance using locomotor and nonlocomotor movements to demonstrate their understanding of rotation versus revolution of the planets (PDF). In a math class, you might see students learning fractions by examining composition in Warhol’s Campbell’s soup paintings. (See more arts-integrated lesson plans from Bates.)

“Engagement can also be leveraged to boost academic growth and improve discipline,” Edutopia argues.

Why our kids hate math





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.”



Fractions are key to math learning

Learning fractions and long division in elementary school leads to math success, according to a Carnegie Mellon research team led by Robert Siegler. In the U.S. and Britain, fifth graders’ understanding of fractions and long division correlated with their ability to learn higher math.

“We need to improve instruction in long division and fractions, which will require helping teachers to gain a deeper understanding of the concepts that underlie these mathematical operations,” said Siegler. “At present, many teachers lack this understanding.” By contrast, East Asian teachers can explain why math operations work.

And college remedial classes are filled with people who never “got” fractions.

Spatial thinking skills predict future math success, reports MindShift.

In a University of Chicago study students in first and second grade who chose the right shape to complete a square “also showed the most growth in their number-line knowledge over the following school year, and scored highest on a measure of mathematics ability at age eight.”

Parents can help their children develop spatial skills.

. . . Temple University psychology professor Nora Newcombe and her coauthors found that parents and children playing with blocks together were much more likely to use spatial terms like “over,” “around,” and “through,” than participants who played with a pre-assembled toy—and that it’s hearing and voicing such words that helps improve children’s spatial awareness.

Another 2011 study, this one from the University of Chicago, reported that the number of spatial terms (like “circle,” “curvy,” and “edge”) parents used while interacting with their toddlers predicted how many of these kinds of words children themselves produced, and how well they performed on spatial problem-solving tasks at a later age.

My first reaction was that kids who are good at math at a young age are likely to be good at math when they’re older. But there’s got to be more to the research than that, surely.

Teach music for music’s sake

Teach music because it’s a universal language and “the arts are our most potent means of human expression,” not because it might help kids learn fractions or raise test scores or develop teamwork, writes Nancy Flanagan, a music teacher.

Yesterday, the Learning First Alliance asked Can Arts Education Help Close the Achievement Gap? I appreciate the perspectives and data assembled by Anne O’Brien–who points out that students from high-poverty schools who study the arts are more likely to graduate HS, attend and finish college, and register to vote. But I believe the real question is:  What do the arts teach children that other subjects can’t?

Teachers defend music, art, dance and drama by arguing they help teach something considered more important, such as “enhanced brain development, spatial/visual/temporal processing, improving memory and attention, physical coordination, personal discipline and teamwork,” Flanagan writes.

But where did we get the idea that artistic expression is less useful or important than the sciences? How did music, art, dance and drama get pushed aside in our American school curriculum? I’m not surprised that studying or listening to music has beneficial effects on learning fractions or other academic skills, but those are side effects.

Kids should study music because it’s central to every human society on earth and has a vitally important role in every aspect of culture, from history to literature to media and communication studies. Music is part of what it means to be a human being.


I’ve got rhythm, I’ve got fractions …

Children are clapping, drumming and chanting to learn fractions at a California elementary school. It seems to be working, concludes a study which will be published in Educational Studies in Mathematics.


Students in Academic Music scored 50 percent higher on a fraction test than students in the regular math class. Lower-performing students narrowed the gap with high achievers.

Fourth-grade math scores have soared since a San Bruno school adopted Academic Music, reports the San Jose Mercury News.

On Tuesday, 29 children at Allen Elementary School tapped out a rhythm with drumsticks as (Endre) Balogh stepped and clapped in 4/4 time at the front of the class. He stepped four times per beat. One clap equaled a whole note, two claps indicated two half notes, and so on.

“Which is larger, the whole note or the half note?” he asked.

“Whole note,” one of the third-graders replied.

“Whole note, but why?” the teacher said.

“Because it’s longer,” another student called out.

Toones Academic Music, a nonprofit, is working to expand the program to more schools.

Coach G has tips for teaching “the dreaded f word, fractions.”

A vote for new math standards


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






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.