Repetition and Memorizing

After Joanne’s introduction and Diana’s open cheerfulness at being a co-guest blogger here, you might think I’d offer up more intellectually stimulating fare than funny pictures of Starbucks references.  For those of you who were disappointed, I’ll endeavor to make it up to you in this post.

In a recent Wall Street Journal piece, Barbara Oakley posits that the Common Core standards, and the pedagogy that is often pushed with those standards, prioritizes “conceptual understanding” at the expense of slighting repeated and varied practice that leads to computational mastery:

Conceptual understanding has become the mother lode of today’s [Common Core] approach to education in science, technology, engineering and mathematics—known as the STEM disciplines. However, an “understanding-centric approach” by educators can create problems….

True experts have a profound conceptual understanding of their field. But the expertise built the profound conceptual understanding, not the other way around. There’s a big difference between the “ah-ha” light bulb, as understanding begins to glimmer, and real mastery.

As research by Alessandro Guida, Fernand Gobet, K. Anders Ericsson and others has also shown, the development of true expertise involves extensive practice so that the fundamental neural architectures that underpin true expertise have time to grow and deepen. This involves plenty of repetition in a flexible variety of circumstances. In the hands of poor teachers, this repetition becomes rote—droning reiteration of easy material. With gifted teachers, however, this subtly shifting and expanding repetition mixed with new material becomes a form of deliberate practice and mastery learning….

True mastery doesn’t mean you use crutches like laying out 25 beans in 5-by-5 rows to demonstrate that 5 × 5 = 25. It means that when you see 5 × 5, in a flash, you know it’s 25—it’s a single neural chunk that’s as easy to pull up as a ribbon. Having students stop to continually check and prove their understanding can actually impede their understanding, in the same way that continually focusing on every aspect of a golf swing can impede the development of the swing.

Understanding is key. But not superficial, light-bulb moment of understanding. In STEM, true and deep understanding comes with the mastery gained through practice.

I recently wrote on a similar theme, quoting from a newspaper article about a Stanford paper that demonstrated, among other things, that children should memorize multiplication tables and addition tables.  Quoting:

Next, Menon’s team put 20 adolescents and 20 adults into the MRI machines and gave them the same simple addition problems. It turns out that adults don’t use their memory-crunching hippocampus in the same way. Instead of using a lot of effort, retrieving six plus four equals 10 from long-term storage was almost automatic, Menon said.

In other words, over time the brain became increasingly efficient at retrieving facts. Think of it like a bumpy, grassy field, NIH’s Mann Koepke explained.

Walk over the same spot enough and a smooth, grass-free path forms, making it easier to get from start to end.

If your brain doesn’t have to work as hard on simple maths, it has more working memory free to process the teacher’s brand-new lesson on more complex math.

‘The study provides new evidence that this experience with math actually changes the hippocampal patterns, or the connections. They become more stable with skill development,’ she said.

‘So learning your addition and multiplication tables and having them in rote memory helps.’

As a math teacher I explain it this way:  to truly understand algebra a student must already have mastered operations with fractions, decimals, and negative numbers.  The simple calculation of calculating the slope of a line between two given points could include all three of those, and if one expends all his/her brain power on that simple calculation, there won’t be as much brain power “left over” to understand what the answer, the slope, actually means or represents.

Some things must be memorized–not for their own sakes, but because they are useful tools, they are means to an end.

In professional development sessions I’m often told, as if it’s an obvious fact that cannot possibly be doubted, that if you cannot explain how something works, then you truly don’t have a “deep” enough understanding of it.  You have rote memorization, nothing more, and rote memorization is useless.  Sometimes I’m even told this by math teachers, who will at lease concede that memorizing the multiplication tables is a valuable exercise.  I put up a division problem, usually something simple like 515/3, and ask “Who can perform this calculation?”  Everyone can and all hands are raised.  Then I ask, “Who can explain why the standard algorithm (which everyone our age knows and uses) works, and why?”  Even most math teachers cannot, but everyone recognizes why that standard algorithm is important, useful, and efficient–everyone, that is, except for those who think that some Indian lattice method leads to “deeper understanding”.  Beyond knowing that division is akin to finding out how many “groupings” of a certain size can be made from a certain number, how “deep” does one need to understand division?  It’s useful only as a tool to get to bigger and better things, IMNSHO.

So repeat and repeat and repeat until the repetition begets memorization.  That’s what Mrs. Barton did until every one of her students knew the multiplication tables.  Don’t allow a pet pedagogical theory to harm students’ ability to calculate.  Teach them what works.  Give them the most efficient tools out there.


The Address

At a private school in Vermont for boys with learning disabilities, students are challenged to memorize and recite Lincoln’s Gettysburg Address, reports a Ken Burns documentary.

Teachers, language specialists, speech pathologists and therapists work with the boys, often one on one. Greenwood’s tuition for day students is $53,475, notes Linda Holmes on an NPR blog. For boarding students, it’s $68,890. “The chilling part of the film is to think about how many kids would benefit from, but don’t get, this kind of attention.”

Smartphones, stupid people

Smartphones Mean You Will No Longer Have to Memorize Facts, argues David Pogue in Scientific American.

When my father was growing up, his father offered him 25 cents to memorize the complete list of U.S. presidents. “Number one, George Washington. Number two, John Adams …”

A generation later my dad made the same deal with me, upping the reward to $5. (The prize had grown, he explained, “because of inflation and because there are more presidents now.”)

This year I offered my own son $10 to perform the same stunt. My son, however, was baffled. Why on earth should he memorize the presidents?

Nowadays, he argued, “everybody has a smartphone” and always will.

Smartphones will outsell regular old phones in 2013, writes Pogue. “Having a computer in your pocket is the norm.”

Should we mourn the loss of memorization skills? “Having a store of ready information” could be more fundamental and important than other obsolete skills, he speculates. But, no, he decides.

. . . we’ve confronted this issue before—or, at least, one that is almost exactly like it. When pocket calculators came along, educators and parents were alarmed about students losing the ability to perform arithmetic using paper and pencil. After hundreds of generations of teaching basic math, were we now prepared to cede that expertise to machines?

Yes, we were. Today calculators are almost universally permitted in the classroom. . . .

In the end, we reasoned (or maybe rationalized) that the critical skills are analysis and problem solving—not basic computation. Calculators will always be with us. So why not let them do the grunt work and free up more time for students to learn more complex concepts or master more difficult problems?

And how has that worked?

With students freed from memorizing facts, maybe they’ll “focus on developing analytical skills (logic, interpretation, creative problem solving) and personal ones (motivation, self-control, tolerance),” Pogue writes.

And maybe winged pigs will play hockey on the ice in hell.

Poetry by heart

Memorizing poetry has gone out of style, writes Brad Leithauser, a professor of writing and literature, in The New Yorker. His students have trouble memorizing a Shakespearean sonnet. They’re not used to memorizing anything. (I took a theater class at the University of Michigan as a 40-year-old journalism fellow. We were given a week to select and memorize a Shakespearean sonnet. I was the only person in the class who could recite the full sonnet.)

Leithauser’s mother paid him a penny a line to memorize poems.

The first one I mastered was Tennyson’s “The Eagle” (“He clasps the crag with crooked hands”), which brought in a haul of six cents. Opportunistically, I moved on to the longer “Casey at the Bat” (“It looked extremely rocky for the Mudville nine that day”) and Byron’s “The Destruction of Sennacherib” (whose title I mispronounced for decades), which netted me fifty-two cents and twenty-four cents respectively. Some Longfellow, some Frost. I straggled through Coleridge’s “Kubla Khan” and enough of his “The Ancient Mariner” to purchase a couple of candy bars.

In the heyday of memorization (1875 to 1950), there were many rationales for verse recitation, writes  Catherine Robson’s new Heart Beats: Everyday Life and the Memorized Poem.

. . .  to foster a lifelong love of literature; to preserve the finest accomplishments in the language down the generations; to boost self-confidence through a mastery of elocution; to help purge the idioms and accents of lower-class speech; to strengthen the brain through exercise; and so forth.

She looks at three classics often required of students: Felicia Hemans’s “Casabianca”  (“The boy stood on the burning deck”), which Tom Sawyer had to learn; Thomas Gray’s “Elegy Written in a Country Churchyard,” and Charles Wolfe’s  “The Burial of Sir John Moore after Corunna.”

“If we do not learn by heart, the heart does not feel the rhythms of poetry as echoes or variations of its own insistent beat,” writes Robson.

Leithauser adds: “You take the poem inside you, into your brain chemistry if not your blood, and you know it at a deeper, bodily level than if you simply read it off a screen.”

Here’s The Burial of Sir John Moore After Corunna.

Old school: Teach word roots, math facts and …

Kids Should Learn Cursive (and Math Facts, and Word Roots), writes Annie Murphy Paul in Time. New researchsupports the effectiveness of “old school” methods such as “memorizing math facts, reading aloud, practicing handwriting, and teaching argumentation,” she writes.

Suzanne Kail, an English teacher at an Ohio high school was required to teach Latin and Greek word roots, she writes in English Journal, though she abhorred “rote memorization.”

Students learned that “sta” means “put in place or stand,” as in “statue” or “station.”  They learned that “cess” means “to move or withdraw,” which let them understand “recess.”

Her three classes competed against each other to come up with the longest list of words derived from the roots they were learning. Kail’s students started using these terms in their writing, and many of them told her that their study of word roots helped them answer questions on the SAT and on Ohio’s state graduation exam. (Research confirms that instruction in word roots allows students to learn new vocabulary and figure out the meaning of words in context more easily.)

For her part, Kail reports that she no longer sees rote memorization as “inherently evil.” Although committing the word roots to memory was a necessary first step, she notes, “the key was taking that old-school method and encouraging students to use their knowledge to practice higher-level thinking skills.”

I learned Latin and Greek word roots in seventh grade. It was lots of fun.

Drilling math facts, like the multiplication table, “is a prerequisite for doing more complex, and more interesting, kinds of math,” Paul writes.

Other valuable old-school skills:

 Handwriting. Research shows that forming letters by hand, as opposed to typing them into a computer, not only helps young children develop their fine motor skills but also improves their ability to recognize letters — a capacity that, in turn, predicts reading ability at age five. . . .

Argumentation. In a public sphere filled with vehemently expressed opinion, the ability to make a reasoned argument is more important than ever. . . .

Reading aloud. Many studies have shown that when students are read to frequently by a teacher, their vocabulary and their grasp of syntax and sentence structure improves.

I’d add memorizing and reciting poetry as a valuable old-school skill. What are some others?

Test-crazy China seeks innovators

China’s education system turns out students who are great at memorizing but not at thinking, writes Helen Gao, who moved from China to the U.S. for her senior year of high school.

In 2010, an international standardized test found that junior high school students in Shanghai had outperformed their peers in rest of the world in math, science, and reading, beating the U.S. averages by a wide margin. . . . (The) nine-year compulsory education system, installed in 1986, has boosted the country’s literacy rate to around 92 percent (it was 67 percent as of 1980) and prepared millions of eligible young people for the rapidly expanding workforce. Now, however, as the economy shows signs of cooling, Chinese leaders are trying to engender more domestic innovation.

They hope to see an educated workforce, rather than toiling on factory floors or sitting in the cubicles of Western companies’ Chinese branches, found their own businesses or brands that will sell to domestic as well as international buyers. They want domestic moviegoers to stop purchasing bootleg DVDs of Western blockbusters, and for foreign viewers to start raving about Chinese films. But the nation’s education system, instead of channeling the youthful energy of China’s next generation, seems to be blocking it.

The gao kao, the college admissions test, determines students’ futures. It’s all multiple choice, Gao writes.
Chinese students spend years cramming for the big test, reports the New York Times.

. . .  new research by the workplace manager Regus shows that Chinese employers are now favoring graduates with internship experience, winning personalities and foreign language skills. Just 9 percent of employers, especially at large companies, now put educational background as the top priority in hiring.

That probably means acing the gao kao, getting into a prestigious university and offering experience, personality and language skills.

Learning by heart

Memorization — or “learning by heart” — is underrated, writes Justin Snider on HechingerEd. As an English teacher, he makes students memorize poetry.

First, it’s a challenge, and one in which those who succeed can take pride….

Second, it’s good exercise for your brain….

Third, and most importantly, new insights are gained in the process of memorization. You see things to which you were previously blind; you uncover a play on words, assonance, alliteration, analogies.

With multiple readings (or viewings or hearings), “we actually begin to understand, see and hear,” Snider writes.

I memorized Wordworth’s The World Is Too Much With Us in high school English 42 years ago. I still know about half of it. I say it to myself sometimes.

The world is too much with us; late and soon,
Getting and spending, we lay waste our powers;
Little we see in Nature that is ours;
We have given our hearts away, a sordid boon!
This Sea that bares her bosom to the moon,
The winds that will be howling at all hours,
And are up-gathered now like sleeping flowers,
For this, for everything, we are out of tune;
It moves us not. Great God! I’d rather be
A Pagan suckled in a creed outworn;
So might I, standing on this pleasant lea,
Have glimpses that would make me less forlorn;
Have sight of Proteus rising from the sea;
Or hear old Triton blow his wreathed horn.

“Hear old Triton blow his wreathed horn” always gets to me.

Drill, student, drill

Despite the education world’s rejection of “drill and kill, rote learning has its uses, writes Virginia Heffernan in the New York Times Magazine.

By e-mail, E. D. Hirsch Jr., the distinguished literary critic and education reformer, told me that far from rejecting drilling, he considers “distributed practice,” the official term for drilling, essential. A distributed practice system, Hirsch explained, “is helpful in making the procedures second nature, which allows you to focus on the structural elements of the problem.”

For knowledge that must be automatic, like multiplication tables, “you need something like drilling,” adds Dan Willingham, a cognitive scientist.

“Colorful, happy apps” can make drilling less boring, Heffernan writes.

Apps devoted to specific subjects always have the right answers in reserve. They unfailingly know stuff that might elude more fallible human drillers, like atomic weights, the order of cranial nerves and African geography. And they can make almost any exercise feel like a video game.

. . . even as they profess reluctance about drilling schoolchildren, adults who themselves are looking to learn something new — from foreign languages to bar-exam material — increasingly turn to apps that animate some version of a multiple-choice or flashcard narrative.

I tutored a girl in algebra who hadn’t memorized the multiplication tables. She had to slog through the arithmetic on every problem, which made it hard to “focus on the structural elements.”

Ten years ago, I tutored a sixth grader who was an excellent phonetic reader with poor comprehension because of her limited English vocabulary. She asked me for the definition of every word she didn’t know and memorized the definitions. I just found her high school-era web page, which lists her favorite books, including The Scarlet Letter.

Japan goes ‘back to basics’

Worried about competition from South Korea and Hong Kong, Japanese schools are  going “back to basics,” reports AP.

In a move that has divided educators and experts, Japan is going back to basics after a 10-year experiment in “pressure-free education,” which encouraged more application of knowledge and less rote memorization.

. . . Japan’s near-the-top rank on international standardized tests has fallen, stunning this nation where education has long been a source of pride.

The Education Ministry is fattening up textbooks and raising expectations as part of the back-to-basics drive.

Science and math textbooks will see the biggest additions, getting 60 percent more pages compared to earlier this decade. Among new concepts: Fifth-graders will learn how to calculate the area of a trapezoid and sixth-graders will learn about electricity.

An hour or two of school will be added each week, depending on the grade, and English will be introduced in fifth grade instead of seventh. Middle and high school students can expect similar changes in subsequent years.

Traditionally, Japanese students have crammed to pass university entrance examinations, then coasted through college.

Getting into the right university goes a long way toward determining one’s job, income level and place in society — a system that many Japanese agree needs to change.

“Pressure-free education” tried to shift emphasis from memorization to applying knowledge. Students were encouraged to think creatively and express their own views.

Curricular requirements were reduced, Saturday half-day classes were phased out, and teachers were told to take three hours each week to engage in learning driven by students’ questions, such as “Why doesn’t a sleeping bird fall from its perch on a branch?”

On the international PISA exam, Japan’s rank dropped sharply in math, science and reading, despite PISA’s stress on applying knowledge to real-life situations.

Japanese students dropped slightly in math and stayed in third place in science on TIMSS, which is more geared toward knowledge.

The current system has been a “huge failure,” said Eiichi Kajita, president of International Pacific University, who helped craft the new curriculum guidelines. Education has become too child-centered, he argued.

“Teachers were told students should be supported, not taught,” Kajita said. “We need to revive a respect for knowledge. We also need more discipline.”

Teachers didn’t get enough training to make the new method work, says Mutsuko Takahashi, vice president of the Japan Teachers’ Union. The union is pushing for smaller class sizes — teachers have up to 40 students — to make it easier to teach new material.

Japan continues to outperform the U.S. in math and science on TIMSS and PISA.

He clasps the crag with crooked hands …

From This Week in Education, a young Superman recites Tennyson’s The Eagle.