Teaching math the Shanghai way

Lianjie Lu, from Shanghai, teaches fractions to year 3 pupils at Fox primary school in Kensington, London.

Lianjie Lu, from Shanghai, teaches fractions to year 3 pupils at a London school. Photo: Frantzesco Kangaris/Guardian

Britain has imported math teachers from high-scoring Shanghai to demonstrate teaching techniques, reports The Guardian.  

Lilianjie Lu stands in front of 21 seven and eight-year-olds in a London classroom, struggling slightly with her English but with a winning smile on her face, as she attempts to teach them all about fractions.

The classroom has been reconfigured to resemble a Shanghai classroom. The carpet has been taken up, desks which are normally clustered in friendly groups are in straight rows, and all eyes are on Lu and her touchscreen.

. . . The class is repetitive, going over and over similar territory, stretching the children slightly further as the lesson progresses, picking up on mistakes and making sure that everyone is keeping up.

British teachers move more quickly, says Ben McMullen, deputy head at Fox school and senior lead in the local maths hub. Chinese teachers “dwell on it for what seems a long time so every single child understands exactly what’s going on.”

Lu is now asking the children what a fraction is. “If the whole is divided in to three equal parts, each part is a third of the whole,” one child explains. The other children follow suit, repeating and adapting their answer to explain the fraction written on the board.

“There’s a lot of chanting and recitation which to our English ears seems a bit formulaic,” says McMullen, “but it’s a way of embedding that understanding.”

McMullen spent two weeks observing at a Shanghai primary school in September. Math lessons are shorter there, but better, he says. “I saw better maths teaching in 35 minutes than I had ever done in an hour and ten minutes.”

In Shanghai every child of the same age is on the same page of the same text book at the same time.

. . . Children have mastered their jiujiu (times tables) back to front and inside out by the time they are eight. Classrooms are bare and text books are basic, minimal, “not that appealing” to look at, admits McMullen, but of exceptionally high quality and thoroughly researched.

Lu studied math teaching for five years at a university and teaches only math at her Shanghai elementary school. In Britain, primary teachers teach all subjects and have little training in how to teach math.

Testing for competency

New Hampshire requires high schools to measure credit in terms of competency rather than “seat time,” writes Julie Freeland. Schools are trying different ways to evaluate competence.

At Sanborn Regional High School, students take pen-and-paper exams, but they can retest if they haven’t achieved mastery.

North Country Charter Academy students follow a self-paced online curriculum with frequent online tests to evaluate mastery. Teachers provide support as needed.

Next Charter School uses student projects.

For example, the students in a social studies course might be asked to write a letter to President Obama proposing foreign policy strategies. The letter might have to include both a historical account of previous foreign policy strategies, a proposed action, and a rationale and justification for why that proposed action was the best option.

If the project doesn’t show mastery, the student can revise it or pick a new project.

From Policy to Practice, by the Christensen Institute, looks at New Hampshire’s shift to competency-based learning.

CreditWren McDonald

Replace the college admissions systems with assessment centers, proposes Adam Grant in the New York Times. Businesses, government and the military use these to evaluate job candidates, he writes. “Today, at a typical center, applicants spend a day completing a series of individual tasks, group activities and interviews. Some assessments are objectively scored for performance; others are observed by multiple trained evaluators looking for key behaviors.”

Competency catches on

Competency-based certificates and degrees — what counts is mastery, not “seat time” — are expanding. Students work at their own pace.

Exams aren’t the enemy

Exams Aren’t the Enemy, writes Talmadge Nardi, a high school English teacher, in The Atlantic.

We must continue to be passionate and skillful teachers of critical thinking, writing and reading. And we must also continue to test our students. I am convinced that the combination of the two is what leads my students to success.

Nardi teaches at the Academy of the Pacific Rim (APR), a Boston charter school where three-quarters of students are black or Hispanic and a majority come from low-income families. The school ranks very high on the 10th-grade English MCAS, Massachusetts’ standardized exam.

I do virtually no explicit test preparation with my students. What I do instead is teach intensive reading, writing, and critical thinking skills to prepare them for my 11th and 12th-grade college-style seminars and beyond.

Since the MCAS is a handwritten test, she requires handwritten essays so students practice writing clearly and getting by without spellcheck. She also teaches them how to handle multiple-choice questions and how to much to write on essay questions. She reviews the plots and characters of books read in class so students will be prepared to write about a book for the long essay. But it doesn’t take much time and can be useful long after they’ve taken the MCAS, Nardi writes.

Part of college and career readiness is getting ready for exams. The MCAS, for example, is both a skill and an endurance test, and it prepares students to take tests of basic content knowledge–the kind of tests most professionals have to slog through to get to where they are. My students will have to take many such tests to gain access to professional fields like medicine, law, teaching and accounting.

Testing is Good for Teachers and Children, argues Matt Barnum on Dropout Nation. As a teacher, half of his evaluation was based on student performance on as many as five standardized assessments a year. “We knew where we stood in terms of performance, and so did our students,” he writes.

Testing helps students achieve mastery by making it possible to learn from mistakes, adds the editor. It also helps teachers and schools diagnose and address learning issues.


From cohorts to competency

Technology makes it much easier to personalize education through show what you know” promotion, concludes The Shift From Cohorts to Competency, a Digital Learning Network Smart Series paper.

The cohort model — children are grouped by age — moves on students who aren’t ready and holds back students who could excel, the authors write. “A competency-based system frees up students to learn at their own pace and according to their own needs,” said Carri Schneider, one of the authors. “Competency education is the ultimate path to personalization.”

“No excuses’ students struggle in college

“No excuses” charter schools send most or all of their low-income, minority students to college. But do “no excuses” students graduate from college? In Education Next, Robert Pondiscio looks at what charter schools are doing to improve their graduates’ college graduation rates.

KIPP is the largest and best known of a class of charter-management organizations (CMOs) that includes Achievement First, YES Prep, Uncommon Schools, Mastery, Aspire, and others. This group shares a set of familiar characteristics: more and longer school days, with a college preparatory curriculum for all students; strict behavioral and disciplinary codes; and a strong focus on building a common, high-intensity school culture. Classrooms and halls are awash in motivational quotations and college banners, typically from the alma maters of the inevitably young, hard-charging teachers who staff the schools. The signature feature is high behavioral and academic expectations for all students, the vast majority of whom are low-income, urban black and Hispanic kids.

Both KIPP and YES Prep track their graduates and report on how well they’re doing. One third of former KIPP middle schoolers have graduated college within six years — four times the average for disadvantaged students, but way below KIPP’s goals.

Black graduates of YES Prep average 1556 in reading, writing and math on the SAT, “far above the national average of 1273 for African Americans, and significantly higher than the 1500 national average for all students.” All graduates have passed at least one AP class. Less than 5 percent of YES Prep grads require remediation in college. Yet the six-year graduation rate is only 41 percent .

 “It wasn’t the academic piece that was holding our kids back,” notes senior director of college initiatives at YES Prep Donald Kamentz. “What we found hands down was it was the noncognitive piece—that tenacity, that grit—that allowed kids to harness those skills and persist when they faced difficulty.”

“What we’ve found with the ‘whatever it takes’ or ‘no excuses’ mentality is that it was very teacher-driven and less student-driven,” says Kametz, acknowledging this is a controversial line of thought in his own halls. A typical No Excuses approach might involve giving demerits or detention for missed assignments or turning in work that’s not “neat and complete.” Kamentz questions whether this tough-love approach helps create the self-advocacy in students they will need to be successful in college. “It’s the largest gaping hole with our kids in college,” he says. “They will constantly say, ‘You structured my life so much that I had to do very little thinking and structuring myself.’”

The no-excuses charters are trying to develop ways to strengthen students’ perseverance, “growth mindset” and grit. Some send  “posses” of students to “right-match” colleges that provide mentoring to first-generation-to-college students. (I love Pondiscio’s phrase: “in helicopter parentis.”)

KIPP, which started with middle schools, is adding elementary and high schools to strengthen academic preparation. The network also is following its alumni through college to help them cope with academic and social challenges. Now there are 1,000 KIPP graduates in college. In a few years, there will be 10,000. KIPP hopes to raise the college graduation rate to 75 percent, as high as students from upper-income families. The short-term goal is a 50 percent graduation rate.

Lemov: How teachers get better

Doug Lemov’s new book, Practice Perfect,gives teachers (and others) “42 rules for getting better at getting better.” In an Amazon interview, Lemov and co-authors Erica Woolway, and Katie Yezzi, call for practicing strengths, instead of focusing on weaknesses. It’s a myth that practice should stop when you achieve competence, they say.

What marks champions is their excellence at something—they may have weaknesses, but their strengths are honed and polished to the level of brilliance. The value of practice begins at mastery!

Practice has a reputation for being dull, but its “fun, exciting, and ideal for adults,” they believe.

“Educrats have long warned of the perils of rote and repetition,” writes Kathleen Porter-Magee in an Education Gadfly review. “But they’re wrong.”

Lemov’s Teach Like a Champion, “based on thousands of hours spent observing outstanding teachers in action” argued that “great teaching requires the mastery of seemingly mundane but crucially important knowledge and skills,” Porter-Magee writes.

Practice Perfect‘s 42 rules “are simple, practical, and grounded in common sense, as well as respect for the practice and repetition that we need to help teachers (and students) achieve mastery.”

They also present a damning critique of the multi-billion dollar teacher professional-development industry. By shying away from skill repetition, most PD programs offer the equivalent of art-appreciation courses and then ask teachers to paint masterpieces.

Teachers need to hone their skills with one another — with coaching and feedback—before they try new skills in the classroom.

Math needs a revolution too

Math Needs a Revolution, Too, writes Barry Garelick in response to The Atlantic story, The Writing Revolution. He first encountered reform math when his daughter was in second grade.

. . . understanding takes precedence over procedure and process trumps content. In this world, memorization is looked down upon as “rote learning” and thus addition and subtraction facts are not drilled in the classroom–it’s something for students to learn at home. Inefficient methods for adding, subtracting, multiplying, and dividing are taught in the belief that such methods expose the conceptual underpinning of what is happening during these operations. The standard (and efficient) methods for these operations are delayed sometimes until 4th and 5th grades, when students are deemed ready to learn procedural fluency.

Students are expected to “think like mathematicians” before acquiring the analytic tools necessary to do so, Garelick writes. Procedural skills are taught on a “just in time” basis.

Such a process may eliminate what the education establishment views as tedious “drill and kill” exercises, but it results in poor learning and lack of mastery. Students generally work in groups with teachers who “facilitate” rather than providing direct instruction.

As reform math has become the norm in K-6 classrooms, high school math teachers are trying to teach algebra to students who “do not know how to do simple mathematical procedures,” he writes.

In math, as in writing, learning the fundamentals may not be fun or engaging. It may require practice. But students who skip the basics rarely develop the ability to “think like mathematicians” or write like “authors.” They’re confused. And bored.

Self-paced math lab replaces remedial classes

Frustrated by high failure rates in remedial math classes, one community college now assigns all remedial students to a math lab, where they work at their own pace, moving on when they achieve mastery.

Free e-books may be a bad deal for tech-poor students, a community college dean writes.

A cheaper, faster, online degree

After a shaky start, Western Governors University — an accredited, low-cost, nonprofit online university — is helping working adults earn degrees quickly and cheaply. WGU degrees are based on mastery, not on “seat time,” enabling the average bachelor’s graduate to finish a degree in 30 months for about $15,000.

Also on Community College SpotlightWomen make up nearly half the community college faculty in science, math and technology fields.