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.

Simple math made complicated — for a reason

The Common Core makes simple math more complicated in order to teach understanding, writes Libby Nelson on Vox.

In the past, “students had this sense that math was some kind of magical black box,” says Dan Meyer, a former high school math teacher studying math education at Stanford University. “That wasn’t good enough.”

Students will learn different ways to multiply, divide, add, and subtract so they can see why the standard method works, writes Nelson. “They can play with them in fun, flexible ways,” says Meyer, who blogs at Dy/Dan.

Using a number line for subtraction lets students visualize the “distance” between two numbers. A father’s complaint about a confusing number line problem went viral on the Internet. Nelson provides a clearer version. 

Students put the two numbers at opposite ends of the number line.


It’s 4 steps from 316 to 320, 100 steps from 320 to 420, 7 steps from 420 to 427.


Then they add the steps together: 4 + 100 + 7 = a distance of 111. LearnZillion, a company that creates lesson plans for teaching to the Common Core standards, has a 5-minute video explaining this technique.

“Students should be able to understand any of these approaches,” said Morgan Polikoff, an assistant professor of education at the University of Southern California who is studying how the Common Core is implemented in the classroom. “It doesn’t mandate that they necessarily do one or the other.”

“A key question is whether elementary school teachers can learn to teach the conceptual side of math effectively,” writes Nelson.

If not, number lines and area models will just become another recipe, steps to memorize in order to get an answer, Polikoff says.

This is a real risk: Many elementary teachers are strong on reading and weak in math (and science). Perhaps we need math/science specialists in elementary school who understand their subject deeply and can teach kids to understand too.

NCTQ: Teacher prep earns D+

Teacher preparation policies earned a D+ in 2012, according to the National Council on Teacher Quality’s State Teacher Policy Yearbook. That’s up from a D in 2011.

The highest grade — B- — went to Alabama, Florida, Indiana and Tennessee. Alabama, Connecticut, Kentucky, New Hampshire, Rhode Island and Vermont made the most progress. Three states – Alaska, Montana and Wyoming – received failing grades.

Only a third of undergraduate teacher preparation programs are sufficiently selective, NCTQ finds. The majority “fail to ensure that candidates come from the top half of the college-going population.” Only 24 states require teacher preparation programs to use a basic skills test to screen applicants.

Standards are low for elementary teachers:

Teaching children to read is among an elementary teacher’s most important responsibilities, yet only 10 states appropriately assess teacher proficiency in effective reading instruction. And only 11 states adequately test new elementary teachers’ knowledge of mathematics.

Even though all but four states require some subject matter tests for elementary teacher licensing, the passing scores are extremely low. Every state (for which NCTQ has data) except Massachusetts sets the passing score for elementary teacher licensing tests below the average score for all test takers (50th percentile), and most states set passing rates at an exceedingly low level.

Only eight states– Colorado, Florida, Georgia, Louisiana, North Carolina, Ohio, Tennessee and Texas – use student achievement data to hold teacher preparation programs accountable for the effectiveness of the teachers they graduate.

Too many (would-be) elementary teachers

State Output

Some states produce enough elementary teachers to fill anticipated openings, but others produce twice as many as needed—or more.

Supply Demand Percent Difference
Colorado 1,169 1,099 106%
Connecticut 701 600 117
Delaware 373 122 306
Illinois 9,982 1,073 930
Kentucky 1,275 730 175
Louisiana 1,033 650 159
Maryland 1,011 723 140
Massachusetts 1,175 1,051 112
Michigan 2,903 1,227 236
Minnesota 1,179 709 166
Mississippi 751 660 114
New York 6,498 2,800 232
Pennsylvania 6,048 1,420 426
Tennessee 1,970 1,380 143

In many states, colleges are churning out too many would-be elementary teachers, reports Education Week.

New York and Michigan prepared twice as many elementary teachers as needed in 2011-12. Pennsylvania turned out four new graduates for every job opening. Illinois issued nine new elementary-teacher certificates in 2009 for every one first-time teacher hired in 2010.

By contrast, Colorado and Michigan produce just enough new elementary teachers to meet demand. (That’s assuming nobody moves from Illinois and Pennsylvania.)

Colleges should be more selective about admitting teacher candidates and train them more intensively, argues the National Council on Teacher Quality.

“We could improve, enhance, and extend the quality of teacher preparation, and therefore produce better-qualified new teacher graduates, but probably fewer in number,” agrees Arthur E. Wise, former president of the National Council for Accreditation of Teacher Education.

Prospective elementary teachers have lower academic qualifications than other college graduates, concludes a 2007 Educational Testing Service report. (Secondary teachers have higher-than-average test scores.)

“We could raise the bar and get teachers with higher aptitudes in classrooms and still have plenty of elementary teachers,” (NCTQ’s Arthur) McKee said.