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.

Koreans achieve, despite schools

Korean students are high achievers “not because of Korea’s schools, but often despite them,” writes Michael Horn in Forbes.

Teachers lecture, while students sleep.

Students spend long hours studying after school, then go to private hagwons for their “real” learning.

. . . if public education remained widely and freely available but not compulsory, many middle- and upper-class parents would stop sending their students to their current schools and instead send them to hagwons for what is often a truly customized and personalized—but quite expensive—learning experience.

That might trigger attempts to customize education in the public schools, writes Horn.

Korea (and Japan) have super-high scores on OECD’s creative problem-solving exam, writes Brandon Wright on Flypaper. There is a “strong, positive correlation between creative problem-solving performance and straightforward, traditional, familiar (if often bleak) math, science, and reading scores,” he writes. “Subject scores seem to buttress problem-solving skills—or at least to originate from the same source, sort of like twins.”

U.S. teens are above average at problem solving

PISA Problem SolvingU.S. 15-year-olds score just above the world average on PISA’s “creative problem-solving” exam, but below students in Asia, Canada, Australia, Finland, Britain and other European countries.   

“Students might be asked to identify the cheapest lines of furniture in a catalog showing different brands,” reports the New York Times. “At a more advanced level, students could be asked to develop a process for figuring out why a particular electronic device was not working properly.

American students did well at “interactive” tasks that required them to find some of the information needed to solve the problem. “This suggests that students in the United States are open to novelty, tolerate doubt and uncertainty, and dare to use intuition to initiate a solution,” the O.E.C.D. said in a statement.

But Asian students — who typically do best in math and science exams — also outperformed the U.S. students on “interactive” problems. 

“To understand how to navigate a complex problem and exercise abstract reasoning is actually a very strong point for the Asian countries,” said Francesco Avvisati, an analyst. 

The results don’t support the U.S. reputation for creativity, writes Joy Resmovits in the Huffington Post. 

Critics say the top-performing Asian countries “aren’t teaching kids to think creatively and problem-solve,” author Amanda Ripley said. “Well, now we have a test that gets closer to measuring those skills than any other — and they are killing it. Again.”

Here are some sample questions.

K-5 teachers: Homework = 2.9 hours per week

Elementary teachers assign an average of 2.9 hours of homework per week, middle school teachers assign 3.2 hours and high school teachers expect 3.5 hours, according to a Harris poll for University of Phoenix.

A high school student taking five courses could have 17.5 hours of homework per week. (When my daughter was in high school, she averaged three hours a night.)

Teachers say homework  helps them see how well their students understand the lessons (60 percent); helps students develop problem-solving skills (46 percent); gives parents a chance to see what is being learned in school (45 percent); helps students develop time management skills (39 percent); encourages students to relate classroom learning to outside activities (37 percent) and allows teachers to cover more content in class (30 percent).

The (not so bright) hopes of the future

Chart 3 final.png

In problem-solving, literacy and numeracy, 16- to 24-year-old Americans rank at or near the bottom on the OECD’s new international survey of adult literacy skills, reports the New Yorker. These young adults are “the folks who will be manning the global economy” for the next 30 or 40 years. Our 16- to 24-year-olds edge young Italians in literacy. That’s the bright spot.


Proud moment from the parents of an 8-year-old…


U.S. adults lag in numeracy, literacy

U.S. adults are dumber than the average human, proclaims the New York Post. A new international study doesn’t quite say that. But it’s not great news.

art“In math, reading and problem solving using technology – all skills considered critical for global competitiveness and economic strength – American adults scored below the international average,” the Post reports.

Adults in Japan, Canada, Australia, Finland and other countries scored higher than the United States in all three areas on the test, reports the Program for the International Assessment of Adult Competencies (PIAAC).

Americans ranked 16 out of 23 industrialized countries in literacy and 21 out of 23 in numeracy. In a new test of “problem solving in technology rich environments,” the U.S. ranked 17 out of 19. Respondents were tested on activities such as calculating mileage reimbursement due to a salesman, sorting email and comparing food expiration dates on grocery store tags.

American baby boomers outperformed people of the same age overseas, reports the Wall Street JournalYounger Americans lagged behind their international peers “in some cases by significant margins.”

The results show that the U.S. has lost the edge it held over the rest of the industrial world over the course of baby boomers’ work lives, said Joseph Fuller, a senior lecturer at Harvard Business School who studies competitiveness. “We had a lead and we blew it,” he said, adding that the generation of workers who have fallen behind their peers would have a difficult time catching up.

“We have a substantial percentage of the work force that does not have the basic aptitude to continue to learn and to make the most out of new technologies,” Mr. Fuller said. “That manifests itself in lower rates of productivity growth, and it’s productivity growth that drives real wage growth.”

Workers in Spain and Italy posted the lowest scores.

We need more tests, but what kind?

American Schools Need More Testing, Not Less, writes Ezekiel J. Emanuel in The New Republic. Students learn more when they take frequent, short tests.

A young neuroscientist named Andrew Butler has gone further, showing that testing can actually facilitate creative problem solving. In Butler’s research, undergraduates were given six prose passages of about 1,000 words each filled with facts and concepts. (Fact: There are approximately 1,000 species of bats. Concept: how bats’ echolocation works.) He had the students just study some of the passages; others, he repeatedly tested them on. Not only did his subjects demonstrate a better grasp of the tested material, but they also fared better when asked to take the concepts about which they’d been quizzed and apply them in completely new contexts—for example, by using what they’d learned about bat and bird wings to answer questions about airplane wings. When students had been tested on the passages, rather than just reading them, they got about 50 percent more of the answers correct. They were better at drawing inferences, thanks to the testing effect.

Only tests written by teachers are useful, responds Diane Ravitch. “Today’s standardized tests are useless.”

What he really admires, and appropriately so, are the regular weekly tests that he took in high school chemistry. His chemistry teacher Mr. Koontz knew what he had taught. He tested the students on what they had learned. He knew by the end of the day or over the weekend which students were keeping up and which ones were falling behind. He could act on that knowledge immediately to make sure that students understood what he thought he had taught and to explain it again to those who did not. He also learned whether to adjust his style of teaching to communicate the concepts and facts of chemistry more clearly to students. Mr. Koontz used the tests appropriately: to help his students.

Standardized exams are being used as “a ranking and rating system, one that gives carrots to teachers if their students do well but beats them with a stick (or fires them and closes their school) if they don’t,” Ravitch writes.

Most researchers say that teacher quality cannot be reliably measured by student test scores, because there are so many other variables that influence the scores, but the federal Department of Education is betting billions of dollars on it.

The job of writing, grading and analyzing tests belongs to “Mr. Koontz, not to Arne Duncan or Pearson or McGraw-Hill,” concludes Ravitch.

Why learn math? To write business plans

Thirty-eight percent of high school seniors in Rhode Island test as “substantially below proficient” in reading or math, putting their odds of graduation at risk, writes Julia Steiny. At a summer “cram camp,” math haters got motivated by crunching numbers for business plans.

 Teachers spent the first day asking students what they don’t like about their community.  Answer:  plenty.

Okay.  So get into teams and pick one problem — like, no place for teens to hang out, bad public parks, a need for animal rescue shelters.  (Yes, many shelters exist, but so what?)  Then, build a business model with a plan that will solve the problem.  Don’t whine; take an entrepreneurial approach.  With your idea in hand, research the costs of rent, labor, utilities, equipment.  Prepare multiple spreadsheets that explain income and outflow, start-up costs and maintenance.  Develop “what if” scenarios for unanticipated expenses.  Talk to local business leaders, provided by the program, about your calculations.

Local businesses offered $1,000 to fund the winning plan. Students pitched their ideas to a panel of superintendents and business leaders.

A group of girls proposes eco-friendly electric mini-buses to chauffeur kids around. They’d wanted a cost-free service, but crunching the numbers ruled that out.

Business planning showed what they could do with math skills, says Christine Bonas, a math teacher turned guidance counselor. “The light dawned on them that this is what math is for.”

“To teach them a slope, we (math teachers) put a formula on the board, give them graph paper and show them the rise over run.  There’s always one kid who says, When am I going to use this?  The teacher says, uh, well, see that roller coaster?  Parabolas are how to keep them from crashing.  That’s no answer.  They don’t care.  But if you ask a kid to show me how your business is going to make a profit, they can show you time on the “x” axis and increase in cost on “y”, suddenly we’re looking at a negative slope.  Oh!, they say. Because we’re teaching in context.  Parabolas have to have something to do with their lives. Making a profit is something they can care about.”

Students won’t learn the skills if they don’t care, says Bonas.

Why does Mr. Snuffleupagus snuffle?

Sesame Street is trying to teach nature, math, science and engineering ideas to preschoolers, reports the New York Times.

. . . (A cow) made it up the stairs to the beauty parlor but now, her bouffant piled high, she’s stuck. Cows can go up stairs, she moans, but not down.

Enter Super Grover 2.0. Out from his bottomless “utility sock” comes an enormous ramp, which, as the cow cheerily notes before clomping on down, is “a sloping surface that goes from high to low.”

It’s not about the letter C or the number 7  any more. Now Sesame Street is tackling “topics like how a pulley works or how to go about investigating what’s making Mr. Snuffleupagus sneeze,” reports the Times.

Zach Hyman

Murray Monster, shown here attending Robo Fun School, appears in science-focused segments with children.

Super Grover 2.0 “uses magnets, springs and ‘superpowers’ of investigation, observation and reporting to solve problems through trial and error. Before settling on a ramp for the stuck cow, for instance, he tries a trampoline.”

Last season, Elmo began starring in a daily musical that incorporates math.

On Sept. 24, Sesame Workshop will launch “Little Discoverers: Big Fun With Science, Math and More” on the web site. “In one game, little fingers manipulate a virtual spring to launch pieces of trash into Oscar the Grouch’s trash can, a Sesame Street version of ‘Angry Birds’.”