U.S. math lag: It’s not just other people’s kids

Don’t blame poor kids for U.S. students’ mediocre performance on international math exams, write researchers in Education Next.  When the children of college-educated parents are compared, U.S. students do even worse than our international competitors.

Overall, the U.S. proficiency rate in math (35 percent) places the country at the 27th rank among the 34 OECD countries that participated in the Program for International Student Assessment (PISA). That ranking is somewhat lower for students from advantaged backgrounds (28th) than for those from disadvantaged ones (20th).

Some states — notably Massachusetts — compare well to OECD students, but they represent a small share of the U.S. population.

In Korea, 46 percent of the children of high school dropouts reach proficiency in math compared to 17 percent of U.S. children with poorly educated parents.

The U.S. ranks 30th in teaching the children of “moderately” educated parents. “The math proficiency rate (26%) for this group is again around half the rate enjoyed by Switzerland (57%), Korea (56%), Germany (52%), and the Netherlands (50%).”

Forty-three percent of U.S. children with college-educated parents are proficient in math. That’s lower than the rate for Koreans whose parents didn’t finish high school. “Countries with high proficiency rates among students from better-educated families include Korea (73%), Poland (71%), Japan (68%), Switzerland (65%), Germany (64%) and Canada (57%).”

“The U.S. education system is . . . weak at the bottom, no less weak at the middle, and just as weak with respect to educating the most-advantaged,” the analysis concludes. Or, as Education Secretary Arne Duncan said, our educational shortcomings are “not just the problems of other person’s children.”

A new path to college math

A Los Angeles-area community college is trying the Carnegie Foundation’s alternative path to math success, an algebra-and-statistics mix called Statway. Success rates for remedial students — normally very low — are rising.

A Denver university is taking back remedial education from community colleges in hopes of boosting success rates.

NAEP: 26% of 12th graders are proficient in math

The latest Nation’s Report Card shows 12th graders haven’t improved in math and reading since 2009. Only 26 percent score as proficient in math and 37 percent in reading. Furthermore, “despite more than a decade of federal policies meant to close achievement gaps, the margin between white and Latino students in reading remains just as large as it was 15 years ago, and the margin between black and white students has widened over time,” reports the Washington Post. White students haven’t improved;  black students’ average reading scores have fallen.

Percentage of students at or above the Proficient level in 2013

A pie chart shows the overall percentage of students at or above the Proficient level in mathematics in 2013 was 26.A pie chart shows the overall percentage of students at or above the Proficient level reading in 2013 was 38.

Fourth and eighth graders are improving — slowly but steadily — on NAEP, but those gains disappear by the end of high school. Rising graduation rates may play a role by keeping weaker students in the testing pool.

Latinos are improving in math, noted Education Trust. So are Asian/Pacific Islanders, who already were far ahead of the norm.

If not for “modest” improvement by the weakest students, scores would have gone down, writes Jill Barshay on Washington Monthly‘s College Guide.

AP for average students

A Pittsburgh high school is “spreading the AP gospel” to average students, not just the high achievers, reports the New York Times. Brashear High, a school with “middling” performance, is collaborating with the National Math and Science Initiative, to get more students to take AP classes — and pass AP exams.

Brashear has offered A.P. classes in biology, chemistry, physics, computer science, calculus and statistics, but few among the school’s 1,400 students excelled. Last year, of the 159 enrolled in those classes, nearly two-thirds did not even take the tests, which normally cost $89 each. (Because of subsidies by NMSI and the school, the fee this year is as low as $9.)

Just 10 students accounted for the 13 passing scores of 3 or higher. No Brashear student has passed the chemistry exam since 2010, or scored higher than 1 in statistics in the two years that course has been taught.

NMSI uses teacher training, student study sessions and cash incentives to raise test-taking and pass rates.

In the first year of NMSI’s help, the number of passing scores on science and math A.P. exams jumps by an average of 85 percent, according to data from the College Board, which administers the A.P. tests. By the end of the three-year effort, the number has nearly tripled, on average.

Students get $100 for a passing score of 3 or better on the AP exam. The teacher also gets $100 — plus a $1,000 bonus for reaching a target number of passing scores.

Many Brashear students are struggling in rigorous AP classes this year, reports the Times. However, Principal Kimberly Safran has turned down most requests to drop AP. “Parents are beginning to understand that the rigor of the course and having the tenacity to complete the course are important for success after high school,” she said.

Advocates say students don’t have to pass the AP exam to benefit from the challenge.

“We think 20 out of 40 passing physics is better than 10 out of 10,” NMSI’s Gregg Fleisher said. “What typically happens is our pass rate usually stays the same, but the kids that were in class that were passing at 30 percent, now they’ll pass at 50 or 60 percent. And the kids who were never given an opportunity would pass at 20 or 30 percent.”

Core opens door to ‘garbage’ math

You’ve seen the viral “Common Core” math problem and the letter from the engineer father who thought it was idiotic. The “stupid” problem predates the Common Core, says Brookings’ scholar Tom Loveless. But it’s only “half right” to say you can’t blame the Core for this. The new standards are  opening the door to “garbage math,” says Loveless.

One of the Core’s messages is: “Kids need to be doing this kind of deeper learning, deeper thinking, higher-order thinking in mathematics,” says Loveless. This is a blast from the past.

“It gives local educators license to adopt a lot of this garbage, this really bad curriculum . . . under the shield of the Common Core,” says Loveless. “And that particular problem is just a terrible math problem and should not be given to kids.”

Phrases such as “mathematical reasoning” are like “a dog whistle to a certain way of approaching mathematics that has never worked in the past,” says Loveless. It’s been tried in the 1960s and again in the 1990s and “failed both times.”

The right answer does matter

Math Curmudgeon is listing “things we need you to stop saying.” Number 1: “The right answer isn’t important. It’s knowing what you’re doing.” The right answer is the whole point of doing the problem … has always been, is now, and will always be, the Curmudgeon argues.  The “knowing what you are doing part” leads to the right answer. If it doesn’t, then you don’t know what you are doing.

What we should be saying is “The right answer is vitally important … so important that we also want students to explain the method and how we all know the answer is correct; they must be able to detect an error if it occurs and describe how to fix it so that the solution IS correct.”

“You can’t detect errors unless you know the right answer, or at least have a sense of what that right answer should be,” the Curmudgeon writes.

Success paths for all

How can high schools ensure graduates are college- and career-ready, asks an Education Next forum.

Students need multiple pathways, writes Robert Schwartz, a Harvard professor emeritus who coleads the Pathways to Prosperity Network. “We have allowed a very important idea—that all students need a solid foundation of core academic knowledge and skills—to morph into a not-so-good idea: that all students need to be prepared to attend a four-year college,” he writes.

If we follow a cohort of 8th graders, roughly 2 in 10 will drop out before high school graduation, and another 3 will graduate high school but choose not to enroll in postsecondary education. Of those who do go on and enroll in four-year institutions, nearly 4 in 10 will drop out before attaining a degree. Of those who enroll in community colleges, roughly 7 in 10 will drop out. The bottom line: by age 25, only 33 percent of the cohort will have attained a four-year degree, and another 10 percent will have earned a two-year degree.

Many good jobs require some education beyond high school but not a four-year degree, Schwartz writes. He likes the northern European model: “All students pursue a common curriculum up through grade 9 or 10, and then choose between an academics-only pathway leading to university and a more applied-learning pathway leading to a vocational qualification.”

Instead of letting students choose their path, we “force march all students” through a math sequence leading to calculus, a goal few will achieve and even fewer will need, he writes.

Yet most community college students and many university students aren’t prepared for college algebra. “In my view, the vast majority of students in two- and four-year institutions would be much better served by getting a solid grounding in data, statistics, and probability in high school,” he writes.

Common foundational skills are essential, writes Cynthia G. Brown, senior fellow at the Center for American Progress. All students should take a college-prep curriculum, but high school students could choose “curricular options that fit their interests, skills, and plans for the future.”

Remedial math leads nowhere

More than two thirds of community college students take at least one remedial education course, usually math. Seventy percent of those placed into remedial math will not even attempt a college-level gateway course within two years.

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.

Screen_shot_2014-04-17_at_5

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

Screen_shot_2014-04-17_at_5

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.

Beyond the buzzwords

Ben always dreaded being asked for his “teaching philosophy,” he writes at Math with Bad Drawings. It seems to come out as:  “We buzzword to buzzword, not for the buzzword, but for the buzzword.”

Now he’s got it in 11 words:  Math is big ideas, approached from as many angles as possible.

For example, here’s a big idea:

5

He teaches from the historical, verbal and scientific angles. Then comes practice.

Math without any computational practice is a mushy math, a math with no spine. To understand what makes, say, linear equations tick, you’ve got to solve ‘em, graph ‘em, play with ‘em in a hundred different ways. You can’t grasp patterns until you’ve worked through examples. Without multiplication facts at your fingertips, you’re unlikely ever to apprehend deep truths about the distributive property. If you’ve never spent a day multiplying out products of the form (ax + b)(cx + d), then you’ll never internalize the methods for factoring quadratics.

13