U.S. Math Education Still in the Doldrums

(Photo: arjin j)

(Photo: arjin j)

Every three years, the OECD, in the PISA assessment, studies 15-year-olds around the world to measure performance in reading, mathematics, and science. The results of the 2012 PISA assessment, which had a particular focus on mathematics, just came out and the United States does not fare well: “Among the 34 OECD countries, the United States performed below average in mathematics in 2012 and is ranked 26th.” I worry not so much about the rank, but about the low absolute level of proficiency to get this rank.

The U.S. students’ particular strengths and weaknesses are even more distressing:

Students in the United States have particular strengths in cognitively less-demanding mathematical skills and abilities, such as extracting single values from diagrams or handling well-structured formulae. They have particular weaknesses in items with higher cognitive demands, such as taking real-world situations, translating them into mathematical terms, and interpreting mathematical aspects in real-world problems.

Thirty-five years ago, the situation was similar. A large study of 13- and 17-year-old students across the United States, the second National Assessment of Education Progress (1977-1978), concluded: “Students appear to be learning many mathematical skills at a rote manipulation level and do not understand the concepts underlying the computation” [Carpenter, et al., Mathematics Teacher 73:329-338 (1980)]. One example was the question: “Estimate the answer to 12/13 + 7/8.” The choices were 1, 2, 19, 21, and “I don’t know.” Among 13-year-olds, 14 percent chose “I don’t know,” and only 24 percent chose 2. Among 17-year-olds, 16 percent chose “I don’t know,” and only 37 percent chose 2. The correct percentages are not much higher than the monkey line.

A frequent explanation for the U.S.’s poor PISA results is poverty — for example, by Daniel Wydo or (after the similar 2009 PISA results) by Stephen Krashen. That explanation is based on comparing wealthy U.S. schools (where fewer than 10 percent of students get free or reduce-price lunches) against the average score in countries with less poverty, such as Finland. The logic is superficially plausible, because Finland has only a few percent of students in poverty.

However, comparing wealthy students to averages of a country is a stacked comparison. The same authors who argue for the poverty explanation concede this point in other arguments, saying that it is unfair to let Shanghai’s PISA scores represent all of China, given that most of China is less wealthy than Shanghai. A fairer comparison is to compare comparable segments of the population.

That is what PISA did in its analysis of the effects of poverty. For example, see Figure II.2.6 (“Mean mathematics performance, by national quarter of socio-economic status”) on page 43 of Volume II of the PISA results (here is the data as a spreadsheet). Each country was divided into quartiles by socioeconomic status (SES), the average mathematics score computed by quartile, and then ranks computed for the top and bottom quartiles. The comparison is of top quartiles against each other, or of bottom quartiles against each other, rather than top quartiles against averages.

If poverty explained the U.S.’s poor performance, with scores of the bottom quartile dragging down and obscuring the alleged great performance of the U.S. top quartile, then the U.S. top quartile should do well internationally. However, when compared against the top quartiles in other countries, the U.S. rank drops from 26th to 32nd. Similarly, U.S. students with a SES at the OECD average do slightly worse than the U.S. average (Figure II.2.5 of the same report).

As a final example, look at the Finland and U.S. by-quartile comparison. In Finland, the bottom quartile has a SES of -0.68 (0.00 is the OECD average), and an average PISA math score of 488 (500 is the OECD average). In the United States, the second-highest quartile has an SES of 0.60 — they are much better off than the worst-off Finns — but almost the same average score, 494. Even though Finland has poor students, they do reasonably well.

In short, the “it’s poverty” explanation is not convincing. The usual U.S. math curriculum is simply weak, even in well-off schools. After decades of reform in the mathematics curriculum, students in the United States are still unprepared for full participation in society.


Gordon Brooks

As a parent, I am dismayed at what my 5th- and 7th-graders are being taught. They are presented with so many alternative ways of performing the same calculation that they never have a chance to master best practices. This is not to say that some students might not benefit by having different ways to approach a problem. But requiring every student to learn every possible method to pass their tests just leads to confusion.

School administrations seem more interested in being up on the latest theories than in teaching students mastery of the subject at hand.

In addition, schools keep cutting back on physical activity (though my 7th-grader's school is wising up on this) and music education; the former aids concentration, and the latter refines mathematical thinking. My teachers and their bosses knew this many decades ago, but we seem bent on forgetting lessons of the past to embrace what we perceive as progress.

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Dan R

Interesting Fact #1: In Finland, it is illegal to enroll a child in school before the age of 7. Kinda blows the concepts behind preschool and "Head Start" out of the water.

Interesting Fact #2: Utah is similar to Finland in terms of ethnic homogeneity and socio-economic homogeneity (and annual snowfall). Utah schools are not noticeably better than other US states, which argues against those factors as being the differentiators for the Finland/US education gap.

Brian

The real problem is parents. Can't discipline rich kids or you will get fired. Can't discipline in the impoverished areas because you could get killed. Can't discipline the average students since you have to alter your discipline policy for the haves and have-nots. That translates into a lot of kids that cannot be motivated to learn, either by force or through trying to show these coddled, disrespectful kids what being educated means for them and the world.

But do not make the mistake that they are not learning. They are just learning what they want, not what schools are supposed to teach. Until parents are taken out of the schools, and education is left to the ones who have dedicated their lives to instruction and learning, then there will be lower expectations for kids behavior. No matter what you teach or how you teach it, the behavior and self-discipline needs to be instilled in the learner first...and teachers and administrators have had their hands tied in this area.

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Lori Patton

One of the reasons I enjoyed Freakonomics was the ability of the authors to look beyond the obvious. Poverty does not always portray the same cultural markers between countries. I've been a high school counselor for 20 years. Poor students who live in a culture that values education tend to do much better that poor students who live in a culture that does not value education. Absenteeism is the biggest problem we face in inner-city Indianapolis schools. Research shows a direct link between income and level of education in the US. We have a chicken/egg problem in that low income and low academic performance seem generationally linked here. Likewise other cultural characteristic of low-income, inner-city families both black and white tend to add to poor academic performance e.g. high mobility; unstable family structure; children being shuffled between relatives; exposure to violence, drugs and prostitution; lack of supervision (allowing students to skip school and not do homework), and a culture of welfare. When trying to convince a student to go to college, I was interrupted when she asked, "why should I do that when my mom and aunt each make $1500 a month on welfare?' There are so very many other factors involved in poverty that create poor school performance in the US that unless the cultures of poverty are compared, simply comparing SES between countries doesn't explain a thing.

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SAO

I get annoyed when people want to exclude the poor from any metric of American achievement, as if they don't matter. All that matters is the middle class kid (ie our kids) are doing well and going to be successful. But, by ignoring the poor, they get condemned to lousy schools and a vicious circle of poverty.

Yet, most comfortably well-off Americans are middle class because our immigrant forefathers were well educated in good public schools. My father's parents were immigrants who found jobs as a school lunch lady and a chauffeur. My husband's parents were immigrants who came to the US with nothing but the memory of not enough to eat.

The engine of American growth is education. Every child counts.