If the title of this blog struck you as brash, I came by it honestly: it's the title of a terrific new paper by three NYU researchers (Protzko, Aronson & Blair, 2013). The authors sought to review all interventions meant to boost intelligence, and they cast a wide net, seeking any intervention for typically-developing children from birth to kindergarten age that used a standard IQ test as the outcome measure, and that was evaluated in a random control trial (RCT) experiment.

A feature of the paper I especially like is that none of the authors publish in the exact areas they review. Blair mostly studies self-regulation, and Aronson, gaps due to race, ethnicity or gender. (Protzko is a graduate student studying with Aronson.) So the paper is written by people with a lot of expertise, but who don't begin their review with a position they are trying to defend. They don't much care which way the data come out.

So what did they find? The paper is well worth reading in its entirety--they review a lot in just 15 pages--but there are four marquee findings.

First, the authors conclude that infant formula supplemented with long chain polyunsaturated fatty acids boosts intelligence by about 3.5 points, compared to formula without. They conclude that the same boost is observed if pregnant mothers receive the supplement. There are not sufficient data to conclude that other supplements--riboflavin, thiamine, niacin, zinc, and B-complex vitamins--have much impact, although the authors suggest (with extreme caution) that B-complex vitamins may prove helpful.

Second, interactive reading with a child raises IQ by about 6 points. The interactive aspect is key; interventions that simply encouraged reading or provided books had little impact. Effective interventions provided information about how to read to children: asking open-ended questions, answering questions children posed, following children's interests, and so on.

Third, the authors report that sending a child to preschool raises his or her IQ by a little more than 4 points. Preschools that include a specific language development component raise IQ scores by more than 7 points. There were not enough studies to differentiate what made some preschools more effective than others.

Fourth, the authors report on interventions that they describe as "intensive," meaning they involved more than preschool alone. The researchers sought to significantly alter the child's environment to make it more educationally enriching. All of these studies involved low-SES children (following the well-established finding that low-SES kids have lower IQs than their better-off counterparts due to differences in opportunity. I review that literature here.)  Such interventions led to a 4 point IQ gain, and a 7 point gain if the intervention included a center-based component. The authors note the interventions have too many features to enable them to pinpoint the cause, but they suggest that the data are consistent with the hypothesis that the cognitive complexity of the environment may be critical. They were able to confidently conclude (to their and my surprise) that earlier interventions helped no more than those starting later.

Those are the four interventions with the best track record. (Some others fared less well. Training working memory in young children "has yielded disappointing results." )

The data are mostly unsurprising, but I still find the article a valuable contribution. A reliable, easy-to-undertand review on an important topic.

Even better, this looks like the beginning of what the authors hope will be a longer-term effort they are calling the Database on Raising Intelligence--a compendium of RCTs based on interventions meant to boost IQ. That may not be everything we need to know about how to raise kids, but it's a darn important piece, and such a Database will be a welcome tool.

When I first saw yesterday's New York Times op-ed, I mistook it for a joke. The title, "Is algebra necessary?" had the ring of Thurber's classic essay "Is sex necessary?" a send-up of psychological sex manuals of the 1920s. 

Unfortunately, the author, Andrew Hacker, poses the question in earnest, and draws the conclusion that algebra should not be required of all students.

His arguments:

• A lot of students find math really hard, and that prompts them to give up on school altogether. Think of what these otherwise terrific students might have achieved if math hadn't chased them away from school.
• The math that's taught in school doesn't relate well to the mathematical reasoning people need outside of school.

His proposed solution is the teaching of quantitative skills that students can use, rather than a bunch of abstract formulas, and a better understanding of "where numbers actually come from and what they actually convey," e.g., how the consumer price index is calculated.

For most careers, Hacker believes that specialized training in the math necessary for that particular job will do the trick.

What's wrong with this vision?

The inability to cope with math is not the main reason that students drop out of high school. Yes, a low grade in math predicts dropping out, but no more so than a low grade in English. Furthermore, behavioral factors like motivation, self-regulation, social control (Casillas, Robbins, Allen & Kuo, 2012), as well as a feeling of connectedness and engagement at school (Archambault et al, 2009) are as important as GPA to dropout. So it's misleading to depict math as the chief villain in America's high dropout rate.

What of the other argument, that formal math mostly doesn't apply outside of the classroom anyway?

The difficulty students have in applying math to everyday problems they encounter is not particular to math. Transfer is hard. New learning tends to cling to the examples used to explain the concept. That's as true of literary forms, scientific method, and techniques of historical analysis as it is of mathematical formulas.

The problem is that if you try to meet this challenge by teaching the specific skills that people need, you had better be confident that you're going to cover all those skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won't transfer.

The best bet for knowledge that can apply to new situations is an abstract understanding--seeing that  apparently different problems have a similar underlying structure. And the best bet for students to gain this abstract understanding is to teach it explicitly. (For a discussion of this point as it applies to math education in particular, see Anderson, Reder, & Simon, 1996).

But the explicit teaching of abstractions is not enough. You also need practice in putting the abstractions into concrete situations.

Hacker overlooks the need for practice, even for the everyday math he wants students to know. One of the important side benefits of higher math is that it makes you proficient at the other math that you had learned earlier, because those topics are embedded in the new stuff. (e.g., Bahrick & Hall, 1991).

So I think there are excellent reasons to doubt that Hacker's solution to the transfer problem will work out as he expects.

What of the contention that math doesn't do most people much good anyway?

Economic data directly contradict that suggestion. Economists have shown that cognitive skills--especially math and science--are robust predictors of individual income, of a country's economic growth, and of the distribution of income within a country (e.g. Hanushek & Kimko, 2000; Hanushek & Woessmann, 2008).

Why would cognitive skills (as measured by international benchmark tests) be a predictor of economic growth? Economic productivity does not spring solely from the creativity of engineers and inventors. The well-educated worker is more likely to (1) see the potential for applying an innovation in a new context; (2) understand the explanation for applying an innovation that someone else has spotted.

In other words, Hacker overlooks the possibility that the mathematics learned in school, even if seldom applied directly, makes students better able to learn new quantitative skills. The on-the-job training in mathematics that Hacker envisions will go a whole lot better with an employee who gained a solid footing in math in school.

Finally, there is the question of income distribution; countries with a better educated populace show smaller income disparity, and suggesting that not everyone needs to math raises the question of who will learn it. Who will learn higher math in Hacker's ideal world? He's not clear on this point. He says he's against tracking, but notes that MIT and Cal Tech clearly need their students to be proficient in math. Does this mean that everyone gets the same vocational-type math education, and some of those going on to college will get access to higher math?

If that were actually implemented, how long before private vendors offer after school courses in formal mathematics, to give kids an edge for entrance to MIT? Private courses that cost, and to which the poor will not have access.

There are not many people who are satisfied with the mathematical competence of the average US student. We need to do better. Promising ideas include devoting more time to mathematics in early grades, more exposure to premathematical concepts in preschool, and perhaps specialized math instructors beginning in earlier grades.

Hacker's suggestions sound like surrender.

Anderson,  J.  R., Reder, L. M., & Simon, H. A. (1996). Situated learning and  education.  Educational  Researcher,  25,  5-11

Archambault, I., Janosz, M, Fallu, J.-S., & Pagani, L. S. (2009). Student engagement and its relationship with early high school dropout. Journal of Adolescence, 32, 651-670.

Bahrick, H. P. & Hall, L. K. (1991). Lifetime maintenance of high school mathematics content. Journal of Experimental Psychology: General, 120, 20-33.

Hanushek, E. A. & Kimko D. D. (2000). Schooling, labor-force quality, and the growth of nations. The American Economic Review, 90, 1184-1208.

Hanushek, E. A. & Woessmann, (2008). The role of cognitive skills in economic development. Journal of Economic Literature. 46, 607-668.