The Algebra Column Andrew Hacker Should Have Written

Yesterday I rambled on about various philosophical problems with Andrew Hacker’s column on not needing algebra, but today I’ve managed to boil down my general frustrations to a single point: Hacker astutely identifies a serious problem and then goes on to propose a ludicrous solution.

Hacker bases his case on the fact that some kids who are capable of contributing to society are shut out of the mechanism through which that can happen — college — because they can’t do algebra. Clearly this is a problem worth solving. Not getting a diploma is a terrible outcome that has a host of negative externalities relating to things like crime and the straining of the social safety net. Hacker’s mistake is that his solution of not requiring kids to learn algebra is killing a fly with a sledgehammer.

If the goal is to help kids who are bad at algebra, there are countless thing we can do that are better than uprooting our current system of standards. For example, why not work to create a legitimate credentialing system for kids who can’t do math? There’s a “Harvard” of everything these days, why can’t there be a “Harvard of people who are bad at math.” If Hacker thinks these kids need to be in the “normal” higher education system, then he should advocate for a rigorous high school aptitude test that doesn’t include math. I’m confident that if students were getting high scores on a math-less, SAT-ish test that had difficult English and humanities sections, colleges would take a look a them. Finally, if Hacker is worried about these kids getting high school diplomas, he should advocate for special no-math graduation tracks for students who demonstrate ability and dedication in other areas. All of these solutions are more feasible and more productive than arguing that our education system should be less focused on STEM.

Hacker’s motivation is noble — he wants the kids who don’t do algebra to be part of the same system as everybody else. But more inclusion isn’t always the answer. Hacker and the kids he’s concerned about will ultimately be better off if he focuses on an attainable, victimless solution, even if it means making some kids part of a separate system.


Not Believing in Stereotypes Can Make You More Creative

If you were a middle-class kid from the suburbs, you’re familiar with the day in elementary school when a community theater group comes in to teach you about the evils of stereotypes (through the magic of the stage!). The lesson was an important one, but a new study suggests that the reason why may be different from what you think. According to two researchers from the University of Kent, when a stereotype is disconfirmed (e.g. female mechanic), it can lead to more flexible thinking and more creativity.

We expected that because exposure to people who disconfirm stereotypes compels students to think “out of the box”, they will subsequently not only rely less on stereotypes, but in more general thinking rely less on easily accessible knowledge structures and be more flexible and creative. As predicted, being encouraged to think counter-stereotypically not only decreased stereotyping, but also, on a divergent creativity task, lead to the generation of more creative ideas – but only for individuals who initially reported a lower Personal Need for Structure.

The finding is fairly intuitive. If you think 30% of old Italian men are mobsters rather than 90%, your brain is going to have to do more creative thinking to create a profile of those 60%.

One another note, one reason I’m optimistic about the future of psychology is that I think we’ll eventually know enough to routinely find these “kill two birds with one stone” situations. Some of them already exist — for example, manipulating lay theories and regulatory orientations can have a variety of positive effects — and as psychologists improve their grasp of the higher-level processes that drive our thoughts and decisions I think we’ll learn about many more. When you figure out how to approach situation with the right outlook, mindset, and thought process, you’ll do better at whatever occurs in that situation.
Goclowski, M.A., & Crisp, R.J. (2012). On counter-stereotypes and creative cognition: When interventions for reducing prejudice can boost divergent thinking Thinking Skills and Creativity DOI: 10.1016/j.tsc.2012.07.001

Is it Worth Sacrificing Algebra to Help the Weakest Students?

There are a number of odd arguments about the importance of math in Andrew Hacker’s NYT Op-Ed, “Is Algebra Necessary?” (John Patty does a nice job running through them), but the section on how math affects attainment was particularly frustrating because Hacker exaggerates the scope of the problem in order to make his solution less controversial. In doing so, he dances around some important issues that get to the heart of what he’s trying to say. Here’s Hacker on the issue of high school dropouts:

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia

Hacker clearly wants to make it possible for more students to get high school diplomas, but at the moment society has intentionally constructed diplomas to signal a certain amount of math skill. This makes the algebra requirement helpful for those who can pass it. When you lower the standards needed to graduate you harm the students capable of reaching the higher standards.

Furthermore, colleges and employers need to know that somebody with a diploma can do a certain level of math. In that sense it’s not a bug that 33% of Oklahoma kids failed to pass, it’s a feature. And given all the anecdotal evidence that there’s a shortage of skilled workers in the country, I’m not sure many would agree that our current level of required math knowledge is above the socially optimal level.

Hacker’s response would be to say “screw society and the high achievers, I’m trying to help the kids who really need help.” That’s a legitimate goal to have, but I wish Hacker would come right out and say that rather disguise it in the dubious notion that eliminating algebra will help everybody. The fact is, the vast majority of students are intelligent enough to pass high school algebra. A significantly lower number actually do so because they attend failing schools, live in deteriorating neighborhoods, or lack interest in educational achievement, but none of these dropouts can be blamed on math. Hacker’s proposal won’t help everybody — think of the kid who falls in love with engineering in college but now lacks a sufficient math background — but he’s right to assume it will help those least likely to graduate from high school.

One of my policy fantasies is to get education reformers in a room and have them hold a debate about Christopher Jencks’ 1988 Ethics article on what makes a fair or equitable distribution of educational resources. In the article Jencks weighs a number of different types of fairness: focusing an equal amount of attention on every student, focusing more on students who achieve the most, focusing more on students who try the hardest, or focusing more on students who are the most disadvantaged. Hacker clearly seems to be advocating for the final option. He can dance around the issue all he likes, but the bottom line is that he’s proposing a radical reorganization of educational standards in order to benefit the very lowest achievers — those whose aspirations are most likely to be stymied because they are incapable of passing high school algebra. That’s a legitimate argument to make, and I wish Hacker would actually put himself out there and make it instead of concocting a story about how lower math standards will help everybody.

What Makes a Political Campaign Important?

Alec MacGillis is the latest journalist to take up the great cause of our time: Putting an end to the media’s practice of printing whatever lies and half-truths are uttered by political campaigns. Most recently, MacGillis excorciated Aaron Blake of the Washington Post for saying some of the Romney campaign’s blatantly false attacks inhabit an area that’s too gray for them to be called lies.

Ah yes. If only there was someone whose job and calling it was to ferret out the truth of such things, to provide some context for voters. Let me think, there must be someone we can think of, a profession of some kind perhaps, sort of like a researcher but also a communicator…

Ultimately, I think the way you see the issue comes down to whether you believe a campaign is worthy of coverage because it’s important in its own right, or whether a campaign is only important in that it’s a lens through which we learn truths about policy, future leadership, and other things that are objectively important. The former view sees a campaigns like the Oscars — anything that anybody does, says, or wears is important because we’ve decided it’s important. The latter view, which is the view MacGillis holds, sees the campaign like a meeting of the Federal Reserve Board — everything is trivial except what we learn about the state of the world and the future of domestic economic policy.

Twenty years ago, before each campaign needed to produce new talking points every 24 hours, these two views were functionally somewhat similar. Covering the campaign involved detailed reporting on actual candidate positions and what their campaigns meant for future policy. There weren’t spare resources to waste on analyzing attack ads. But in the last few years cable news and the professionalization of political communications has been a boon for campaign coverage. Now a seemingly original piece of news or analysis can be written every day.

The problem is that most of these pieces only have value if you adhere to the first view that anything campaign related is important. Although much of the Washington press corps shares that view, 99% of the country does not. Most voters don’t care what tactics candidates are using. They just want to know what the president intends to do.

This why I think MacGillis’ view is 100% right, and those who disagree tend to be engaged in some cognitive dissonance gymnastics in order to avoid realizing that most of their work has no value. The problem for MacGillis is that his drive to change the way of doing things can only be successful if the media’s goal is to educate the public about what they need to know, not to make money or validate the self-importance of beltway pundits. As I’ve written before, I think this assumption is unlikely to be true, and thus MacGillis’ efforts are ultimately doomed, at least with regard to the current election cycle.

Can Viewing Art Literally Move You?

The subjective nature of art makes it an odd fit for something as computational as cognitive psychology, but a new study at the nexus of those two subjects suggests something surprising about the way we respond to certain paintings. Through a series of five experiments researchers from Purdue and Colorado State believe they have found the first evidence that  looking at a painting can unconsciously lead people to simulate the actions of the painter.

Participants in the study were shown a series of paintings that appeared to have been made with gestural brushstrokes that moved to the left or to the right. After initially placing their finger on a center button, participants were asked to press a button on the right or left based on the painting’s color (experiment 1) or an unrelated symbol superimposed on the painting (experiment 2). The researchers found that it took less time for participants to move their finger when they were moving it in the same direction as the painting’s brushstrokes. After ruling out certain visual factors that could account for the difference in times, the researchers concluded that participants were faster when moving in the direction of the brushstrokes because they were already unconsciously simulating the actions of the painter.

The researchers went on to speculate about what it means for understanding how we experience art:

Observers automatically simulated the actions implied by a painting’s brushstrokes, revealing a connection between the artist and audience never before demonstrated by cognitive science. This result confirms the action painters’ anecdotal insight that action is expressed through painting. It is remarkable because it implies a new aspect of the cognitive processing of abstract, gestural art. These processes can no longer be limited to strictly visual patterns on the canvas; instead, we have shown that an artist can resonate with her audience via her action. Consequently, attempts to understand the cognitive processing of gestural art should include the science of action observation.

The interesting follow-up question is why our brains behave this way. I think one possible explanation is that it’s part of a deep-rooted and unconscious learning mechanism. When we see something that’s been made, we unconsciously mimic the actions we believe were taken to make it. That way if a situation should arise in which we want to reproduce what was previously observed, our procedural memory contains a stronger trace of whatever movements were used to create it.

Alternatively, one could take the study to mean that there really is a tiny artist inside all of us who’s screaming to be let out. But whatever you do, don’t let him out. He knows too much and can’t be trusted.
Taylor, J.E.T., Witt, J.K., & Grimaldi, P.J. (2012). Uncovering the connection between artist and audience: Viewing painted brushstrokes evokes corresponding action representations in the observer Cognition DOI: 10.1016/j.cognition.2012.06.012

Why Do We Need Research On Merit Pay?

A new Roland Fryer study on loss aversion and merit pay has been creating quite a stir. Essentially, the study found that when teachers are given a sum of money but told they will be asked to give it back if their students don’t hit certain benchmarks, student achievement rises. The study managed to give Diane Ravitch a conniption and induce a scathing anti-science rant (her second of the season!)

The thing I’ve never understood is why merit pay proponents are so desperate to link it to short-term test score gains. Obviously the type of evaluation is key, but haven’t the last 100 years of business and government management demonstrated that in the long-run when the best employees get paid more money institutions tend to be healthier, more stable, and capable of attracting and keeping higher quality people? Why is paying more money to people who get better results something that needs research? Is it not an accepted best-practice? Would not paying for performance fly in any other business, non-profit, or government? (Warning: This post might break my rhetorical question record.)

The bulk of the arguments against merit pay tend be absurd conceptual leaps that begin with research on motivation and make heavy use of the fact that teachers are “different” from anybody who’s ever held a job throughout the course of human history. Here’s an idea. If paying the best teachers more is a bad idea, why don’t we pay the worst teachers more? What’s that? You say it’s unwise to reward bad teachers? Here’s the thing. Logically speaking, rewarding a bad teacher by paying them more than a good teacher isn’t that different from rewarding a bad teacher by paying them the same as a good teacher. Either way, You’re paying them more than you should.

The fact that there is even a debate about merit pay shows the enormous power of teacher’s unions to call into question anything that involves an objective evaluation of teacher performance. After all, if a merit pay system is allowed to identify good teachers, it follows that it will also be able to identify bad teachers, and if bad teachers can be identified, bad teachers can be fired, and if bad teachers can be fired, a below average teacher who is mistakenly identified as a bad teacher could be fired, and if a below average teacher can be fired then ?????, and if ?????, then our education system will crumble to the ground. Or something like that.

Kids Who Sleep Later Do Better In School

The ideological battle over our education system has transformed the banal adage of prioritizing the needs of students into a politics-infused idea dripping with anti-union sentiment. This is a shame, because there are many archaic and less-controversial aspects of our education system which carelessly disregard the needs of students. For example, evidence is building that we harm kids by making them wake up unreasonably early.

This paper uses data on all middle school students in Wake County, NC from 1999-2006 to identify the causal effect of daily start times on academic performance. Using variation in start times within schools over time, the effect is a two percentile point gain in math test scores – roughly fourteen percent of the black-white test score gap. I find similar results for reading scores and using variation in start times across schools. The effect is stronger for students in the lower end of the distribution of test scores. I find evidence supporting increased sleep as a mechanism through which start times affect test scores. Later start times compare favorably on cost grounds to other education interventions which result in similar test score gains.

The argument for starting the school day so early is that it allows parents to see their kids off. But the result is that some kids are too tired to learn, while others end up being left alone for a few hours once school ends. It’s arguably more important that parents be there in the morning so they can ensure their kids actually go to school, but given the downsides of this arrangement it seems odd that society isn’t trying harder to create a better system.

Believe it or not, there are reasons to not have every school run by the same bureaucracy that have nothing to do with lazy teachers or thieving businessman, and this is one of them. Ideally, at some point in the future there will be a real system of school choice, and this will allow parents to maximize the utility derived from their child’s sleep and schedule compatibility rather than be forced to follow the limited options offered by the local school system.

It’s also worth noting that the study is another instance of the lowest achievers making the biggest progress when the status quo changes. I made this point the other day, but sometimes the biggest reason kids struggle is not because they’re dumb or lazy, but because for whatever reason the design of the school day isn’t working for them. The result is that big improvements from low-achievers is something we should come to expect when a school undergoes real change.
Edwards, F. (2012). Early to Rise? The Effect of Daily Start Times on Academic Performance Economics of Education Review DOI: 10.1016/j.econedurev.2012.07.006