The Problem With Math Is That It Makes People Seem Smart

In 1996 physicist Alan Sokal succeeded in getting a unique article published in the journal Social Text. The article was titled “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity,” and it was unique because it was complete gibberish. Known as the Sokal Hoax, it was a crowning moment for pretense-haters everywhere.

While journal editors have managed to avoid similar public shamings of late, a Swedish researcher named Kimmo Eriksson decided to investigate whether academics are in fact impressed by things they don’t understand, even if those things are nonsense. Specifically, Eriksson wanted to see how people with research experience judged abstracts containing a nonsense math equation (pdf):

Participants were presented with the abstracts from two published papers (one in evolutionary anthropology and one in sociology). Based on these abstracts, participants were asked to judge the quality of the research. Either one or the other of the two abstracts was manipulated through the inclusion of an extra sentence taken from a completely unrelated paper and presenting an equation that made no sense in the context. The abstract that included the meaningless mathematics tended to be judged of higher quality. However, this “nonsense math effect” was not found among participants with degrees in mathematics, science, technology or medicine.

Obviously it’s distressing to see research-savvy people base their judgments on nonsense, but beyond that there are two ways to spin the deeper meaning of the findings. The positive spin is that because math is judged to add quality, people will be motivated to learn and use mathematics. The negative spin is that math improves judgments of quality because it suggests the mastery of a difficult skill that people want no part of. In this case math has been shut out to the point that an equation is strictly a signal rather than something to be understood and evaluated.

The potential to develop this kind of hands-off attitude toward math is one reason it’s important not to let elementary school kids take on a “math is not for me” identity. It’s fine if a kid decides not to become an engineer, but it can be problematic if you’re so uncomfortable with math that you develop faulty heuristics to use when you have to deal with it.
Eriksson, Kimmo (2012). The nonsense math effect Judgment and Decision Making, 7 (6), 746-749

When It Comes to Education Policy, We’re All Young-Earth Creationists

The new CREDO report (pdf) on New Jersey charter schools paints a fairly rosy picture, particularly with regard to Newark, and right on cue the findings have elicited the expected cheerleading from charter proponents and nitpicking from charter critics. It’s an exercise we go through every time a noteworthy report is released, whether it’s an evaluation of the SIG program or a paper on merit pay. Proponents focus on the good things, critics focus on the bad things, and nobody makes much of an effort to re-think their assumption or weigh new evidence.  All that matters is the spin.

It all reminds me of something I once read about preparing to engage in a debate with somebody who is not exactly open to the scientific method (e.g. a hardcore young-earth creationist.) It was advised that before you begin, ask them what hypothetical piece of evidence would cause them to change their mind and admit you are right. If they can’t name anything, turn around and walk away because you’re not about to have an actual debate.

All sides of the education reform debate are getting dangerously close to failing this test. Could Diane Ravitch ever admit that charter schools are benign? What if, relative to district schools, every charter school in New York City enrolled more English language leaners, more special education students, and more students receiving free lunch, and posted better test scores? Even then it’s hard to believe she would change course. Charter proponents are less duplicitous in their efforts to move the goalposts, but it’s hard to imagine them acting any differently. What if ten years from now charters are producing fewer college ready seniors and fewer college graduates? Will Eva Moskowitz and Richard Barth close up shop? Not likely.

This doesn’t make education any different from standard political disputes involving taxation and environmental regulation, but you would expect unquestioned close-mindedness in other policy areas because the disagreements have spanned decades and they tend to be the focus of excruciatingly public re-election battles. The hope was always that education policy could avoid those pitfalls, but that now seems increasingly unlikely.

Doomsday pessimism aside, I do think it would be helpful for figureheads to make public proclamations about what are and are not acceptable outcomes. One reason education reform has become so polarized is that there is a lack of trust. Many traditionalists believe that charters are a vehicle for a nefarious corporate takeover, and therefore no educational outcome, no matter how severely negative, would ever slow charter growth. Similarly, many believe that regardless of charter school performance, unions will forever oppose them because charters are a threat to union power. If somebody like Mayor Bloomberg or Randi Weingarten made a public statement that named some semi-concrete circumstances that would merit future growth, at the very least it would make the conversation marginally more constructive and less spin-tastic.

Separating Rewards Into Meaningless Categories Increases Motivation

There’s an ancient riddle that goes something along the lines of, “What would you do for a Klondike Bar?” While psychologists are still searching for a complete answer, a new study (pdf) by USC’s Scott Wiltermuth and Harvard’s Francesca Gino provides a partial answer: Not as much as you would do for half a Klondike bar and half a chocolate covered ice cream square made by Klondike.

Wiltermuth and Gino were interested in how the way we categorize rewards influences our motivation, and so they designed a series of six experiments that followed the same general pattern. Participants performed a task where their performance was based on motivation — for example, the amount of time spent transcribing a text — and they were rewarded for their performance. A weak effort would earn one reward and a stronger effort would merit two rewards. The rewards were a “mix of stationary and food items” that were plainly visible in two buckets.

The experimental manipulation was that people in the first group were allowed to pick any reward from any of the two identical buckets, while people in the second group had to choose their first reward from bucket #1 and could only gain access to bucket #2 if they earned the second reward. Participants could see the rewards before the experiment began and were aware the buckets held the same items. Nevertheless, the fear of losing out on whatever was in bucket #2 led to the latter group to demonstrate increased motivation.

Across six experiments, people were more motivated to obtain one reward from one category and another reward from another category than they were to obtain two rewards from a pool that included all items from either reward category. As a result, they worked longer when potential rewards for their work were separated into meaningless categories. This categorization effect persisted regardless of whether the rewards were presented using a gain or loss frame. Using both moderation and mediation analyses, we found that categorizing rewards had these positive effects on motivation by increasing the degree to which people felt they would “miss out” if they did not obtain the second reward.

The study has a lot of implications for nudging behavior — for example, motivation might increase if employees who work a certain amount get a bonus that includes cash and stock — but the thing that jumps out to me is how poorly designed the school day is for taking advantage of these motivational tendencies. Think about the types of rewards students can obtain by doing well in school. There’s knowledge itself, a grade that signals proof of knowledge, praise from parents and teachers, and increased educational and professional opportunities. But though students may have a few different types of rewards, they all come from the same actions, and they are the same for every single class. If a student does well in math class, there’s not a different type of reward that can be obtained by doing well in biology.

Now imagine a educational model where students learn six different subjects in six different ways and acquire six different types of knowledge. Perhaps there is an apprenticeship in a chemistry lab where the reward for learning is being able to use complex machinery. Perhaps there in an engineering project where the reward is playing in the treehouse you helped build. Perhaps history is learned through teaching lessons to younger children. Here the reward for learning is passing on knowledge to others. The point is that in a school system where every subject essentially confers the same rewards and is learned the same way it’s impossible for students to reap the full benefits of being motivated by different categories of rewards. Until we break out of the institutionalized school model we’ve been using for the last 100 years we’ll never be able to utilize our full arsenal of motivational tools.
Wiltermuth, S., & Gino, F. (2012). “I’ll Have One of Each”: How Separating Rewards Into (Meaningless) Categories Increases Motivation. Journal of Personality and Social Psychology DOI: 10.1037/a0030835

The Cure For Shopaholics: Go Shopping With a Same-Sex Friend You Don’t Like

One of the great quests of mankind is the search for an acceptable excuse husbands can use to avoid going shopping with their wives. For those with spouses who are particularly deferential to social science research, the quest may finally be over. A new study by a group of Taiwanese researchers suggests that when people go shopping with somebody of the same sex, they’re less likely to make impulsive purchases.

The results of the three studies show that shoppers were more likely to exhibit impulse purchase behavior when shopping with an opposite gender companion. In addition, shoppers who were in the low-cohesive condition and who shopped with an opposite gender companion were more likely to exhibit impulse purchase behavior than those who shopped with the same gender companion, and those who were susceptible to interpersonal influence were also more likely to exhibit impulse purchase behavior when shopping with an opposite gender companion

But not so fast husbands. One explanation for the findings is that more “social distance” exists between people of opposite genders:

When a high degree of social distance exists between two people, they tend to be less dependent on others and less likely to comply with the expectations of others. We posit that the sense of guilt that impulse purchasing generates could be a great barrier when a shopper goes shopping with the same gender companion.

One would think that when it comes to married couples there’s not a lot of social distance, and therefore a husband’s presence might be beneficial for restricting impulse purchases. But not so fast wives:

In Study 2, we used shopping companion gender and group cohesiveness as two independent variables, and the results showed that shoppers, both male and female, who shared a high-cohesive relationship with their companion were more likely to exhibit impulse purchase behavior than shoppers who shared a low-cohesive relationship with their companion.

Couples also a have a high degree of group cohesiveness, and that’s bad for restricting impulse behavior. Perhaps the best conclusion is that husbands should be off the hook, but only if there’s an alternative shopping partner who their wife knows very well, but doesn’t like enough to consider part of her group. (And all of this also applies to husbands with impulse buying problems whose wives want to reduce their spouse’s unnecessary purchases.)

The broader lesson is that who you do things with influences how you do them. If you have a bad habit you want to break, it’s helpful to think about the kind of social environments you create for yourself.
Cheng, Y., Chuang, S., Wang, S., & Kuo, S. (2012). The Effect of Companion’s Gender on Impulsive Purchasing: The Moderating Factor of Cohesiveness and Susceptibility to Interpersonal Influence Journal of Applied Social Psychology DOI: 10.1111/j.1559-1816.2012.00977.x

Is Your Organization’s Commitment to Diversity Harming Minorities?

Society pays so much lip-service to the concept of diversity that it’s surprising some crazy right-wing talking head hasn’t made a big stir by advocating homogeneity in the school and workplace. For many organizations this commitment to diversity involves the creation of “diversity structures” — initiatives such as management trainings, workshops, and diversity statements that are designed to quash any discriminatory practices that might occur.

To MBA-toting VPs, diversity structures may all may seem hunky dory. But to a group of psychologists led by the University of Washington’s Cheryl Kaiser, there’s trouble brewing.

We propose that diversity structures have the potential to create an illusion of fairness, whereby high-status group members’ perceptions of how fairly members of underrepresented groups are treated may be influenced by the presence, not the efficacy, of a diversity structure. This illusion, in turn, impairs high-status group members’ ability to detect discrimination against members of underrepresented groups and causes them to react more harshly toward members of underrepresented groups who claim to experience discrimination.

The reasoning is that the presence of a diversity structure signals fairness and effectively legitimizes the status quo. As a result, evidence of discrimination is more likely to seem misleading, and people who allege discrimination are more likely to appear dishonest.

In a series of six experiments the researchers tested and confirmed their suspicions. In the most common experimental design participants read a company’s diversity statement or its mission statement (the control) and then learned about the company’s hiring or promoting history. Even when it was obvious that racial or sexual discrimination was present in the company’s employment practices, participants who read the diversity statement were significantly more likely to say the company was fair and that the discrimination claims were invalid.  These findings held over four kinds of diversity structures and two types of discrimination.

None of this is to say that diversity structures are inherently a bad thing. In fact, when they’re substantive and lead to more procedural fairness they’re obviously a good thing. However, when diversity structures serve as nothing more than a signal they’re not only useless, they have the potential to cause harm.

The broader point is that when you design a policy to help a certain group of people it’s important that the policy actually help them because people will treat them as though the help is real. If the policy proves to be ineffective, the target group will be worse off than before because others will assume their need for help is now less legitimate.
Kaiser, C., Major, B., Jurcevic, I., Dover, T., Brady, L., & Shapiro, J. (2012). Presumed Fair: Ironic Effects of Organizational Diversity Structures. Journal of Personality and Social Psychology DOI: 10.1037/a0030838

It’s True, Your Shit Doesn’t Stink, And You Can Thank Evolution For It

Fine, your shit probably does objectively stink, but because you know you’re less likely to catch an unfamiliar disease from it, it disgusts you less. Here’s the abstract from a forthcoming paper by Ming Peng, Lei Chang, and Renlai Zhou that supports an evolutionary explanation for the “source effect.”

Known as the source effect, feelings of disgust have been found to differ depending on the source of the disgusting material, with that emanating from oneself and familiar others eliciting less disgust than that of strangers. We tested the source effect on self-report of disgust feelings (Study 1), physiological response in heart rate (Study 2), and behavioral response in terms of approach–avoidance movement (Study 3). The results showed significantly higher levels of disgust feelings, more reduced heart rates, and faster avoidance behavior when processing disgusting material associated with strangers compared to that of familiar persons. Together these findings support the evolutionary view that disgust, as part of the human behavioral immune system to drive avoidance from disease-carrying agents, will likely be activated more intensely and quickly in response to unfamiliar as compared to familiar conspecifics who carry common germs more defendable by our shared physical immunity.

Now you’ll think twice next time you want to make fun of a dog for sniffing another dog’s poop.

NFL Teams Should Play Their 11 Fastest Players on Desperation Plays

Last night the Pittsburgh Steelers faced a situation that often afflicts NFL teams. With 12 seconds remaining they had the ball down by three, on their own 28-yard-line, and possessed no timeouts. Needing a miracle on what was likely to be the last play of the game, they resorted to the standard strategy of throwing a short pass and attempting to score a touchdown through a series of laterals. As invariably happens, the ball eventually ended up in the hands of a slow-footed, stone-handed offensive lineman, effectively ending the game.

So here’s my question: Why do teams play offensive lineman in these situations? Offensive teams are required to line up five players who are not eligible receivers, but there is no requirement that those players weigh 300 pounds. In desperation situations requiring 70+ yards there’s no real need for pass blocking because defenses concede the short pass. So why not put your 11 fastest players on the field? Find some combination of receivers, running backs, and tight ends, line five of them up as lineman, and then let them join the lateraling fun once the pass is thrown. The upside is that every player who might touch the ball is hard to tackle and has good hands. The downside is…well, there is none. Except that you’d have to do things differently than they’ve always been done by every team. I suppose it’s possible that defenses will adjust by rushing the passer and defending short routes more aggressively, but given the increased risk that seems unlikely. I assume that once one team stops playing linemen all the other teams will follow suit, and playing lineman on the final play will disappear faster than straight-ahead kicking.

To make a crazy leap and apply this to public policy, one reason I’m a policy optimist is that when it comes to health care, education, and energy there are bound to be easy improvements we’ve never considered because the old way of doing things is so institutionalized. As technology makes it easier for people’s voices to be heard, I think we’ll begin to uncover theses inefficiencies at a faster rate.