Thursday, February 21, 2008

Hey Girl, You're Really Bad at Math!



Right? Girls are bad at math, aren't they? Former Harvard president Larry Summers seem to think so...

According to Wikipedia,
Stereotype threat is the fear that one's behavior will confirm an existing stereotype of a group with which one identifies. This fear may lead to an impairment of performance.

. . .

Stereotype threat has also been found to apply to sex differences in mathematical achievement. A common stereotype is that men have stronger abilities in mathematics than women. When women believed sex differences could be revealed by a mathematics test, the men performed better. If the test was presented as gender fair, the sexes performed equally well (Spencer, Steele, & Quinn, 1999).
[For more info, see Combating Stereotype Threat in the Wild].

ResearchBlogging.org


So let's do a neuroimaging study (Krendl et al., 2008) with...
right-handed female undergraduates at Dartmouth College (N = 28; 14 control subjects) [who] were highly identified with math, as determined by their response to the following question: "It is important to me that I am good at math." A response of 4 or higher on a 7-point Likert scale was required for participation.
...to see what parts of the brain "light up" during stereotype threat.1 The participants were tricked into thinking the study measured "the neural mechanisms engaged in cognitive tasks that require both speed and accuracy." Half of them experienced a "threatening" condition, the other half a control condition.

How was stereotype threat induced? Why, it's our old friend the IAT (Implicit Association Test)!
In the threat condition, participants were told they were going to complete a task that would assess their "math attitudes" because "research has shown gender differences in math ability and performance." These instructions served as the primary threat induction, as previous research has suggested that reminding women of gender stereotypes in math ability activates stereotype threat (e.g., O'Brien & Crandall, 2003...). However, because this study was the first attempt to induce stereotype threat while participants were in the scanner, the second categorization task we administered in this condition was the math/arts IAT (Nosek, Banaji, & Greenwald, 2002b), in which participants categorized words as being related to math, arts, males, or females. We intended for this task to further reinforce the salience of gender stereotypes regarding math ability, and indeed, pilot testing revealed that administering this IAT was sufficient to induce the stereotype-threat effect.
The non-threatening condition was the
liberal/conservative IAT, which involved categorizing words as being related to liberals, conservatives, unpleasant, or pleasant (Nosek, Banaji, & Greenwald, 2002a). Thus, control participants received no reminder of gender stereotypes regarding math ability.
Both groups of women started out with the neutral flower/insect IAT2 followed by a set of simple difficult math problems (Time 1). Then the threat/control conditions were followed another set of more difficult math problems (Time 2). The threat manipulation did, indeed, have detrimental effects on performance [but only at p=07], as shown in the figure.

[NOTE: but why did the control group perform significantly better at Time 2, when the problems were much more difficult, than at Time 1?] CORRIGENDUM: practice effects, the problems at Time 1 and Time 2 were both difficult.

What were the fMRI results? In brief, an analysis of brain regions that were more active at Time 2 than at Time 1
...showed that the control participants recruited more left-lateralized activation in the inferior prefrontal cortex (Brodmann's area, BA 47), left inferior parietal cortex (BA 40), and bilateral angular gyrus (BA 39) over time. By contrast, the threatened participants revealed greater activity in the ventral anterior cingulate cortex (vACC; BA 32/10 [NOTE: no one would call BA10 the vACC ]) on the second test than on the first (Fig. 2).
What does it all mean? From philidendron:
MC overheard two of her students discussing math class last week.

Girl 1: "Damn girl. I thought you dug math."

Girl 2: "Hell no. Girl? (tongue-click) Hell no. Hell times hell to the hell-powered no! Damn!"

Footnotes

1 Why?? you may ask.
In order to effectively override the stereotype-threat phenomenon, it is vital to understand clearly the core processes that underlie it. In pursuing this goal, researchers may benefit from using neuroimaging to identify brain regions engaged during stereotype threat.
2 In the flower/insect IAT,
The categories are presented in congruent blocks (i.e., "flowers" and "pleasant" paired together) and incongruent blocks (i.e., "insects" and "pleasant" paired together). Categories that were paired together were presented on the same side of the screen, and participants were required to use the same response key to categorize stimuli belonging to these categories (e.g., when "flowers" and "pleasant" were paired, participants pressed the same key to categorize the word tulip as a flower and to categorize the word rainbow as pleasant); implicit bias was measured by calculating the difference in response times between the congruent and incongruent blocks.
Reference

Krendl AC, Richeson JA, Kelley WM, Heatherton TF. (2008). The Negative Consequences of Threat: A Functional Magnetic Resonance Imaging Investigation of the Neural Mechanisms Underlying Women's Underperformance in Math. Psychological Science, 19(2), 168-175. DOI: 10.1111/j.1467-9280.2008.02063.x

This study used fMRI to identify the neural structures associated with women's underperformance on math tasks. Although women in a control condition recruited neural networks that are associated with mathematical learning (i.e., angular gyrus, left parietal and prefrontal cortex), women who were reminded of gender stereotypes about math ability did not recruit these regions, and instead revealed heightened activation in a neural region associated with social and emotional processing (ventral anterior cingulate cortex).


Links to Math Girl episodes are on the website of Dr. Veselin Jungic in the Department of Mathematics at Simon Fraser University.

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5 Comments:

At February 21, 2008 12:01 PM, Blogger stephen said...

Contrary to popular belief, Larry Summers did not say women are any worse at math than men. He said that one thing contributing to skewed gender ratios in higher education is that on many traits have higher variance across males than females.

Imagine you only want to accept the best 10 people for some program, and your population of people is composed of a high-variance group and a low variance-group -- since you're picking from the far tail, you'll get mostly the high-variance group.

Note that this holds not just for "good" traits, but also bad ones. For example, imagine instead of "does crazily well at math" you were selecting for "plays crazily poorly with others". What gender ratio would you expect here? So, among the many things that make prisons male-dominated, the higher variance -- independent of mean -- of male social skills may contribute.

 
At February 22, 2008 12:33 AM, Blogger The Neurocritic said...

I was being glib with that comment, here's what he actually said:

"There are three broad hypotheses about the sources of the very substantial disparities that this conference's papers document and have been documented before with respect to the presence of women in high-end scientific professions. One is what I would call the-I'll explain each of these in a few moments and comment on how important I think they are-the first is what I call the high-powered job hypothesis. The second is what I would call different availability of aptitude at the high end, and the third is what I would call different socialization and patterns of discrimination in a search. And in my own view, their importance probably ranks in exactly the order that I just described."

So he ranked women's supposed reluctance to work 80 hr weeks while bearing and raising children above the higher-variance-in-men issue.

 
At February 26, 2008 7:20 AM, Blogger Bob O'Hara said...

The social mechanisms have been explained recently too, although not in a peer reviewed journal.

 
At February 29, 2008 7:57 PM, Anonymous calculatedly anonymous said...

The Neurocritic asked:

[NOTE: but why did the control group perform significantly better at Time 2, when the problems were much more difficult, than at Time 1?]

That's a fair question, but the answer could be just as easy as: practice effects. The bane of many pre/post intervention test experiments is the fact that people just don't sit there and exude their skills. They tend to learn about the test they are taking and very often improve. I don't know whether or how much harder the T2 math problems were here, but we are talking Dartmouth undergraduates here, and practice could explain why there were so many T2 stars (heh; a little fMRI humor there).

 
At March 01, 2008 12:25 PM, Blogger The Neurocritic said...

...practice could explain why there were so many T2 stars (heh; a little fMRI humor there).

Calculatedly nerdy humor...

You're correct about practice effects. I reread the methods, and the easy problems were given at the beginning of the scanning session, before either of the IATs were administered. The two critical sets of problems were both difficult, (e.g., "Is 19 × 6 – 6 ^ 2 = 78?" and "Is 98/7 + 19 × 3 = 81?").

 

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