Social factors and (under)representation in mathematics

Margaret Beck (BU) and Moon Duchin (Tufts)

Summer@ICERM, August 2016

“We must eliminate barriers that prevent the full mobilization of ournation’s talent in addressing the challenges before us.”

National Research Council conference Seeking Solutions

“Presumptions of equality are false, as individualist equality may be writteninto law and policy while material inequality thrives.” Kyra

“She was doing everything I was doing, but just like Ginger Rogers, it wasbackward in heels.” Obama on Clinton, DNC, July 27, 2016

Stats on Women in Mathematics

From the AMS 2014 Annual Survey:

Stats on Women in Mathematics

From the AMS 2014 Annual Survey:

Stats on Women in Mathematics

From the AMS 2014 Annual Survey:

Stats on Women in Mathematics

From the AMS 2014 Annual Survey:

Tenure, Grants, Editorships

By another count, percentages of women in math: around 28% of PhDs (stablefor decades), 15% of faculty in doctoral departments; 11% of tenured faculty inthose departments

Rob Kirby: “In 1992, about 7 to 9% of... NSF grants (in pure math) went towomen and this did not vary too much according to field (there were roughly70 women and 800 men)”

Topaz and Sen: 435 math journals have 13067 editor positions; 8.9% belong towomen

So, Why So Few?

We’ll look at some factors and partial explanations for underrepresentation ofwomen in math, keeping in mind that biases and stigmas are far strongeragainst other groups and identities.

• Implicit bias

• Stigmatization

• Stereotype threat

• Rejection sensitivity

• Microaggressions and multipliers

We’ll close with some positive suggestions for improving the climate in math.

Implicit Bias

Implicit social cognition: thoughts and feelings outside of conscious awarenessand control; can activate stereotypes and result in bias

Deeply ingrained and nearly-universal social messaging creates associations ofwhite/male with intelligence and leadership qualities

Well-meaning efforts to correct bias can backfire badly

• Perceptions of preferential policies create a vicious stigma where you’reconstantly told you’re getting more than you deserve

• People are demonstrably bad at countering implicit bias: see Goldin andRouse, Orchestrating Impartiality: The Impact of “Blind” Auditions onFemale Musicians (2000)

Findings: Use of a screen to hide the auditioning musician increases by 50%the likelihood that women will advance from early rounds, and increases by“severalfold” the likelihood of having a women chosen first overall.

Where Is Implicit Bias Found?

Absolutely everywhere that people need to rate or evaluate each other.

Implicit gender bias in science faculty [Moss-Racusin et al 2012]:

• Faculty at research-intensive universities asked to rate student applicants

• Applicants randomly assigned male or female name

• “Faculty participants rated the male applicant as significantly morecompetent and hireable than the (identical) female applicant”

• Male applicants offered higher starting salary and more mentoring

• Gender of the faculty participant did not affect the response

Citation analysis across STEM:

• Articles with women in dominant-author positions received fewer citationsthen those with men in the same positions [Sugimoto et al 2013]

Take an implicit bias test:

https://implicit.harvard.edu/implicit/takeatest.html

Implicit Bias in Letters of Recommendation

Letters for female applicants to medical faculty were [Trix and Psenca 2003]:

• Shorter and contained fewer status terms, e.g., scientific terminology

• Higher percentage of “doubt raisers,” e.g., health issues, unmet goals

• “women as teachers and students”; “men as researchers andprofessionals.”

Findings extremely robust across many independent studies

[Madera et al 2009], [Schmader et al 2007], [Biernat-Eidelman 2007], [Heilman et al

1988]

Implicit Bias in Evaluations...or, as the NYTimes put it in a headline:

Is the Professor Bossy or Brilliant? Much Depends on Gender

“Men are more likely to be described as a star, knowledgeable, awesome or thebest professor. Women are more likely to be described as bossy, disorganized,helpful, annoying or as playing favorites. Nice or rude are also more often usedto describe women than men.”

Amazing visualization: http://benschmidt.org/profGender/

Stigma

Stigma: A mark of disgrace or infamy, regarded as impressed on a person orthing; A distinguishing mark or characteristic (of a bad or objectionable kind)

• In modern language, social stigma is a taint of disapproval or disdain thatattaches to people who have transgressed against cultural norms or whobelong to a disfavored group; Goffman used the term “tribal stigma” torefer to group disapproval

Stigma can be:

• Internalized, shaping individual behavior (perceived through bodylanguage, eye contact, nature of praise and criticism, appraisal of threat,feelings of superiority and inferiority, inclusivity, or shame); or

• Structural or institutionalized, to the disadvantage of stigmatized groups(treatment by doctors and police, availability of loans)

The absence of (tribal) stigma is: being seen, acknowledged, and treated asnormal or belonging to the in-group.

Stigma and Group Identityhttp://xkcd.com/385/

Effects of Stigma

High-status person wants to be liked and worries about seeming prejudiced;Stigmatized person wants respect and worries about being subject to prejudice

Within a mentoring context, women and minorities receive more praise, butfewer resources than others (Vescio et al 2005); Praise often conforms tostereotypes (Madera et al 2009)

• Impeded trust: feedback distortion may cause members of stigmatizedgroups to

− Discount negative feedback, assuming it results from bias

− Discount positive feedback, assuming it is due to overcompensationor preferential policies

• Reduces motivation to respond to feedback

[Goffman 1963], [Cohen and Steele 2002], [Remedios 2015], [Kleinman and

Halll-Clifford 2009]

Stereotype threat

Stereotype: generalized expectation or belief applied to group

Stereotype threat: “a situational predicament in which individuals are atrisk...of confirming negative stereotypes about their group” [Inzlicht andSchmader 2012] and this threat triggers reduced performance

Stereotypes of math ability [Steele 2011, Shih et al 1999]:

• Direct: Reminding women of sexist stereotypes leads to reducedperformance on test

• Indirect: White men perform worse if reminded of stereotype that Asiansare better at math

• Implicit: Even having women fill out a gender field on a test suffices totrigger this effect

Stereotype threat can result in avoidance and attrition from high-threatsituations, which can drive stigmatized groups out of STEM fields

Rejection Sensitivity

Rejection sensitivity (RS): a personality disposition developed through earlyexperiences of rejection, causing heightened fears/expectations ofrejection/failure; often triggers maladaptive responses like hostility andaggression

[Ahlqvist et al, 2013] studied female freshman and sophomore STEM majors:

• Women with higher RS were more likely to reduce their “identitycompatibility” over time, perceiving clash between their various groupidentities;

• This led to reduced STEM GPA and sense of belonging, and an increasedsusceptibility to stereotype threat.

The Petrie Multiplier

...or, “Quadratic Snark.”

Thought experiment by Karen Petrie(Dundee, CS) popularized in blog postby Ian Gent (St Andrews, CS)

Math model explains why, in the pres-ence of very imbalanced group ratio,even casual “microaggressions” can bemagnified to create a hostile atmosphere

• Assumption: Group A and Group B are equally likely to make a clueless orsnarky remark to a person of the other group.

• Result: If ratio of A to B is 1/R, A members receive R2 as many snarkyremarks as B.

• Reasoning: There are R times as many B to give snark, so R times asmuch B-snark is given. There are R times fewer A to receive it, so each Ais R times as likely to receive a given remark.

http://blog.ian.gent/2013/10/the-petrie-multiplier-why-attack-on.html

Intersectionality

• Describes how multiple identity factors (gender, race, sexuality, class,mental health, parent status, etc) can overlap and interact

• Term coined by Kimberle Crenshaw in 1989 in context of black feminism

• Key idea is that identity factors cannot be easily separated, and oppressioncan be additive (or superadditive)

• “Identity compatibility” undermined by community structure where normsare ostensibly neutral but actually geared to high-status group

NSF data on scientists and engineers, 2010

Now rerun Petrie multiplieron, say, three overlappingstigmatized identities...

Why Diversity Matters

In addition to moral issues about (explicit or implicit) exclusion, diversity isknown to lead to better outcomes in a variety of settings.

Hong and Page (2004) studied problem-solving in large groups and found

• Randomly selected, and hence more diverse, groups outperform groupscomprised of the highest-scoring individuals

• For large groups, diverse groups have broader ideas about representing andapproaching problems

• Surprisingly, this is particularly important in tasks, such as problem solving,where the success of a single individual implies success for the entire group.

In racially diverse juries [Sommers 2006]

• There is more communication: longer deliberation and a wider range ofinformation considered

• Fewer factual errors are made, and inaccuracies more likely to be corrected

• Whites are more open to discussing race-related considerations

• Benefits of diversity not dependent on contributions of minority members

Improving the Climate

Build community. Practice self-care.

Work on “effortful thinking” tocounter stereotypes and stigmas.

With respect to higher-status groupsthat you are in, make space formarginalized groups to center theirown narratives. Step aside when it’sappropriate and speak up when youcan. Fight against defensiveness.

Root out Impostor Syndrome, butdon’t be a blowhard.

Become a mentor! Lots of evidenceshows that the best way to accept ad-vice is to give it.

Resources

Organizations at Boston University:

• GWISE: http://www.bu.edu/gwise/

• WISE@Warren: http://sites.bu.edu/wiseatwarren/

• ARROWS: http://www.bu.edu/arrows/

• Howard Thurman Center: http://www.bu.edu/thurman/

Organizations at Brown University:

• WiSE: https://www.brown.edu/academics/college/support/women-in-science-and-engineering/

• Rose Whelan Society and Brown AWM Chapter:https://www.brown.edu/academics/applied-mathematics/

graduate-program/applied-mathematics-student-groups

• STEM & URM Conversation Series (CSREA):https://www.brown.edu/academics/race-ethnicity/category/

event-categories/stem-urm-conversation-series

A couple good blogs:

• Cathy O’Neil’s “Mathbabe”: https://mathbabe.org/

• Piper Harron’s “The Liberated Mathematician”:http://www.theliberatedmathematician.com/blog/

• Vi Hart’s blog: http://vihart.com/

Resources: National organizations that promote diversity

Gender-specific resources:

• Association for Women in Mathematics Mentor Program:https://sites.google.com/site/awmmath/programs/mentor-network

• The Edge Program: http://www.edgeforwomen.org/

• Women in Math Project: http://darkwing.uoregon.edu/~wmnmath/

• Nebraska Conference for Undergraduate Women in Mathematics:http://www.math.unl.edu/~ncuwm/19thAnnual/

• Center for Women in Mathematics at Smith College:http://www.math.smith.edu/center/

• American Association of University Women: http://www.aauw.org/

• Association for Women in Science: https://awis.site-ym.com/

Other Diversity Resources:

• Alliance for Building Faculty Diversity in the Mathematical Sciences:https://www.math.ncsu.edu/alliance/index.php

• Infinite Possibilities Conference: Celebrating and Promoting Diversity inthe Mathematical Sciences:http://www.ipcmath.org/index.html

• Advancing Chicanos/Hispanics and Native Americans in Science:http://sacnas.org/

References

• Ahlqvist, London, and Rosenthal, “Unstable identity compatibility: How genderrejection sensitivity undermines the success of women in STEM fields,”Psychological Science (2013)

• Aronson et al, “When White Men Cant Do Math: Necessary and Sufficient Factors inStereotype Threat,” Journal of Experimental Social Psychology (1999).

• Biernat and Eidelman, “Translating subjective language in letters of recommendation:The case of the sexist professor,” Eur. J. Soc. Psychol. (2007)

• Cohen and Steele, “A barrier of mistrust: How negative stereotypes affect cross-racementoring,” in the book “Improving Academic Achievement: Impact ofPsychological Factors on Education,” (2002).

• Goffman, “Stigma: notes on the management of spoiled identity,” (1963).

• Goldin and Rouse, “Orchestrating Impartiality: The Impact of Blind Auditions onFemale Musicians,” American Economic Review (2000).

• Heilman, Martell, and Simon, “ The Vagaries of Sex Bias: Conditions Regulating theUndervaluation, Equivaluation, and Overvaluation of Female Job Applicants,”Organizational Behavior and Human Decision Processes (1988).

• Hong and Page, “Groups of diverse problem solvers can outperform groups ofhigh-ability problem solvers,” PNAS (2004).

• Inzlicht and Schmader, “Stereotype Threat: Theory, Process, and Application,” (2012).

• Kleinman and Hall-Clifford, “Stigma: a social, cultural and moral process,” J.Epidemiol. Community Health (2009).

References

• Kyra, “How to Uphold White Supremacy by Focusing on Diversity and Inclusion,”Model, View, Culture (2014).

• Madera, Hebl, and Martin, “Gender and Letters of Recommendation for Academia:Agentic and Communal Differences,” Journal of Applied Psychology (2009).

• Moss-Racusin et al, “Science facultys subtle gender biases favor male students,” PNAS(2012).

• Page, “The Difference: How the Power of Diversity Creates Better Groups, Firms,Schools, and Societies,” (2007).

• Remedios, slides on “Mentoring in diverse settings,” from the conference “MentoringWorkshop for Graduate Advisors in Mathematics” (2015).

• Schmader, Whitehead, and Wysocki, “A Linguistic Comparison of Letters ofRecommendation for Male and Female Chemistry and Biochemistry JobApplicants,” Sex Roles (2007).

• Shih, Pittinsky, and Ambady, “Stereotype succeptibility: Identity Salience and Shifts inQuantitative Performance,” Psychological Science (1999).

• Sommers, “On Racial Diversity and Group Decision Making: Identifying MultipleEffects of Racial Composition on Jury Deliberations,” Journal of Personality andSocial Psychology (2006).

• Spencer, Steele, and Quinn, “Stereotype Threat and Womens Math Performance,”Journal of Experimental Social Psychology (1999).

References

• Steele, “Whistling Vivaldi: How Stereotypes Affect Us and What We Can Do,” (2011).

• Sugimoto et al, “Global gender disparities in science,” Nature (2013).

• Topaz and Shen, “Gender Representation on Journal Editorial Boards in theMathematical Sciences,” preprint (2016).

• Trix and Psenka, “Exploring the color of glass: letters of recommendation for femaleand male medical faculty,” Discourse and Society (2003).

• Vescio et al, “Power and the Creation of Patronizing Environments: e Stereotype-BasedBehaviors of the Powerful and eir E ects on Female Performance in MasculineDomains,” Journal of Personality and Social Psychology (2005).

• “Seeking Solutions: Maximizing American Talent by Advancing Women of Color inAcademia,” Summary of a Conference, National Academy of Sciences (2013).

• NSF pie chart: http://www.nsf.gov/statistics/wmpd/2013/digest/theme4.cfm

• AMS Annual Surveys:http://www.ams.org/profession/data/annual-survey/annual-survey