Research reports, "Males show a larger advantage on visuospatial tests," but spatial relations is teachable to those who may need it

Not all women are bad at math and spatial relations. It is a stereotype, so it is not true for all women, but it is statistically true over the group, and this statistical gender gap has been demonstrated even in 5-month old infants. Furthermore, that same David Moore paper cites several studies that correlate testosterone with spatial ability.

Spatial reasoning ability (tested by questions such as the one below) affects math ability, and thus how many women enter STEM fields, including Data Science. The Twitter group Women In Data lists just 94 members, and that includes not just Data Science but other data-related fields as well including Business Intelligence and Databases. Women who have made it in Data Science publicly call for more to join them.

But increasing the number of women in STEM, including Data Science, and of women's general ability in math and spatial ability, is not dictated by birth circumstances. There is, in fact, a great deal of social influence. The gender gap in math ability has been correlated with women's social-political standing by country as measured by the Gender Gap Index. The GGI takes as input socioeconomic factors such as educational attainment statistics and ratio of women in parliament. Countries with greater emancipation of women also have smaller gender gaps in math ability.

Other non-hormonal factors that have been identified include (quoting verbatim from Sheryl Sorby's paper from the link):

  1. playing with construction toys as a young child
  2. participating in classes such as shop, drafting or mechanics as a middle shcool or secondary student
  3. playing 3-D computer games
  4. participating in some types of sports
  5. having well-developed mathematical skills

These societal influences snowball, especially when it comes to math. Once one falls behind in math, if not from negative social influence then perhaps that one year with a mediocre teacher, it is difficult to catch up. The pedagogy of math in conventional schools then mirrors that of the pedagogy of art and sports in those same schools: "education" by shame. Those with pre-existing skill (either innate or learned outside of school) are rewarded and given more attention while the rest are shamed into minimal or no participation. I.e., all those subjects don't really get taught in school, but rather school filters those who learn outside of school or just have natural ability.

There is hope: Sheryl Sorby has demonstrated that spatial skills can be taught. Born out of frustration while she was an engineering student herself and later as an instructor of those same courses and seeing her female students struggle as well, she sought out to see whether spatial reasoning ability could be taught. She devised workbook, software, and combined workbook/software variations, and the workbook proved to be most effective.

Her course is being taught at dozens of universities now, and takes just a couple of hours per week over a semester. Students taking the class she designed perform better in STEM classes. Best of all, the workbook from her course is available for purchase at Amazon.

Sorby cites Piaget and states, "Topological skills are primarily two-dimensional and are acquired by the age 3-5." Piaget based this theory of staged development on the work of Dr. Maria Montessori, who called them "sensitive periods." Montessori's sensitive periods included time frames for acquisition of language, acquisition of gross motor skills, acquisition of fine motor skills, and more -- during which the child has a high aptitutude and after which a window is closed. We can see the effect of the closed window especially when adults try to learn another language.

As Maria Montessori was an engineer and mathemetician before she became a physician and eventually an educator, the Montessori method is especially effective and broad when it comes to exercising spatial relations and teaching math spatially:

She was a scientist and an astute observer of children. Nevertheless, during her research at the turn of the century her observations were more qualitative than the strict statistical approach we see scientists take today. However, recent studies have quantified and thereby confirmed Maria Montessori's qualitative observations, and have been documented in Angeline Lillard's book Montessori: The Science Behind the Genius and in her 2006 paper (full text available for free via magic hyperlink at Lillard's personal website).


But despite the sensitive periods, it is possible for adults to learn additional languages. And it is possible for adults to learn spatial reasoning. Thankfully, adults have easy access to Sorby's research in the form of her workbook available on Amazon.

And for a real head start, the Montessori method can develop spatial reasoning at a time when children can easily acquire it.

The biggest hurdle, however, may be the socio-economic-political one: not discouraging females from learning math.

UPDATE 2014-11-30: Why Did I Write This? A Personal Note

I was asked, "What would possess me to write such an article? After all, Larry Summers was driven out of Harvard for saying much the same thing."

Perhaps if I provide some my own personal background, it may explain my motivation.

I was enthused at discovering Sorby's work, having come across it while on Twitter. I was enthused that there is a means to help my daughter overcome her lack of spatial reasoning, compared to the spatial reasoning that my son and I have. Oh, she's at the head of her class in math anyway, but from what I have observed, she is approaching math linguistically, like my wife does, rather than spatially. I immediately ordered Sorby's workbook for my daughter this weekend.

One important difference between this blog post and Summers comments is that I point readers to resources to overcome the difference. Summers suggested affirmative action as a solution.

In terms of getting more women into Data Science, I am proposing the opposite of affirmative action. I think especially when it comes to intellectual pursuits, it would be an understatement to say that affirmative action is insulting. Police academies have lower standards for women. We do not and should not lower standards to get more women into Data Science. Rather, we should acknowledge the roles both of hormones and of societal discouragement of 3D activities for females (sports, videogames, construction toys and even math itself) and compensate for these acknowledged deficiencies through targeted training such as Sorby and Montessori (both women of exceptional capability, by the way).

I reject the post-Summers taboo of not talking about gender differences in math, whether those differences are nature or nurture. Math, STEM and Data Science are important skills for the future, and to allow women to participate, we should not delete the gender column from our data sets and turn a blind eye. Rather, we should follow in Sorby's footsteps, devise training instruments, and measure in full sunlight -- with the gender column not deleted -- what training is effective.

UPDATE 2015-03-05: Change in title

The title of this blog post was formerly, "Women Are Bad at Spatial Relations; But It Can Be Taught". Owing to the sensitive nature of the topic, the title has been changed to instead start off with a direct quote from one of the peer-reviewed papers cited in this blog post.

One of the goals of the Data Science Association is to encourage more women in STEM, just as it is my own personal goal to have my own daughter excel in math. The Data Science Association turns to science and data science for solutions.