## Tuesday, August 25, 2009

### 2009 Math SAT Scores Are In: Gender Gap Persists

SAT test scores for 2009 were released today by the College Board, and the male-female gender gap for the mathematics test increased to 35 points to the highest level since 2004, reversing the narrowing gender gap over the previous 4 years (see bottom chart above). The average male score for the math exam was 534 points compared to the average female score of 499 points (see top chart above). What should also be noted is:

1. The variability of male math test scores (standard deviation of 118) was significantly higher than the variability of female math test scores (standard deviation of 112).

2. For math test scores above 700, males outnumbered females by a ratio slightly greater than 2:1 (8.7% of males vs. 4.32% of females scored above 700).

3. Females have higher overall GPAs than males, 3.39 vs. 3.24, and females outnumber males at the highest GPAs: more than 60% of students with GPAs equivalent to A and A+ are female.

4. For mathematics courses only, female and male students both have average GPAs of 3.14.

Bottom Line: Based on both overall GPAs and GPAs for math courses, we would expect female students to perform as well as, or better than, males on the math SAT exam, and yet we find exactly the opposite: a gender gap on the math exam in favor of males that persists over time.

At 8/26/2009 6:02 AM,  Walt G. said...

"Based on both overall GPAs and GPAs for math courses, we would expect female students to perform as well as, or better than, males on the math SAT exam, and yet we find exactly the opposite: a gender gap on the math exam in favor of males that persists over time."

Wouldn't this contradiction be evidence that either math GPAs or math SAT scores are not a valid performance measurement for mathematical abilities? If so, which one?

At 8/26/2009 6:14 AM,  Charles said...

This makes me question the whole grading methodology in schools.

"For mathematics courses only, female and male students both have average GPAs of 3.14."

Really? The average is 3.14? Not when I was in school...

At 8/26/2009 7:09 AM,  Walt G. said...

Charles: Why would you question the grading system in school instead of the standarized test scores?

The instructor might know the abilites of his or her students better over a full semester than a one day test would show.

Teaching in a trade that has a national certification test, I am always at odds of teaching what the students need to know for a test or what the students need to know from my 30+ years of experience in the field. It's not the same thing, and I have a limited amount of time--80 class hours--to get them ready for their profession. What would you do?

At 8/26/2009 8:27 AM,  Rand said...

How come no one ever shows the gap between female and male verbal scores on the SAT? Perhaps it's because females outperform males in verbal skills.

But then, it's difficult to claim to be a victim when you get better scores.

At 8/26/2009 8:29 AM,  Mark J. Perry said...

Rand: Excellent point.

When I get time, I'll try to post some analysis of the verbal scores.

At 8/26/2009 10:49 AM,  Andy said...

My explanation for this is a combination of two effects:
1. Males do better than females at math because they are more interested in it. Females do better than males at reading because they are more interested in it.

This is true for both children and adults. For example, readers of fiction are much more likely to be female, and people in math-heavy professions are much more likely to be male.

2. The way schools are taught benefits females rather than males, in terms of grading.

So if you combine those two effects, you get the observed results--women do better in school overall, but particularly in reading. In a more equal test, women do better at reading and men do better at math.

At 8/26/2009 11:34 AM,  Prof Frink said...

Why would you question the grading system in school instead of the standarized test scores?

Standardized tests should be unbiased. It's hard for me to imagine how a standardized test for math could be biased against women. Please explain.

Your hypothesis could easily be tested by designing a standardized test for mathematical aptitude that was biased against men.

At 8/26/2009 11:59 AM,  Walt G. said...

Prof Fink,

Our teamwork workshops usually have women naturally collaborating before answering a question or solving a problem, however, men usually want to work by themselves. Men have to be forced to work as a team. Using that criterion, which gender would be favored on a standardized test? Maybe the test is not biased against women but the delivery system is.

At 8/26/2009 2:05 PM,  Prof Frink said...

Walt G,

I guess I don't understand your point. Professors, teachers, schools, and universities are free to base grades upon whatever criteria they like. Ability to work well with others, problem solving, is a fantastic skill, but it's not pertinent to mathematical ability.

The question at hand (I think) is: Are men naturally better at math, especially at the highest aptitude levels. The data seems to back up this proposition, except for GPA, but it sounds like this metric is tainted because it evaluates abilities besides math, like teamwork.

At 8/26/2009 2:12 PM,  Tex said...

My own experience with grading is that there is a bias towards girls. Once example is the trend to require more writing in math classes, frequently requiring students to explain their answers in detailed prose form rather than just showing the mathematical steps. Since girls are more verbally advanced than boys are at every grade level, they are more likely to score higher in this area. Beyond explaining your answer, math journals are standard in our middle school. Each week students must write an short essay on prompts like, “The part of math I like best is . . .” or “Last year math was different because . . .” I’d guess that girls generally outshine boys in journal writing.

At 8/26/2009 2:16 PM,  Tex said...

Speaking of bias, at our high school's awards night two years ago 60% of the overall recipients were girls. There could be valid reasons for this, but it does make me wonder.

For the math awards in particular, girls received only 40% of the achievement awards (based on grades or other performance measures, I’m assuming) yet they received 60% of the "outstanding effort” awards. From these numbers I surmise that, while boys actually performed better than girls in math, the teachers thought the girls tried harder.

At 8/26/2009 5:38 PM,  Walt G. said...

Prof Frink:
I agree females and males are different, and I am really glad about that, but I am not sure a standardized test proves real-world mathematical ability when applied to practical problem solving in a complex environment. My definition of any type of ability, natural or otherwise, is of achieving a desired outcome.

Take a hypothetical case of a complex bridge that must be built over a river and assign the engineering of that bridge to two teams. One team consists of the top three female engineers of a graduating class of a college and the other team consists of the top three male engineers of the same graduating class of the same college. Which team will reach a consensus and build the most cost efficient and safest bridge? Who knows. But I think it’s fairly safe to say a standardized test is not a good performance measurement when taken out of context of the testing room and applied to having to work with other people and their money.

I guess there will always be a discussion about who is “smarter.” We like to put people in little boxes. And some people will even quit or be fired from prestigious universities about which boxes which people fit into and why. But I think the discussion is rather pointless until we define what “smarter” really means in the twenty-first-century.

At 8/26/2009 7:11 PM,  Dr. T said...

Teacher Walt G. continually looks for justification of grading policies and teaching techniques that don't work well when measured by a standardized test (the SAT) that is known to correlate strongly with math grades in college. (High school math grades correlate poorly with college math grades.)

I'm a clinical pathologist (and a medical educator), and I use math and statistics frequently. I don't do so within group projects or collaborations or problem-solving sessions. I do the math and statistics on my own, and share the information with others. That's how it usually works in the real world. This over-emphasis on group tasks is just another way to compress the grading scale, which now seems to run from 4.0 to 2.8 with a mean value of 3.5. Public schools do everything possible to eliminate distribution tails (literally and metaphorically).

At 8/26/2009 7:53 PM,  Walt G. said...

Dr. T, I am not defending grading policies in high schools. I am saying it's possible that the delivery methodology of standardized tests might bias the results of the test towards people who do well on standardized tests.

Teaching is only my part-time profession--most of my time is spent in problem solving and project management nowadays.

Most of our major industrial projects have inputs, mathematical and otherwise, from a wide range of individuals with different talents and skill levels. Unlike your field, not much of our work is accomplished at the individual level.

At 8/27/2009 8:32 AM,  Prof Frink said...

Walt G,

Three top women engineers might build a fantastic bridge, but this doesn't speak to the general mathematical aptitude of the sexes.

I'm only interested in "smarter" in so far as it guides policy. There are more male mathematicians and scientists. Is this a failure of the system? Does the system need to be overhauled to "fix" this discrepancy? Or is this simply the natural manifestation of men's greater mathematical aptitude?

At 8/27/2009 8:58 AM,  Walt G. said...

Prof Frink,

Are you defining “aptitude” as an innate ability? If so, how can you separate aptitude and achievement and determine that aptitude is the driving factor in having more male mathematicians and scientists? GPAs are rewarded for achievement by design and the SAT is not an aptitude test either—they state in their literature the test is designed to test “learned” skills.

At 8/27/2009 1:13 PM,  Prof Frink said...

how can you separate aptitude and achievement and determine that aptitude is the driving factor in having more male mathematicians and scientists?

I don't have to. Men perform better on standardized tests for mathematics and science. The SATs are just one data point in a trend. There are more male mathematicians and scientists. Therefore, men achieve more in math and science than women. Greater aptitude leads to more achievment.

Why do you think there are fewer women mathematicians and scientists?

At 8/27/2009 3:14 PM,  Walt G. said...

Prof Frink said: "Why do you think there are fewer women mathematicians and scientists?"

I don't know why. I have not seen any evidence that would convince me it's gender based though.

Ethnicity maybe? Asian females outscore white males on the SAT with a score of 572 compared to white males of 555. Shouldn’t a theory of male mathematical aptitude superiority using the SAT apply across ethnicities?

I don't know about the number of men compared to women in the engineering field that you are using to support your position, but I have worked with some phenomenal Asian women engineers from the top engineering college in the nation over the last few years. A few months with them broke me of some of my male and female stereotype thinking. If someone wants to say they are statistical outliers and remove them from the analysis you need to remove the male statistical outliers, too. But that poses a problem because using the male outliers that are two, three, or four standard deviations from the mean is one of the main premises that support the conclusion that males are superior to females in math.

I’ll need to see more proof before I am convinced males are born with superior mathematical abilities.

At 8/28/2009 8:36 AM,  Prof Frink said...

Walt G,

Despite being 6 feet tall, I encounter women all the time who are taller than me. This doesn't "break" me of my stereotype that women are generally shorter than men.

The discrepancy between men and women is small, and only really significant at the highest aptitude levels. Thus, the fact that you have worked with some phenomenal asian engineers is not surprising, nor does this anecdotal evidence tend to discredit the copius amounts of data that support the argument I'm making.

You're also opening a whole new can of worms by bringing up ethnicity. I'm sure you're aware that asians outperform whites and whites outperform blacks on IQ and standardized tests. Therefore, you need to compare asian women to asian men, not to white men.

At 8/28/2009 10:42 AM,  Walt G. said...

Hi Prof Frink,

This is an interesting argument and one that has gotten people fired. Isn't it great our jobs don't depend on this oblique discussion?

The analysis cannot exclude the women outliers (your > six-foot-tall women or my Asian engineers) because, as I understand it, the argument depends on the men outliers at both ends of the SAT test to show male mathematical superiority/inferiority. I don't think you can eliminate one set of outliers without eliminating the other set.

I thought this was essentially an X and Y chromosome argument, so what can of worms am I opening with ethnicity? Are Asian females genetically different than females in the U.S?

At 10/29/2009 1:29 PM,  Anonymous said...

In response to the comment on why is the discrepancy between males and females in verbal scores not talked about.....because the higher paying fields are traditionally all linked to science, technology, finance etc all of which require higher math scores. Lower math scores lower the chances of women getting into science and technology fields and so the gender gap in wages, power,etc continues. I think maybe college board should curve each section separately for males and females.

At 6/10/2010 7:43 PM,  Anonymous said...

Everyone here has missed an important point, which I would have as well, if I had not happened across the New York Times article which points out why this gap exists (http://www.nytimes.com/2008/07/25/education/25math.html).

In summary: because more women are college-bound than men, more take the SAT. Therefore, the distribution of women taking the test is more broad, skewing the mean toward the lower scores.

Two states which have made ACT testing mandatory for all high school students (Colorado and Illinois) have seen the gap disappear for that exam.