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Awesome things from 2016

Preparation for AMC and AIME

As I prepare for the AMC 10 and 12 and AIME this year, I find it very hard to see similarities in preparation for these challenging exams.

For starters, AMC exams have 25 problems that you need to solve in 75 minutes with multiple choices. This means that you have on average 3 minutes per problem. If you qualify for AIME by scoring high on AMCs then the time constraints are very different. AIME exams have 15 problems and you get three hours to solve them which means 12 minutes per problem and there are no multiple choices. Guessing on AIME does not work as the answer could be anywhere from 000 to 999. The average score among these AIMEs is typically between 3 to 6. For example, 2016 AIME II had an average score of 3.52 among 975 students who took it in USA.  There are also very few students who score more than 10 in AIME.  For USAMO qualification, one has to score typically in the range of 7-9 assuming high scores on AMCs.

Here is what I am doing this year. I practice for both AMCs and AIMEs using past exams. For AIME, I have enrolled into AoPS class in addition. The class goes over the concept and then there are 10 problems that you solve within a week which reinforces the concept. These are not easy problems and some assignments have taken 3-5 hours for me to solve. I find AIME solutions to be a lot more tedious and involve multiple steps where you can make silly calculation mistakes as compared to AMCs. I don’t mix the days where I practice both of the tests. For example, during the holidays, there are days when I take just AMCs and there are days when I just took an AIME per day. My scores have improved as I practice more but I still have a long ways to go in being an expert. The AIMEs are a lot more humbling exams than AMCs.

Good luck to everyone as they prepare for the tests in 2017!  The AoPS website is your best source for past exams and solutions.


Mathematics — Critical for STEM related career choices

Watt, H.M.G., Hyde, J.S., Petersen, J. et al. Sex Roles (2016) recently published a study that fewer women pursue mathematically inclined fields in sciences such as physics as compared to men and there are a variety of factors that contribute to this phenomenon.  The study also states that STEM (Science, Technology, Engineering, and Math) is too broad of a qualifier and there are various participation levels for females within sciences, for example, biology has a sufficient representation of females and where physics doesn’t.

This study was done with help of high school students in USA (9th to 12th grades) and Australia (9th to 11th grades). The study focused on preferred career choices in physics, biology, chemistry, and mathematics of these students based on mathematical performance, motivations, and mothers’ perceptions in the past.

The Australian study concluded that female students’ mathematics self concept was closely tied to their past performance and their perception on their mathematical abilities impacted their performance more than those of the boys. The American study produced similar results.

There are a lot of good data points in this research and it reinforces the impact of high school curriculum choices, performance in mathematics and most importantly its impact on students’ choice of  a college major and a future career.  As per Janet Hyde, one of the study’s authors said via email to US News and World Report,  “The gender gaps are in physics, computer science, and engineering … Only a minority of students take physics in high school — a big mistake — and girls are less likely to take physics courses than boys are.”




Interpretations of Extreme Math Intelligence

It is very encouraging that the number of girls who score high in the SAT section of Math has gone up over the past three decades. The children are defined as “highly gifted in mathematics” (by Study of Mathematically Precocious Youth) if they score at least 700 on the quantitative section of the SAT before the age of 13. Recent study by Makei and others point out that the ratio of boys to girls have shrunk in the upper tail of the performance. This study also finds similar parallel results for tests conducted in India. For example, the ratio of boys to girls in top math scores in SAT in the United States for the high achieving 7th graders have shrunk from 8:1 in the past to 2.5:1 recently.

However, it has been argued that the performance of girls in the upper tail of scores in SAT does not necessarily mean that they have extremely high intelligence in mathematics. Both prior SATs and the revised one in 2016 are multiple choice tests that do not necessarily require sophisticated problem solving skills or test concepts that are explained in the higher levels of mathematics. This is not to say that the girls who have top scores in SATs are not bright.

We have to encourage girls to not only score well in SATs but also take part in various math competitions that are available through out the year and of varying levels of difficulty. Problem solving skills are critical in this competitive world and high SAT score in mathematics section is just one data point that shows how girls are doing better now. World will definitely benefit from more girls math researchers, Field medalists, IMO, and Putnam competition winners. Scoring high on math section of SAT is necessary but by no means sufficient at all to show that gender gap has narrowed in the field of higher level mathematics.


My first Math Prize for Girls @ MIT

Last week I participated in Math Prize for Girls at MIT  in Cambridge, MA for the first time. 280 girls from US and Canada participate in this annual competition which is organized by the Advantage Testing Foundation. The qualification is based on the scores of the AMC10/AMC12 competitions offered by MAA and qualification typically requires that you score a few points more than the score required for AIME qualification.

It was a very well-organized event. Girls traveled from all over the country and Canada, and there was a session hosted by the MIT Admissions Office on the day before the contest, which was very informative. This was followed by a fun game night full of activities and food.


The contest was in the morning, and the registration process was very smooth. It is nice to look around the room and see so many amazing girls whose heads are down trying to solve math problems. There are 20 problems and you get 150 minutes to solve them. The problems are very hard and challenging. I found them harder than the AIME exam I took in March this year.

There are scores of volunteers and many students from MIT who help put this event together. After the exam in the morning, lunch is provided to all the contestants. The award ceremony was very inspirational. There were fun and inspirational talks from the alumnae who are now studying at MIT. Dr. Radhika Nagpal gave a talk on collective artificial intelligence, which was brilliant and something I have never thought of. She is currently a professor of Computer Science at the Harvard school of Engineering and Applied Sciences.

Overall, the contest was fun, informational, and inspirational. There have been some articles about the effectiveness of such competitions. However, I can tell you that there is nothing more amazing than being surrounded by girls who share the same interests and passions who encourage each other. I also made so many new friends by being part of this competition.


Females favored in STEM fields in France

Science magazine recently wrote a great article on research published in France related to gender hiring biases in academia in underrepresented fields such as STEM.

There are various studies done which highlight the gender bias hiring issues both ways. On one side of the coin, there is an argument that females get negatively discriminated in male dominated fields, while the other side of the coin says the exact opposite argument: females get positively discriminated in such fields because of under representation. The details on the study can be accessed here.

Thomas Breda and Mélina Hillion of the Paris School of Economics have done a comprehensive analysis of aspiring middle school and high school teachers who take written and oral exams. They have inferred that in male dominated fields such as STEM, the placements favor females by as much as 10% over males and the opposite is true for female dominated fields for male. However, they only favor them by 2-6% more.

Regardless of the applicability of this French study universally (experts have weighed in on its applicability and methods), it is always encouraging if female participation in teaching positions is getting better, for they would act as good mentors and role models for aspiring young girls who want to pursue STEM fields.


Brilliance requirements lead to lower girls’ representation in STEM

Last year, I came across this great piece of research by Dr. Leslie, Dr. Meyer, and others.

A lot has been written about mindset and why girls’ representation is very low in STEM fields whether it is related to picking STEM related college majors, tenured faculty positions at academic institutions, or corporate leadership positions in technology companies.

This study introduces a new concept called FAB (field-specific ability beliefs). Basically, the main outcome of this study is that if a particular field is believed to require innate brilliance (further reinforcing stereotype that men are more brilliant than women), then most women will be discouraged to enter such fields. Such FABs combined with cultural stereotyping will lead more girls to have fixed mindsets and unless we spread awareness, the patterns will remain largely unchanged.

The research highlights percent of American Ph.D.s earned by women in 2011 (obtained through NSF survey of earned Ph.D.s). What stood out for me was that less than 30% of Ph.D.s were earned by women in the fields of Physics (18%), Computer Science (18.6%), Engineering (22.2%), and Mathematics (28.6%). These statistics make sense and it is also clear that more women drop out from Bachelor’s degree to Doctorate’s because the Bachelor’s degree female percentages are higher.

We have to make sure that we get rid of linkage of raw brilliance with STEM fields. If Ph.D.s earned by women are less than 50%, that means there will be fewer role model professors/researchers who can help break gender stereotypes and change FABs.

Dr. Leslie has done a great job on in this video which makes the message very clear.




Girls Math Competitions

Recently, The Atlantic published an article titled “Math for Girls Math for Boys” by A.K. Whitney. It is a well-written article and offers a good perspective on competitions designed for girls. As I have blogged before, it is definitely worrying that there are very few girls who get qualified every year to participate in the International Math Olympiad (IMO), and the girls’ qualification numbers from the United States have been very discouraging and disappointing for the past many years.

I would like to point out that competitions such as the European Girls Math Olympiad are very important on international stage. Such a competition not only gives a platform for girls to compete with other top girls at an international level, but also helps build a great international community for these girls who are representing their countries.

It is very easy to say that such competitions are inferior to the IMO, however, until we have a gender equality in qualification (typically in the US, 1 out of 5 girls qualify for USAMO and the number reduces much further to almost zero by the time IMO qualification is reached) for such competitions. MIT Math Prize for Girls is also such a competition where nearly the top 300 girls from high schools in the US participate based on their scores from the AMC 10 (top 2.5%)/AMC12 (top 5%) competitions every year. From what I have heard, girls love participating in this competition and it has very high prizes as well.

Overall, we need more girls to participate in math competitions, parents and educators need to encourage them from early years, and we need great female mentor/coaches to create and increase girls’ participation and excellence in math competitions.


College Admissions and Gender (dis)Advantage

Nick Anderson at The Washington Post did a nice job analyzing gender acceptance rates at top 200 universities and liberal arts colleges in 2014 using Federal data. Some of the colleges that stood out for me were the ones that had strong engineering and sciences programs. These colleges had much higher women acceptance rates than men. The reverse is also true for some other colleges.

Some of the interesting ones were:

-Worcester Polytechnic Institute (acceptance rates for women 54% and 40% for men). In WPI class of 2018, females were 33% of incoming class.
-CalTech, Georgia Tech, and Purdue had 10% higher acceptance rates for women than men.
-MIT had almost double the acceptance rates for women (13% vs 7%)

If we look at MIT’s class of 2019, 53% of the class were males and 47% females. However, the acceptance rate for females tends to be almost double for the past few years at MIT. There could be a lot of reasons on why women have higher acceptance rates. MIT’s dean of admissions told The Washington Post, ““The data don’t show that it is easier to be admitted as a woman applicant — that would only be true if our male and female applicant pools were equivalent. But the women who apply are a more self-selecting group.” The article also does a nice job of pointing out colleges such as Harvard and Stanford where there are no gender advantages.

Here is the list of colleges from the article where women had higher acceptance rates:
Worcester Polytechnic Institute (54 percent women, 40 percent men) 14 points
Clark (60 percent women, 46 percent men) 14 points
Stevens Institute of Tech (53 percent women, 41 percent men) 12 points
Georgia Tech (41 percent women, 30 percent men) 11 points
Brigham Young (51 percent women, 41 percent men) 10 points
Caltech (16 percent women, 6 percent men) 10 points
Purdue (65 percent women, 55 percent men) 10 points
Colorado School of Mines (43 percent women, 34 percent men) 9 points
American (49 percent women, 41 percent men) 8 points
California-Davis (44 percent women, 36 percent men) 8 points
Lehigh (39 percent women, 31 percent men) 8 points
Vermont (77 percent W, 69 percent men) 8 points
Wisconsin-Madison (61 percent women, 53 percent men) 8 points
Delaware (71 percent women, 64 percent men) 7 points
Illinois at Urbana-Champaign (63 percent women, 56 percent men) 7 points
Iowa (84 percent women, 77 percent men) 7 points
Marquette (70 percent women, 63 percent men) 7 points
MIT (13 percent women, 6 percent men) 7 points
Michigan State (70 percent women, 63 percent men) 7 points
Texas at Austin (43 percent women, 36 percent men) 7 points
SUNY Env. Sciences (55 percent women, 48 percent men) 7 points
Carnegie Mellon (28 percent women, 22 percent men) 6 points
Penn State (53 percent women, 47 percent men) 6 points
Boston U. (37 percent women, 32 percent men) 5 points
Colorado Boulder (87 percent women, 82 percent men) 5 points
Florida (48 percent women, 43 percent men) 5 points
Michigan (35 percent women, 30 percent men) 5 points
UC-Santa Barbara (39 percent women, 34 percent men) 5 points
Cornell (16 percent women, 12 percent M) 4 points
Georgia (57 percent women, 53 percent men) 4 points
Miami of Ohio (68 percent women, 64 percent men) 4 points
Minnesota-Twin Cities (47 percent women, 43 percent men) 4 points
N.C. State-Raleigh (54 percent women, 50 percent men) 4 points
Rensselaer Polytechnic Inst. (40 percent women, 36 percent men) 4 points
San Diego (48 percent women, 44 percent men) 4 points
Texas A&M (73 percent women, 69 percent men) 4 points
Texas Christian (50 percent women, 46 percent men) 4 points
UC-Irvine (39 percent women, 35 percent men) 4 points
Virginia (30 percent women, 27 percent men) 3 points
Baylor (57 percent women, 54 percent men) 3 points
Case Western Reserve (40 percent women, 37 percent men) 3 points
Denver (78 percent women, 75 percent men) 3 points
Massachusetts-Amherst (63 percent women, 60 percent men) 3 points
Ohio State (54 percent women, 51 percent men) 3 points
Rutgers-New Brunswick (62 percent women, 59 percent men) 3 points
UC-Santa Cruz (57 percent women, 54 percent men) 3 points