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“Math departments fail too many calculus students….

David Bressoud is a well-known mathematician who is a Professor of Mathematics at Macalester College and a former President of the Mathematical Association of America (MAA).  In this article, he advocates for colleges changing the way they teach calculus. He argues that the current model of instructor-led teaching is outdated and that even the students who pass the introductory courses in calculus are not always prepared for the higher level ones. Dr. Bressoud recommends active engagement in mathematics, which is usually referred to as “active learning.”

NSF funded a $3 million five-year project called SEMINAL, which stands for Student Engagement in Mathematics Through an Institutional Network for Active Learning. 12 public universities are working together on this project to show how active learning can be used in mathematics classes from precalculus through higher forms of calculus.

Even in 2018, I feel that calculus and related courses are seen as tough and gatekeepers for many aspiring students, whether they want to pursue STEM related education or economics and finance. In my high school, performance in calculus courses is critical to advance to the next level and to qualify for honors level courses in subjects like Physics or Computer Science. Even the Wharton @ Penn undergraduate admissions list shows the requirement to “have taken calculus during high school.”

I am fully in agreement with this article, in that we need to revamp how calculus is taught in high schools and colleges. Calculus is not seen as a very inclusive class which discourages many girls and minorities to enroll, with media as well stereotyping calculus students in a negative way. This research report from Dr. Bressoud and others does a nice job of giving a lot of details including this profound statement: “The worst preparation a student heading toward a career in science or engineering could receive is one that rushes toward accumulation of problem-solving abilities in calculus while short-changing the broader preparation needed for success beyond calculus.”

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Math Majors Gender Distribution

“Do girls who participate in math competitions through high school typically major in STEM fields when in college?” I get asked this question many times. I have done a few surveys on this topic and will share the results in the next few weeks.

I wanted to share the analysis done by the National Student Clearinghouse® Research Center™. The Research Center works across many higher education institutions and educational organizations to inform practitioners and policymakers about student educational pathways as per their website.

The following charts shared in the report basically outline that the number of girls who pursue Bachelor’s degrees in mathematics have declined from 2004 through 2014. The Master’s and Doctorate numbers have remained constant and continue to be discouraging.

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Women are approximately 15% of tenure faculty positions (makes sense based on the Doctoral data above) in mathematical sciences research universities in the United States. Dr. Sen and Dr. Topaz found out that 8.9% of the 13067 editorships in mathematical sciences (435 journals) were held by women. The research concluded that the degree of underrepresentation of women on mathematical sciences journal editorial boards is far more severe than in the mathematics field overall.

I personally believe that all of these data points are related and attrition of girls continue to be higher at the higher levels in the field. We as a society and community need to continue to encourage girls at each and every stage (master’s; doctorate, faculty, tenure track and so on…) to break this trend.

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My PUMaC experience

The Princeton University Mathematics Competition (PUMaC) is a student-run competition organized by the Princeton University Math Club since 2006 in Princeton, NJ.  2017 competition was held on Princeton campus on November 18th. You can find all the previous years’ problems and solutions here which can be very helpful to prepare for this competition. I would highly recommend to read the FAQs before participating in this competition.

I found PUMaC to be very intense and challenging competition. One week before the competition, you get Power Round questions. Power Round is a tough and time consuming round. You get the opportunity to work with your team for a week on these problems. You submit the power round before the competition begins on the campus. You will take individual tests in two sections of your choice (algebra, number theory, combinatorics, geometry), then compete in a team round, a live Round, and if you qualify then the Individual Finals. Princeton student volunteers had fully organized this contest and I found them nice, warm, and welcoming whenever we had questions or clarifications. Besides fun math activities and delicious lunch, there was also a session about majoring in math at Princeton with Prof. Mark McConnell which was super helpful.

I really enjoyed being part of a competition team and I met most of my team members for the first time on the day before the competition. This competition challenges you individually and as a team which I found a great learning experience.

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USA Mathematical Olympiad – Gender Distribution

The United States of America Mathematical Olympiad (USAMO) is an invitation only high school mathematics olympiad that is held annually in the United States. USA(J)MO serves as the final round of the AMC 10/12 contests. USAJMO was introduced to qualify students based on their scores in AMC 10+AIME exams where as USAMO qualification is based on AMC12+AIME exam scores.

MAA (Mathematical Association of America) was kind enough to provide me with various statistics of USA(J)MOs for the past five years. Unfortunately, given the drastic drop in number of female students who qualify for the AIME, the trend of female qualifications in USA(J)MO is equally discouraging. As you see below, the qualification of girls have stayed mostly constant over the past five years. Each year nearly 500 students qualify for USA(J)MO and the average number of girls who qualify has stayed constant ~10%.

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I also found it interesting that the average scored of males vs females were not that different, however, most of the high scoring students in USA(J)MO are males. MAA now invites a few girls based on their scores in USA(J)MO to Mathematical Olympiad Summer Program (MOSP) who are then further trained for European Girls Mathematical Olympiad.

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Emergence of Gender Stereotypes and its impact on girls’ interests

I’ve always been a huge fan of the profound research done by Dr. Leslie and Dr. Cimpian on gender stereotypes.  Their study on how misplaced importance on brilliance in a field sometimes discourages the minority in that field (women and African-Americans) is a fascinating one. In their latest study, they surveyed 2,000 professionals in 30 academic fields. The purpose of the survey was to determine how strongly the respondents believed that signs of brilliance, as measured by field-specific ability belief index, resulted in doctorate degrees being awarded in their discipline. It makes a lot of sense that fields with a higher index such as computer science, math, engineering, chemistry and philosophy, awarded relatively fewer advanced degrees to women and African-Americans whereas Art History, Psychology, Literature and other humanities disciplines awarded many more advanced degrees to women and minorities. I especially liked the critical observation related to the comparison between a fixed and growth mindset made in this study. The obsession in STEM fields with being brilliant or genius and the reinforcement of that in society, schools, media and others deter the very same people who we want to encourage to participate more. I see this phenomena occur often in the case of math competitions in middle school and high school, where unfortunately hard work and a growth mindset are not encouraged at all, and the society continually wants to reinforce the concepts of brilliance. For example, when girls do well in math, then “it must be because of their hard work” whereas boys when they do well then “it must be because they are brilliant”. This creates a vicious cycle that causes girls to shy away from participating in problem solving-based math competitions, which could benefit them a lot and eventually help them pursue advanced degrees in STEM including Ph.D.s.

Dr. Leslie and Dr. Cimpian were also featured on primetime television where they disclosed findings from their new study.

This study offered insights that girls at the age of 6 are less likely than boys to believe that they are really smart. Girls then start to avoid activities that they believe require them to be really smart. In Silicon Valley and a few other industries, there are a lot of efforts to encourage hiring of more women in STEM-related disciplines. However, if we do not address the issues outlined in the study where gender stereotypes are formed early in girls, most of the diversity-related initiatives will have mediocre success at best.

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