Skip to main content

Awesome things to know


Gender similarities in the brain during mathematics development

CNN recently published this article based on the research done by Dr. Jessica Cantlon and her team at Carnegie Mellon University. The full report can be found here. I am really encouraged by such research which continues to debunk the myth that boys are better than girls at math.

 

(CNN)Several studies have already debunked the myth that boys are innately better at math than girls, but those are largely based on analysis of test scores.

Now, researchers also have brain imaging that proves young children use the same mechanisms and networks in the brain to solve math problems no matter their gender. The study was published Friday in the journal Science of Learning.
To answer this question, Cantlon and her team got 104 kids between the ages of 3 and 10 to perform cognitive tests and watch videos of engaging math lessons while in an MRI scanner. It’s the first study to use neuroimaging to evaluate biological gender differences in the math aptitude of young children.
“We looked at which areas of the brain respond more strongly to mathematics content in the videos and tasks, compared to non-math content like reading or the alphabet. So you can define the math network that way by looking at regions that respond more strongly,” she said.
“When we do that in little girls, we see a particular network of the brain (respond), and when we do that same analysis in boys we see the exact same regions. You can overlay the network from girls on top of the network from boys and they are identical,” she added.
What Cantlon’s study doesn’t answer is why the belief that boys are stronger in STEM subjects than girls still persists. The stereotype is so pervasive that one research team even issued a consensus statement clarifying that “no single factor,” including biology, “has been shown to determine sex differences in science and math.”
Cantlon said she thinks society and culture are likely steering girls and young women away from math and STEM fields.
Previous studies show that families spend more time with young boys in play that involves spatial cognition, while teachers also preferentially spend more time with boys during math class, she said. Also, children often pick up on cues from their parent’s expectations for math abilities.
“Typical socialization can exacerbate small differences between boys and girls that can snowball into how we treat them in science and math,” Cantlon said. “We need to be cognizant of these origins to ensure we aren’t the ones causing the gender inequities.”
Share
FacebookTwitter

Does Society need IMO Medalists? A student’s view…

I published this blog orginally on MAA’s MathValues.org in July-2019.

A paper written by Dr. Man Keung Siu, a professor of math at the University of Hong Kong, titled “Does Society need IMO medalists?” poses an important question: how do math competitions fit in with the field of math at large? He starts by describing the International Mathematical Olympiad (IMO), including his experience with the competition, and mentions names of IMO winners that have gone to become famous mathematicians. He also ponders the relevance of the IMO winners to society and considers specifically the impact of the IMO winners on the field of math.

The 2018 US team at the International Mathematical Olympiad.

Winners of the IMO are highly trained in math competitions. As a high school student who competed in math competitions, I read Dr. Siu’s paper with interest and believe he asks an important question. Dr. Siu discusses the training and skill sets gained through preparation for the competitions. He states that training for math competitions allows students to acquire logical thinking, confidence, and “academic sincerity”.

However, he also notes that some of the drawbacks of this type of training include the ways competition problems differ from mathematical research, the potential for overtraining, and the possibility that competitive spirit is sometimes different from passion for the subject.

Personally, I believe that the points Dr. Siu brought up are fair, but based on my own experience and observations of other competitors, it seems that in order to do well in math competitions a genuine passion and drive for the subject is necessary to keep one motivated.

I agree with the point in Dr. Sui’s paper from Dr. Petar Kenderov, a math professor at the Bulgarian Academy of Sciences, who points out that math competitions disfavor students who work “slower”, as most competitions involve time pressure. Time restrictions can inhibit a student’s performance.

Kenderov also says that math competitions miss out on a fundamental aspect of math, which is posing questions and problems. Dr. Siu goes on to say something similar by mentioning that research isn’t just about the answer, but exploring a concept to the full depth.

One interesting aspect of the article is that Dr. Siu gives three examples of math problems that are solved in two different ways, to generalize that there are two fundamental methods of solving math problems. One method is the standard, longer approach of systematically solving the problem, which is typically taught in school and classroom settings, and the other is a method of finding clever ways to solve the problem in a nonconventional way, which he believes is the methodology taught in math competitions.

He states that both are crucial to the subject of math, but notes that schools don’t typically teach students math using math competition problems, which narrows most students’ horizons into thinking of math in one way. He claims that for a deeper understanding of the subject of math, all aspects should be explored. I strongly agree with Dr. Siu’s statement as the education system traditionally focuses on math solely in a way that is procedural, and it is crucial for students to see math in all facets.

To respond to Dr. Siu’s point that math competitions lack some aspects fundamental to mathematical research, like posing unique questions. However, it’s nearly impossible for tests to include all the components that provide students with a sufficient background in research. Although math competitions don’t comprehensively provide students background needed for a research project, math competitions do allow students  to experience creativity in math that most wouldn’t get exposure to otherwise. That creativity is a crucial component for mathematical research.

At the end of the paper, he shifts the focus to say that “society needs friends of mathematics.” By saying this, he denotes that it is essential to have people in the world who don’t necessarily pursue math but understand the significance of mathematics to the world at large. He claims that there does not exist a substantial amount of people that not only support the field, but also comprehend the value of mathematics. I think Dr. Siu makes a phenomenal point at the end, as lack of support undermines the value of making mathematical breakthroughs because  people aren’t cognizant of math as a field that impacts society.

Share
FacebookTwitter

IMO Medalists and their contributions

I wrote this blog which was originally published on mathvalues.org

—–

International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for high school students. The first IMO was held in 1959 in Romania and only 7 countries participated that year. Now, the competition has expanded to over 100 countries spanning major regions of the world. The team from the United States won the first place title in the most recent IMO, the 2018 International Mathematical Olympiad and also won the title in both 2015 and 2016.

Dr. Viorel Barbu, a participant in the first IMO, who has become President of the Mathematics Department at the Romanian Academy brilliantly wrote that “Mathematics has always been a fresh and dynamical field of human creativity and a fundamental science to the benefit of scientific knowledge and technical achievements. It is the role and duty of young mathematicians to bring and develop new ideas and to construct new bridges between mathematics and other scientific fields.”

I have always wondered about the contribution of IMO participants to the field of mathematics and science overall. I came across this fascinating research from Dr. Agarwal and Dr. Patrick Gaule. These researchers analyzed data examining the career and scientific output of participants who competed and performed well in IMO over a 20 years period. This research points to a very positive correlation between the points scored at the IMO and the mathematical knowledge produced, which was measured by the number of mathematical publications and mathematics citations. It also proved that students who performed well on IMO are more likely to become professional mathematicians, measured by getting a Ph.D. in mathematics.

I found some really interesting observations in the research, listed below:

Strong performers at the IMO have a disproportionate ability to produce frontier mathematical knowledge compared to PhD graduates and even PhD graduates from elite schools.

-The conditional probability that an IMO gold medalist will become a Fields medalist is two order of magnitudes larger than the corresponding probability for of a PhD graduate from a top 10 mathematics program.

-Dr. Maryam Mirzakhani, who passed away at a very young age, was an IMO gold medalist with a perfect score, and the first woman to win the Fields medal, the most prestigious award in mathematics. Terence Tao received a gold medal at the 29th IMO and went on to win the Fields medal and is one of the most productive mathematicians in the world.

-Around 22% of IMO participants have a PhD in mathematics; of those, around a third have a PhD in mathematics from a top 10 school (7% of the total IMO participants). 1% of IMO participants became IMC speakers, and 0.2% became Fields medalists.

This research paper clearly articulates the contributions of IMO participants to the field of mathematics. This paper gives strong reason to encourage everyone to participate in math competitions beginning in elementary school, and through college, as problem-solving skills acquired through participating in math competitions have long lasting positive effects that helps you whether you pursue a professional or academic career.

The last time a female qualified for the IMO from the United States was in 2007 and 3 female US students have scored medals at IMO. Their mathematics career and contributions validate the research findings. Sherry Gong represented the United States in 2005 and 2007, winning a Gold Medal in 2007. She famously scored over a 100 in Harvard’s problem solving course, Math 55, and went on to get her Ph.D. at MIT in mathematics. Alison Miller represented the United States in 2004 and also won the Gold Medal. Alison Miller studied mathematics at Harvard and finished her Ph.D. in mathematics at Princeton University. Melanie Wood represented the United States in the 1998 and 1999 IMO and won Silver Medals in both years. She was the first female to qualify for the IMO from United States. She completed her Ph.D. in 2009 at Princeton University and is currently a Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin.

Share
FacebookTwitter

Summer Math Camps

It’s that time of the year when many of you are researching which middle school summer camps to attend. I have attended a variety of summer camps since 7th grade that were mainly focused on mathematical problem solving and proofs. I frequently get asked if these camps are gender diverse or not, and the short answer is yes. Typically 25 to 30% of the attendees at most of these camps are girls, and I have made some of my best friends through many of these camps. I have met interesting students from all over the country, and there are many international attendees as well at many of these camps from Europe and Asia.

Here are some of the camps for middle school girls:

  1. Awesome Math Summer Program: This is one of the best camps for mathematical problem solving training. They usually have 3 different locations every year spanning the East Coast, the Central US, and the West Coast. More information about the locations can be found here. There are very specific course selection guidelines that I followed when registering for the camp and to get the best value out of this summer camp. I have not taken classes in their Year-Round program but I have heard those are good as well for students who cannot commit to Awesome Math’s summer schedules.
  2. MathPath: This is a four-week residential summer program for middle school students who are serious about mathematics. The program also provides them a rich social and recreational experience. MathPath encourages applications from female and minority students.
  3. Prove it! Math Academy: Even though this program will not be offered in 2019, it is one of the best math summer programs I have attended. It gave me a really solid foundation in proofs. Prove it! acts as a bridge between mathematical problem solving and proof writing, both of which are essential for various mathematical olympiads. This program will return in 2020, and is one of the rare programs that focuses on mathematical proofs, offered in beautiful Colorado.
  4. Idea Math: This is a summer math workshop for students in middle schools who wish to expand their mathematical knowledge, also while enhancing their problem-solving skills. Idea Math offers this camp at four different locations in the United States. They have year-round programs as well, which are offered in Boston, NY, TX, and the SF Bay Area.

In addition, please check out the following links for other summer camps including many online programs offered by AoPS.

Share
FacebookTwitter

Math Anxiety: Research

As I have written before, mathematics is becoming critical in today’s scientific and technological age. Advanced mathematics is helping with research in understanding our genes, diagnosing and preventing killer diseases, artificial intelligence, and driving many advances in computing. Math proficiency always helps with higher education, a professional career, and even something as basic as managing personal finances. I believe that more research should be done related to mathematics anxiety (MA) because if not understood and addressed, MA can be a significant barrier in learning basic and advanced mathematics. Mathematics anxiety has been defined by Dr. Richadson and Dr. Suinn as “a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in … ordinary life and academic situations”

Dr. Dreger and Dr. Aiken were the first ones to publish a study on what they coined ‘number anxiety’ in 1957. The main purpose of this study was to detect presence of emotional reactions to arithmetic and mathematics among 700 college students at Florida State University. They concluded that number anxiety was separate from general anxiety, was not related to general intelligence, and impacted math grades when it was high.

Dr. Ann Dowker is a University Research Lecturer at Oxford. Dr. Dowker and others have done extensive research on individual differences in arithmetic in both children and adults, and on the phenomenon of ‘mathematics anxiety’. Dr. Dowker is also the lead researcher on the Catch Up Numeracy project, which is an individualized intervention program for primary school children with low performance achievements in math. Catch Up Numeracy project has been implemented in 45 local authorities in the UK and is being extended to Ireland and Australia. Dr. Dowker with other researchers at Oxford published the latest compilation on MA, Mathematics Anxiety: What Have We Learned in 60 Years? This report does a nice job of defining MA, and its distinction from other forms of anxiety. I really liked how the research tries to identify the possible factors such as genetics, age, gender, and culture that could influence varying levels of MA.

I came across this another research from one of the co-authors of previous study where the research team used voxel-based morphometry (VBM) to identify the structural brain correlates of MA in 79 healthy children in Spain aged 7–12 years. MA is believed to develop in later years of primary education, and the study identified that “increased MA was associated with reduced attention, working memory and math achievement.”

There are various tips and tricks to reduce MA whether you are an educator or a student.

[Image Credit: Bob Staake, The NY Times]

Share
FacebookTwitter

Math Talent and their contributions: IMO Medalists

As stated on the International Math Olympiad website, “The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High School students and is held annually in a different country. The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents.” The team from the United States won the first place title in the 2018 International Mathematical Olympiad and also won the title in 2015 and 2016.

I really liked the following quote from Dr. Viorel Barbu, who is the President of the Mathematics Department at the Romanian Academy and a participant in the first IMO: “Mathematics has always been a fresh and dynamical field of human creativity and a fundamental science to the benefit of scientific knowledge and technical achievements. It is the role and duty of young mathematicians to bring and develop new ideas and to construct new bridges between mathematics and other scientific fields.”

I always wondered about the contribution of IMO participants to the field of mathematics and science overall. I came across this fascinating research from Dr. Agarwal and Dr. Patrick Gaule. These researchers analyzed data examining the career and scientific output of the participants who competed and performed well in IMO over 20 years period. This research points to a very positive correlation between the points scored at the IMO and the mathematical knowledge produced, which was measured by the number of mathematics publications and mathematics citations. It also proved that students who performed well on IMO are more likely to become professional mathematicians as measured by getting a Ph.D. in mathematics.

I found some really interesting observations in the research, listed below:

Strong performers at the IMO have a disproportionate ability to produce frontier mathematical knowledge compared to PhD graduates and even PhD graduates from elite schools.

-The conditional probability that an IMO gold medalist will become a Fields medalist is two order of magnitudes larger than the corresponding probability for of a PhD graduate from a top 10 mathematics program.

-Dr. Maryam Mirzakhani, who passed away at a very young age, was an IMO gold medalist with a perfect score, and the first woman to win the Fields medal, the most prestigious award in mathematics. Terence Tao received a gold medal at the 29th IMO and went on to win the Fields medal and is one of the most productive mathematicians in the world. 

-Around 22% of IMO participants have a PhD in mathematics; of those, around a third have a PhD in mathematics from a top 10 school (7% of the total IMO participants). 1% of IMO participants became IMC speakers, and 0.2% became Fields medalists.

This research paper clearly articulates the contributions of IMO participants to the field of mathematics. This is why I encourage everyone to participate in math competitions beginning elementary school, and through college, as problem-solving skills acquired through participating in math competitions have long lasting positive effects that helps you whether you pursue a professional or academic career.

I researched the gender distribution of participants from all participating countries over the past 55+ years and it shows encouraging trends of female qualifications in IMO including female Gold Medal winners over the last two decades as compared to before.

Share
FacebookTwitter

New research: Dynamics of the Gender Gap in high math achievement

One of the first papers I read when I started observing gender performance gaps in math competitions was The Gender Gap in Secondary School Mathematics at High Achievement Levels: Evidence from the American Mathematics Competitions by Dr. Ashley Swanson and Dr. Glenn Ellison. It was very insightful and made a lot of sense because I read it while I was going through the math competition journey myself. Even though this particular research was done almost a decade ago, unfortunately, macro performance trends have not changed much when it comes to performance gaps at high achievement levels. I have analyzed the data from the most recent decade, and the female percentage qualification for AIME, USAMO, and MOP have largely remained constant and low. As you see below, the following two graphs show the gender performance data in the United States from the AMC 12A in 2009 and the AMC 12A in 2015. The range of possible scores for the AMC 12A goes from 0 to 150 for 25 problems. For each possible score, you see the percentage of boys who received a given score in red and the percentage of girls who received the same score in blue. Girls are still not represented enough at the higher achievement levels, which is shown by there being a lot more red than blue as you move towards the higher scores on the chart.

The same researchers have published a brilliant new paper, observing the presence of a clear gender gap starting in the 9th grade and going forward. This gender gap becomes even more acute by the 12th grade. I included the authors’ conclusion and my perspective (in bold) below.

  1. A full analysis of pre-high school performance data has to be done to understand the gender gap in high math achievement among high school students. AMC 8 and MATHCOUNTS are popular competitions which would potentially aid in providing more clarity on the achievement gaps. I have analyzed data of AMC 8 from 2011-2017 and there are variety of reasons such as time pressure (40 minutes), anxiety, stereotype threats, and others that are potentially at play and need to be researched.
  2. The gender gap in high math achievement expands over the high school years with the biggest drop from 9th to 10th grade. The AMCs are not accessible to everyone and not always well advertised in the schools. Only a self-selecting group of students tend to prepare for the exam via math clubs, math circles, AoPS, or other means. There is also the factor that students get really busy with standardized tests prep and college applications in their junior and senior year. Also, many seniors lose interest in taking the AMC 12 given the test is in February, by which time many of the high achieving students will have already been accepted to their college of choice.

The leadership at Mathematical Association of America (MAA) is fully aware of various gender gaps at high achievement levels in many of the prestigious competitions they offer. They are systematically figuring out the reasons and how to start making changes to the competition types and format to ensure that the field of math competitions is even more inclusive and gender performance gaps narrow. I am looking forward to hopefully seeing a lot more progress narrowing these gaps in the next decade.

Share
FacebookTwitter

Math Prize for Girls – 2018

I am really excited about the 10th Math Prize for Girls which is scheduled for Sunday, September 23, 2018 on MIT campus in Cambridge. I appreciated that the competition is on Sunday as most students who fly from the western US end up missing part of school on Friday when the competition was on Saturdays. I always look forward to the activities that happen on the day before the event and the award ceremony with guest speakers after the competition is always fantastic. Besides solving challenging problems, I love seeing my friends who fly from all over the country to be at this competition. There are typically 300 girls who are qualified and invited to the competition based on their scores in AMC 10 or AMC 12. The organizers and scores of volunteers do a fantastic job to ensure we have a great experience. Plus, the weather is always nice in Cambridge this time of the year.

Dr. Boppana who is the Director of the contest was very kind to let me survey the participants who were qualified for 2016 Math Prize for Girls. I was always curious on how these amazing girls got here and so I asked them a few questions. I got an overwhelming response which showed me that it is a very supportive and vibrant community. For the first time, I am sharing the results of my survey. When I look back at some of these questions, I realize that I should have done a better job at asking these questions. However, directionally, the survey results were very insightful. Please check out the  survey results here.

Share
FacebookTwitter

Amazing experience at MOP 2018 (Mathematical Olympiad Program)

I first started dreaming about qualifying for MOP when I found out about it via some random conversations with the instructors at one of the summer math camps I attended in the 8th grade. I met a few Moppers (as they call themselves) and was inspired to learn about the program and most importantly the experience of attending the program.

It is really tough to make it to MOP whether you make it via scoring high in USAJMO or USAMO so I always thought it would be highly unlikely that I actually would qualify for it. After all, they take 50-60 students across all high schools from 100s of thousands of students who self select to participate via initial rounds of American Mathematics Competitions.

So what is MOP? It is basically an awesome summer program that is held annually at Carnegie Mellon University in Pittsburgh for 3+ weeks. The main purpose of MOP has always been to select and train the six members of the United States team for the International Math Olympiad and recently, to train qualifier girls to also represent United States to European Girl Math Olympiad (EGMO).

When I got the email from Dr. Po-Shen Loh on May 7th inviting me to MOP 2018, I just could not believe it for a few minutes followed by some crying, and then screaming loudly in my room. I ran and shared the news with my mom, brother, and texted my dad who was traveling. I also was proud to share it with my friends, math teachers, and math coach.

The program started on June 3rd and ended on June 27th. I have attended many excellent math camps in previous summers but my experience and learnings at MOP were absolutely the best. It was an amazing experience as not only was I with the top students in math from USA but also, they invited 20 students from the top 10 countries (in math) in addition. We took past International Math Olympiad style tests every other day including Saturdays and there were classes and seminars related to various math topics, math research, and applying math to every day life.

Dr. Loh who is the coach for the team USA and overall director of the program did an amazing job in creating a welcoming and inclusive environment. We had study sessions with great teachers and teaching assistants where students in all of the classes worked together on problems in either number theory, combinatorics, geometry, or algebra. We played foosball, table tennis, and board games and explored Pittsburgh on Sundays. I learnt a lot especially during group study sessions where you see how different students approach problems in a very different way and still get to the same answers. It was really nice to be with a community that loves math and I am really happy that I made many new and strong local and international friendships. It was also inspiring to see the IMO team representing USA being trained there. The US team went to Romania after MOP and won 1st prize at the IMO with many Gold Medals.
Dr. Loh wrote the following in his invitation email the following which turned out to be more than  100% true and exceeded all my expectations. “Although this may sound like a competition camp, I do not run it that way. When I attended MOP in the late 1990s, I enjoyed the camaraderie and witty conversations, and I made lifelong friends, and our paths continue to cross to this day. It is our mission to ensure that MOP is a similarly memorable, fun, and inspiring experience for you.”
Share
FacebookTwitter

Do boys out perform girls in math up through 8th grade?

The latest research from Stanford University suggests that, on average, girls perform at the same level as boys up to eighth grade. For some of the latest statistics on how many students are enrolled across different school districts, please check this source. The comprehensive analysis was done to estimate male-female test score gaps in Math and English Language Arts (ELA). The research team analyzed data from 10,000 school districts in the U.S., taking into account performance data from 260 million state accountability tests from third through eighth grade students over a 7-years period. The average school district had no performance gap in math and a slightly higher performance for girls in ELA.

I found the following from the research really interesting: “We find that math gaps tend to favor males more in socioeconomically advantaged school districts and in districts with larger gender disparities in adult socioeconomic status. However, we find little or no association between the ELA gender gap and either socioeconomic variable, and we explain virtually none of the geographic variation in ELA gaps.”

The research discusses the impact of gender stereotypes about the traditional conservative household roles, expected behavior of boys vs girls, and perceived academic talents of males and females. Traditional conservative gender stereotypes unfortunately still reinforce that males are more talented in math and sciences and women are more talented at reading. It is suggested that students become aware of these stereotypes sometimes as early as second grade.  These stereotypes have an impact on students’ beliefs about their academic capabilities, interest in various subjects inside and outside the classroom, and performance in those subjects.

The researchers recommend making students, parents, and educators recognize that math is not an innate skill and can be learnt. Also, exposing children to various activities that are not dominated by one gender and providing motivation and confidence to do better in school is critical.

Share
FacebookTwitter