A very interesting discussion of the three stages of mathematical education by the amazing Terence Tao:
Posts Tagged ‘education’
Here is an interesting article from MIT on patterns in high math achievement based on a study of AMC data. This research follows on the heels of the paper written by Dr. Andreescu and his colleagues last year. The study seems to conclude that girls (and presumably also boys) thrive when they are able to study math in a community that reinforces their interests and encourages their talents.
Here are some key excerpts from the article:
Ellison and Swanson arrived at their findings by using a novel source of data: the American Mathematics Competitions (AMC), a 60-year-old annual contest involving 125,000 exceptional high-school students. A select group of students who do especially well on the AMC compete in a series of annual competitions, the U.S. Mathematical Olympiad and the International Mathematical Olympiad. This focus on standout students differs from most studies about math and gender in schools…
The numbers Ellison and Swanson scrutinized indicate that the gender disparity among star math students widens as performance levels increase. In 2007, about 800,000 girls took the math SAT, compared to about 700,000 boys. Yet at the 99th percentile of the math SATs, boys outnumber girls two to one. In their research, Ellison and Swanson divide that upper tier into even smaller segments, using AMC results. Among students in the 94th percentile of the AMC tests, they found, the top boys outnumbered the top girls four to one; at the 99th AMC percentile, six to one; and at the 99.9th AMC percentile, 12 to one…
Ellison thinks this huge gender disparity is linked to another fact: Among those students scoring so highly on the AMC and participating in the math Olympiads, the range of high schools represented is much greater for boys than for girls. “The top boys in the Olympiads come from all over the United States,” says Ellison. “Some of them are from big powerhouse schools, and some are from schools where they’re the only student who’s really good at math. But it’s these 20 high schools where the majority of the girls are coming from.” Those institutions range from Phillips Exeter Academy, an elite New England prep school, to a fistful of public high schools in Northern California, from Palo Alto to San Jose. By contrast, Ellison and Swanson note, half of the boys in the Olympiads come from about 200 high schools…
O’Keeffe, who has a daughter who competed in the math Olympiad, is inclined to agree. “Anecdotally, I do think the difference a community makes is enormous,” she says. “If you’re lucky enough to be at a school with a math club, you might be the only girl in it. At Exeter or Stuyvesant [a prominent Manhattan public high school], you might be in a minority, but you won’t be alone.” To be more rigorous, though, Ellison wants to track many individual students over time…
Richard Rusczyk linked to a great article based on some recent research suggesting that students benefit from struggling with Hard Problems.
“We’ve found there is a healthy amount of frustration that’s productive; there is a satisfaction after having struggled with it,” says Roberta Schorr, associate professor in Rutgers University at Newark’s Urban Education Department. Her group has also found that, though conventional wisdom says certain abilities are innate, a lot of kids’ talents and capabilities go unnoticed unless they are effectively challenged; the key is to do it in a nurturing environment.
“Most of the literature describes student engagement and motivation as having to do with their attitudes about math — whether they like it or not,” Schorr says. “That’s different from the engagement we’ve found. When students are working on conceptually complex problems in a supportive environment, they do better. They report feeling frustrated, but also satisfaction, pride and a willingness to work harder next time.”
“Motivation is a key aspect of achievement that we often ignore in math; it’s the missing link,” Schorr says. “We need to provide kids with conceptually challenging math problems in an emotionally safe environment, and the teacher plays a critical role in that. Kids can view frustration as an opportunity for success instead of an indication of failure, but that won’t happen without teachers letting the students experience productive struggles.”
A good friend of the Metroplex Math Circle, Dr. Arthur Benjamin, is a popular speaker at the world famous TED conference. Recently, he offered his own idea for fundamentally changing math education in our country. Like Richard Rusczyk, he sees the singular focus on Calculus as insufficient and distracting from a full math education.
One of our favorite guest lecturers, Dr. Paul Stanford, was recently recognized for his work teaching college algebra, applied calculus, matrices and vectors, calculus and linear algebra.
The Regents’ Outstanding Teaching Award, which Stanford received in the category of contingent faculty, carries a $15,000 stipend. Nominees are selected through a rigorous campus-based process beginning with deans and department chairs, relying heavily on student and peer faculty evaluations within academic departments, and then progresses through various stages of evaluation up through the university, resulting in a recommendation from the campus president. The selection committee evaluates annual reviews, evidence of continuous improvement, commitment to high quality undergraduate education, and other factors.
We look forward to having Dr. Stanford share his great talents with the Metroplex Math Circle again in the 2009-2010 season.
CNN published a story about the Most Lucrative College Degrees base on a study by the National Association of Colleges and Employers. Of the top 15 careers, they all depend upon a strong background in mathematics and problem solving. Here are some key quotes from the article:
“Math is at the crux of who gets paid,” said Ed Koc, director of research at NACE. “If you have those skills, you are an extremely valuable asset. We don’t generate enough people like that in this country.”
“It’s a tech-driven world, and demand [for engineers] is only going to grow,” said Farnoosh Torabi, employment expert and Quicken blog editor. “You can’t say that about many fields, especially in a recession.”
There are far fewer people graduating with math-based majors, compared to their liberal-arts counterparts, which is why they are paid at such a premium. The fields of engineering and computer science each make up about 4% of all college graduates, while social science and history each comprise 16%, Koc noted.
As a result, salaries for graduates who studied fields like social work command tiny paychecks, somewhere in the vicinity of $29,000. English, foreign language and communications majors make about $35,000, Koc said.
“It’s a supply and demand issue,” he added. “So few grads offer math skills, and those who can are rewarded.”
Wenhua Ma brought an interesting article to our attention from the Notices of the AMS:
The Math Circle Experience
Extracurricular circles in a variety of subjects began in Hungary in the 1800s, all with the goal of providing young students opportunities to pursue personal interests to the fullest. Today they are considered a standard part of the Eastern-Europeanstudent experience, and participation in them is regarded as just as natural as participation in sports activities is viewed in the U.S. Although there is no set protocol to a math circle experience, all circles have the same goal of sharing the intellectual appeal and beauty of mathematics with as large an audience as possible. They engage faculty from both secondary and post-secondary institutions in their operation and successfully welcome students of all backgrounds to the mathematical experience.
Circles now exist in many countries, including the U.S. (see also , for instance), and follow multiple styles and approaches. Given the success of the Eastern European model it is natural to ask then whether some version(s) of the math circle experience could be incorporated into the U.S. cultural norm. Could even more be accomplished?
Dallas, TX, January 31, 2009. Dr. Alexey Root will present on chess applications of graph theory to secondary math education. She will highlight the concepts of domination and independence and show how they can be illustrated through chess problems. “The concept of domination is one of the central ideas in graph theory, and is especially important in the application of graph theory to the real world” according to Watkins in Across the Board: The mathematics of chessboard problems. Dr. Root’s lecture will be held on January 31st at 2:00 PM in room 2.410 of the Engineering and Computer Sciences Building (South), at the University of Texas at Dallas.
Dr. Alexey Root has a Ph.D. in education from UCLA. Root has been a tournament chess player since she was nine years old. Her most notable chess accomplishment was winning the U.S. Women’s championship in 1989. She also holds the title of Women’s International Master. Since the fall of 1999, Root has been a senior lecturer at The University of Texas at Dallas (UTD).
From 1999-2003 Dr. Root was the Associate Director for the UTD Chess Program, the number one college chess team in the U.S. Root’s current assignment for UTD is to teach education courses that explore the uses of chess in classrooms. Her courses are available worldwide, via the UT TeleCampus online platform. Her books are Children and Chess: A Guide for Educators (2006), Science, Math, Checkmate: 32 Chess Activities for Inquiry and Problem Solving (2008), and Read, Write, Checkmate: Enrich Literary with Chess Activities (2009).
In Dr. Alexey Root’s presentation, participants will try two domination activities from her books: Mobility (Children and chess: A guide for educators) and Covering the Board: Kings (Science, math, checkmate: 32 chess activities for inquiry and problem solving). Participants will also solve the eight-queens problem (Science, math, checkmate: 32 chess activities for inquiry and problem solving). The eight-queens problem highlights the concept of independence.
The Eide Neurolearning Blog is an interesting resource for keeping up with the current advances in neuroscience and brain imaging. In a recent post they discuss the uniqueness of mathematically gifted minds.
It will not surprise math circle participants to hear that such brains approach math problems quite differently. Traditional school programs may offer such students little support and it is the community of interest provided by a math circle or the time to play with hard problems that these students crave.
By temperament, strong math minds will tend to be introverted and have high focus and task persistence for activities of intrinsic interest. This may mean they are difficult to direct in the traditional or even non-traditional classroom (prefer studying lines of own interest), and they may be benefited particularly by mentors (often relatives or math teachers at higher levels of education) willing to discuss topics, ideas, and problems far in advance of their years.
The Eides also recommend the PBS video Fermat’s Last Theorem for aspiring mathematicians.