Shortly after launching a website for high-performing math students, I received an email from a fellow Princeton alum who wrote lamenting that he didn't have access to similar resources when he was a student. The lack of such resources, he felt, left him unprepared for mathematical study at Princeton. But he couldn't point to poor performance in middle and high school as a cause of his difficulties at Princeton. In fact, he wrote,
I went through junior high and high school without ever missing a question on a math test, and then took [Math] 103 and 104 at Princeton, which was one of the most unpleasant and bewildering experiences of my life and poisoned me on math for years.
His experience attests that a student who aces every math test in middle and high school is not necessarily a success story for his school. Such a student presents his parents and teachers with a new challenge: how to prepare the student for the greater challenges he will face in college and beyond. Acceleration within the standard curriculum is the most common approach for adjusting the education of gifted math students. Unfortunately, acceleration does not address the core problem that a high-performing math student faces in the standard curriculum. Specifically, most curricula are written for near-average students at the relevant level of study. Not until well into undergraduate math classes are the near-average students 2-3 standard deviations above the general population in mathematical ability. A sixth grade student who is 3 standard deviations above average in her middle school algebra class will likely still be far above average in an AP Calculus class. Therefore, at no point in the standard algebra-to-calculus sequence will she see a curriculum designed to meet her needs.
While acceleration will bring a gifted math student to appropriately challenging collegiate material sooner, the student will still have several years of wading through insufficiently challenging material before she reaches a curriculum designed for her. Moreover, she will eventually be judged by a much higher standard in both top tier colleges and in the most internationally competitive careers. The standard curriculum will completely fail her in this regard, no matter how quickly she proceeds through it.
Exposing students to problems of greater depth than the typical curriculum offers benefits far outside mathematics. I saw this firsthand in college. I attended an average high school in Alabama; we had a graduation rate of 60-70%, and very few students went to college out of state. I only took two AP tests in high school, and did not attend any college classes. I was concerned that I wouldn't be as prepared as my Princeton classmates who went to magnet high schools or elite private schools. I quickly found that my training in challenging problem solving mathematics through math contests had prepared me very well for Princeton, and not just in my math classes. My science, computer science, engineering, and economics classes also offered challenges like those I found in math contests in high school. Tests featured problems that appeared to be very unlike homework, but required understanding the same fundamentals used to solve the homework problems. Moreover, the tests and homework were designed to challenge even the strongest students. The work required problem solving skills rather than memorization and regurgitation. I developed these problem solving skills in my math clubs and math teams in middle and high school, not in my regular math classes. Students who lacked access to these extracurricular programs, including many of those who attended magnet or private schools, often suffered a severe culture shock as they were forced to adjust to the greater depth and rigor of college studies.
Fortunately, now there are many more opportunities for students to encounter challenging mathematics. There are some more challenging curricula available, such as Singapore Math for younger students and our Art of Problem Solving series for students who are ready for algebra. There are also many more local math circles, summer camps, and online resources for outstanding students. One critical aspect of many of these opportunities is that they offer a culture of excellence to inspire students to continue their mathematical development at a high level. Many local efforts have been built by parents of gifted children, so if you don't have such a program in your area, starting your own can be an excellent way to cultivate your child's ability and interest in mathematics. If you seek advice on where to start in providing these opportunities to your children, you can contact us at Art of Problem Solving at email@example.com.
In providing these opportunities and challenges to gifted students, we help more than just the students. Technology now allows us to leverage the efforts of a few to the benefit of many to a greater extent than ever before possible. We know who many of those few are in the next generation -- they are the top students in math classes today. By helping them, we help ourselves, because it's not only their future that's in their hands; they hold our futures in their hands, too.
This article is provided as a service of the Davidson Institute for Talent Development, a 501(c)3 nonprofit dedicated to supporting profoundly gifted young people 18 and under. To learn more about the Davidson Institute’s programs, please visit www.DavidsonGifted.org.
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