What does it take to be successful at mathematics?
I just finished reading Malcom Gladwell's book "Outliers" for the second time. What a great read. I like re-reading books from time to time and I'm surprised at what I glean from a book the second time through. Often it's something that I overlooked the first time through or perhaps new wisdom has me looking at it in a different way.
For starters, in his section "rice paddies and math tests" Gladwell presents some pretty convincing evidence for Asian aptitudes in mathematics as many Asian dialects have easier translations for number systems, making calculating them easier as well.
This however, wasn't what really interested me this time through. I came across a researcher in this chapter, Alan Schoenfeld, that did some experiments on mathematical understanding through learning experiences which he videotaped. The most compelling to me was actually an experiment that I did two years ago with my students as well. It starts by giving the class an unsolvable math problem, or clearly one that is too difficult for them such as some higher level calculus. Students try to solve the problem but then make note of how much time elapses before they give up. Through his research (and mine too) the students that give up first are typically the students who are the worst in mathematics. The conclusions are that students that try hard tend to be better in any subject. "Success is a function of persistence and doggedness and the willingness to work hard for twenty-two minutes to make sense of something that most people would give up on after thirty seconds"
Fellow teachers often lament how some students are poor performers in their subjects, and any subject is bound to have them no matter how good a teacher is. Teachers are quick to label the students as "lazy" and generally, they are correct. Through my experience I have also noted that my worst acheivers are usually the students that are derelict with homework, don't participate much in class and don't come in for help. In contrast, the best students are the ones that go above and beyond and do all the aforementioned tasks. Attitude and the desire to try hard, remediate areas of difficulty are always enlightened by understanding. Students that drop out and tune out are the ones that don't.
I have been presenting this contrast to my students for years on the first day of school. Most see the connection and vow to try harder. I do the same with parents on "back to school night" and they vow to make sure that Johnny gets his work in on time. Most of them do too, but some do not. At whatever rate that students or parents have the revelation that more practice equals higher rates of success in education, the sooner they'll be successful in whatever they put their mind to.
For starters, in his section "rice paddies and math tests" Gladwell presents some pretty convincing evidence for Asian aptitudes in mathematics as many Asian dialects have easier translations for number systems, making calculating them easier as well.
This however, wasn't what really interested me this time through. I came across a researcher in this chapter, Alan Schoenfeld, that did some experiments on mathematical understanding through learning experiences which he videotaped. The most compelling to me was actually an experiment that I did two years ago with my students as well. It starts by giving the class an unsolvable math problem, or clearly one that is too difficult for them such as some higher level calculus. Students try to solve the problem but then make note of how much time elapses before they give up. Through his research (and mine too) the students that give up first are typically the students who are the worst in mathematics. The conclusions are that students that try hard tend to be better in any subject. "Success is a function of persistence and doggedness and the willingness to work hard for twenty-two minutes to make sense of something that most people would give up on after thirty seconds"
Fellow teachers often lament how some students are poor performers in their subjects, and any subject is bound to have them no matter how good a teacher is. Teachers are quick to label the students as "lazy" and generally, they are correct. Through my experience I have also noted that my worst acheivers are usually the students that are derelict with homework, don't participate much in class and don't come in for help. In contrast, the best students are the ones that go above and beyond and do all the aforementioned tasks. Attitude and the desire to try hard, remediate areas of difficulty are always enlightened by understanding. Students that drop out and tune out are the ones that don't.
I have been presenting this contrast to my students for years on the first day of school. Most see the connection and vow to try harder. I do the same with parents on "back to school night" and they vow to make sure that Johnny gets his work in on time. Most of them do too, but some do not. At whatever rate that students or parents have the revelation that more practice equals higher rates of success in education, the sooner they'll be successful in whatever they put their mind to.
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