I could write a book on this topic. My AP calculus students are for the most part exceptional math students. Many have never been taught to think. The emphasis in all their classes has been on scoring well on the Regents exam. So much emphasis is put on calculator use that some have forgotten basic arithmetic. One of my students has been in my class in 9th grade and I remember her doing all her calculations by hand with no difficulty. It took me months to wean her away from her calculator dependency.
Good students will be able to pass on their own, but they need guidance as much or even more than the weak ones. By ignoring this group, we are creating a bunch of intellectual idiots.
pissed off teacher
Good students will be able to pass on their own, but they need guidance as much or even more than the weak ones.
For Americans, this notion -- that good students need teaching as much or more than weak students -- is sooooo counterintuitive.
I don't say this as a criticism of the U.S., particularly. It's just the way things are. I first learned that other cultures don't think about talent & achievement the same way we do reading Stevenson & Stigler's The Learning Gap.
The cultural difference between American and Asian cultures on this question is so significant that the National Mathematics Advisory Panel report addressed it in its Fact Sheet:
Student Effort Is Important
Much of the public's "resignation" about mathematics education is based on the erroneous idea that success comes from inherent talent or ability in mathematics, not effort. A focus on the importance of effort in mathematics learning will improve outcomes. If children believe that their efforts to learn make them "smarter," they show greater persistence in mathematics learning.
Here's a study by David Uttal:
Abstract The poor mathematics performance of children in the United States has become a topic of national concern. Numerous studies have shown that American children consistently perform worse than their counterparts in many parts of the world. In contrast, children in China, Japan, Taiwan, and other Asian countries consistently perform at or near the top in international comparisons. This paper examines possible causes of the poor performance of American children and the excellent performance of Asian children. Contrary to the beliefs of many Americans, the East Asian advantage in mathematics is probably not due to a genetically-based advantage in mathematics. Instead, differences in beliefs about the role of genetics may be partly responsible. Asians strongly believe that effort plays a key role in determining a child's level of achievement, whereas Americans believe that innate ability is most important. In addition, despite the relatively poor performance of their children, American parents are substantially more satisfied with their children's performance than Asian parents. The American emphasis on the role of innate ability may have several consequences for children's achievement. For example, it may lead children to fear making errors and to expend less effort on mathematics than their Asian counterparts. As research on genetic influences on behavior, traits, and abilities increases scientists should be careful to ensure that the public understands that genetics does not directly determine the exact level of a child's potential achievement.
Beliefs about genetic influences on mathematics achievement: a cross-cultural comparison
Genetica November 02, 2004
rich schools & biology
This leads me to a topic I have meaning to get posted for months: Richard Elmore has found that wealthy schools are particularly committed to biological explanations of student performance:
In more affluent communities, I also found that variations in student performance were frequently taken for granted. Instead of being seen as a challenge to the teachers’ practice, these differences were used to classify students as more or less talented. Access to high-level courses was intentionally limited, reinforcing the view that talent, not instruction, was the basis of student achievement.
What (so-called) low-performing schools can teach (so-called) high-performing schools
by Richard Elmore
National Staff Development Council VOL. 27, NO. 2 SPRING 2006 schools by
My all-time favorite experience of this phenomenon (I've had many) was the day Ed and I met with the Earth science teacher and the chair of the science department discuss C's erratic grades in the class, which ranged from A to F.
Their explanation: "C. can't think inferentially."
Unfortunately I wasn't quick enough on my feet to ask why it was he could think inferentially on A & B days but not on C, D, & F days.
Probably because I am a real American.
and see: Carol Dweck: The Secret to Raising Smart Kids