Thursday, December 18, 2008
Dear Extra Credit Readers:
Jerry W. Miller's suggestion ["In the Real World, Advanced Math Doesn't Always Add Up," Oct. 30] that schools might be requiring too much math inspired so many letters that I needed several extra fingers and toes to count them:
Dear Extra Credit:
I think that one reason we don't see how we use math, especially algebra, in our daily lives is that we use it so much and so automatically that we don't realize it, sort of like breathing. I have to admit that I am a math geek, although I did not excel in math in school. My professional life, though, has been spent mostly as a researcher, and for a while I taught college statistics.
There is a lack of understanding of how math, and even arithmetic, factors in our daily life. I could give many examples of people's inability to calculate simple formulas for common things, such as how to increase a recipe that serves four to one that serves six.
Or percents: I am constantly amazed at the lack of familiarity with something as necessary as percents. Once, I took a class that aimed to teach how to shop for a low-fat diet. The rule was that no more than 30 percent of one's daily calories should come from fat. A student, over 40, asked what she could eat for supper if her lunch calories were 25 percent fat, and breakfast had 25 percent calories from fat. She said, "I'm already up to 50 percent, and I have a whole meal to go!"
Dear Extra Credit:
I'm 44 years old and have received four associate degrees from Northern Virginia Community College in Alexandria. I'm working on my fifth associate of arts, in business administration, but have not been able to get the degree because of the math requirement. I have been in the government, private and nonprofit sectors and never required more math than the basic equations in an Excel file (ratios, sums, etc.).
Also, with English being a second language for me, math is harder. The wording for math problems is very difficult to translate and then figure out the math. I hate the idea that I have to go back and take algebra and other basic math review courses so I can complete two courses in calculus that I won't use. Higher education and high school educators need to reflect that we are not all going to college, and vocational skills such as plumbing pay just as much as other jobs.
Dear Extra Credit:
Miller's assertion that "advanced math is rarely used and so should not be required" is flawed in two distinct ways.
First, very little of what we are taught is going to be directly useful in the day-to-day activities for which we are compensated, but that is an insufficient reason to avoid teaching it. Miller's argument is the equivalent of saying, "I shouldn't be asked to read John Donne, or to discourse on it, because I want to be an engineer."
Although the forced application of the 10th Holy Sonnet might not inspire a student to dip a quill the student might otherwise have left dry, a sound arts education polishes and tints the lens through which we view the world -- at work and at play. A strong math background does the same.
Second, Miller seems to equate the manual computation -- and solution -- of complex calculus problems with "using advanced math."
Over the course of an advanced math education, certain recurring systems of problems emerge and are dealt with so frequently that nobody so educated thinks in terms of the underlying equations and symbols anymore. In this sense, a practicing engineer might not "use" the experience with differential equation systems to hand-compute the optimum thickness of, say, a steel shaft. This engineer simply knows how changing the diameter will affect the component and, by extension, the system.
This critical step, from rote calculation to real-world problem-solving and internalization, cannot occur without thinking in abstractions.
Virginia should immediately bar Miller's engineer friends from practice, as they have told him that they are incapable of gut-checking their CAD tools. And he should find a new physician immediately, since the good doctor doesn't understand the decay models of the drugs he's prescribing.
Dear Extra Credit:
I would suggest that schools no longer give courses that might stretch students' minds, such as math, physics and chemistry, or any other intellectually challenging subject. Many of the older generation took three to four years of Latin, with very few ever using this knowledge in their later life. However, certainly an appreciation of such subjects has enriched the lives of those who chose to take such courses.
While all of us cannot be Nobel Prize winners, it was discouraging that the prizes awarded in physics, chemistry and medicine this year were given either to foreign scientists or to researchers who came from non-American secondary schools, with only one having what could be termed an American upbringing. The United States' performance in international competition in math and sciences at the secondary school level has been generally abysmal.
The statement has been made that we use less than 10 percent of what we have learned. Does this make the other 90 percent inconsequential?
Thanks for the thoughtful responses. I still think advanced math in school helps us learn good study and thinking habits, particularly in problem-solving. But I haven't read all of your letters yet and might run some more.
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