Friday, March 18, 2005
Dumping calculus
I was reading about integrated mathematics at Scholar's Notebook early this morning and left a comment to Matt asking what was the impetus for something that seems to be goofing up our students' learning of math. In response, he sends me to this article discussing the history of K-12 math ed.
This is fundamentally disconcerting to those of us who teach in areas where some ability to use algebra -- not calculus, but simply being able to take y = 3x + 7 and get x onto the left hand side and everything else to the right -- is no longer evident in our principles students. I agree that the problems we might solve in a principles class aren't all that "real world", but an ability to deal with abstraction should be something a college student can do. Increasingly, they can't.
The problem is not so much that this style of learning is taught. It might increase the math preparation for students who are unlikely to attend college, which still is a majority of high school students. Only 26% of America has a bachelor's degree. But for those that do attend, integrated math probably prepares them poorly, and is causing universities to either reduce their math requirements or do loads of remediation, since college level math courses are not integrated.
Perhaps the boldest and most far reaching recommendation of An Agenda for Action was its proposal for "Mathematics educators and college mathematicians" to "reevaluate the role of calculus in the differentiated mathematics programs." The report argued that "Emerging programs that prepare users of mathematics in nontraditional areas of application may no longer demand the centrality of calculus that has traditionally been demanded for all students." The de-emphasis of calculus, when carried out on a large enough scale, would support the move away from the systematic development of the prerequisites of calculus: algebra, geometry, and trigonometry. The so-called "integrated" high school math books of the 1990s contributed to this tendency. While those books contained parts of algebra, geometry, and trigonometry, the developments of these traditional subjects were not systematic, and often depended on student "discoveries" that were incidental to solving "real world problems."
This is fundamentally disconcerting to those of us who teach in areas where some ability to use algebra -- not calculus, but simply being able to take y = 3x + 7 and get x onto the left hand side and everything else to the right -- is no longer evident in our principles students. I agree that the problems we might solve in a principles class aren't all that "real world", but an ability to deal with abstraction should be something a college student can do. Increasingly, they can't.
The problem is not so much that this style of learning is taught. It might increase the math preparation for students who are unlikely to attend college, which still is a majority of high school students. Only 26% of America has a bachelor's degree. But for those that do attend, integrated math probably prepares them poorly, and is causing universities to either reduce their math requirements or do loads of remediation, since college level math courses are not integrated.
