National Assessment of Educational Progress (NAEP) Mathematics Achievement for 12th Graders, 1990-2000
In 2000, 83% of 12th-grade students scored below the proficient level in mathematics on the National Assessment of Educational Progress (NAEP) exam. What does this mean? They could not calculate the distance between two cities on a map or analyze percentage data. The percentage of students who reached the proficient level increased since 1990, but the percentage of those who did not reach this level far outweighed those who did.
The debate over the best method for teaching mathematics has been going on since the nineteenth century29. Jean Piaget's research in child psychology led him to the theory that children "have real understanding only of that which they invent themselves, and each time that we try to teach them something too quickly, we keep them from reinventing it themselves."30 John Dewey believed that education was a lifelong process, not a process in preparation for life. He advocated that teachers adopt a "hands-off" approach. They should only guide the students' experiences. Dewey believed that all subjects should be learned in the context of the "real world." He advocated classes in cooking, sewing, and manual arts to provide "real world" circumstances in which subjects like mathematics can be taught.31
William Heard Kilpatrick, who studied and worked with Dewey, invented the "project method" of teaching. Students were to work collectively on a project tailored to students' interests. During this process it was believed that students would learn all that they needed to know to become productive members of society. He believed that only subjects that had direct practical value (or student interest) should be taught. Kilpatrick's style of education was popular from the 1920s to the 1950s. As a result, the percentage of students in high school algebra dropped from 56.9% in 1909-10 to 24.8% in 1954-55. But the meaning of "direct practical value" changed during these years. Math became important.
After the Soviets launched Sputnik in 1957, math teaching received an overhaul. David Snedden's32 premise that "algebra…is a…valueless subject for 90 percent of all boys and 99 percent of all girls…"33 no longer held true. The National Defense Act (1958) provided almost a billion dollars to attract students to science, mathematics, and engineering. The new math curriculum proposed was labeled "New Math." No longer were students only told how — they must discover why. The use of manipulatives, such as Cuisenaire rods34, became prevalent. The rods would teach students the relationship among numbers and arithmetic. According to Lynn Steen, a math professor at St. Olaf College in Northfield, Minnesota, the "New Math" led to "absurd lessons in which students were drilled on how to spell such terms as 'commutative,' as in the 'commutative property' - which simply means 2 + 3 = 3 + 2" (Colvin).
By 1966 "New Math" had lost favor and the "Back to Basics" movement was taking hold. Traditionalists argued that students weren't learning basic skills. Traditionalists believe that children learn by memorization and by learning to use algorithms to solve problems in math. (Many of us probably remember the "invert and multiply" rule for doing division with fractions. But how many of us know why it works?) Arithmetic drills and multiplication tables were back in the classroom during the late 1960s and 1970s.
Then A Nation At Risk appeared in 1983. It chronicled the failures of the American school system. The Reform movement proposed changes in the way math was taught.
Traditional "Back to Basics" was out again. Discovery Learning was back in the saddle. This time it was called Whole Math35. The National Council of Teachers of Mathematics (NCTM) released standards in 1989. They called for decreased emphasis on rote practice and memorization and increased emphasis on manipulatives, problem solving, and use of calculators and computers.
In 1997, Jerry Rosen, a math professor at Cal State Northridge said: "Things the average student would know backward and forward 12 years ago, these students don't know at all." Elaine McEwan, an Arizona-based author and educator, stated: "…when you turn kids loose to constructivist math and you haven't taught them any of the basics, you have chaos." To counter the critics, Lee V. Stiff, president of the NCTM, stated that "we need to uncover math to show how it works. If there were nothing wrong with the traditional math of the '70s and '80s, our kids would be at the top of the pack, and adults wouldn't be lamenting the fact that they hated fractions or don't know algebra."36
But is Whole Math any better? The NCTM's 1989 Principles and Standards for School Mathematics shows examples of what students should be learning. A basic NCTM skill 9-12th grade students should be able to demonstrate: given a fixed interest rate, students (using a calculator) should know how to determine the amount of money in an account over a 10-year period by applying a simplified version of the formula for compound interest. An NAEP advanced skill for 12th-graders: "given a table of interest rates, students should be able to determine which bank account would have the most money after two years."37 In the year 2000, 11 years after the NCTM standards were published, only 2% of 12th-grade students were able to demonstrate this skill on the NAEP exam.
The next panel will discuss character education.
Sources: U.S. Department of Education. National Center for Education Statistics. "The Nation's Report Card: National Mathematics Achievement-Level Results, Grade 12: 1990-2000." Online. Available: http://nces.ed.gov/nationsreportcard/mathematics/results/natachieve-g12-pf.asp. June 11, 2002. and "The Nation's Report Card: Grade 12 Item Map." Online. Available: http://nces.ed.gov/nationsreportcard/mathematics/itemmapgrade12.asp. June 11, 2002. John Dewey. "My Pedagogic Creed." informal education. Online. Available: http://www.infed.org/archives/e-texts/e-dew-pc.html. June 18, 2002. Beyer, Landon E. "William Heard Kilpatrick." PROSPECTS, vol. XXVII, no. 3, (September 1997). "Slates, Slide Rules, and Software: Teaching Math in America." Online. Available: http://american-history.si.edu/teachingmath/. June 19, 2002. Marilyn Burns. "Math for the 21st Century - Back to Basics?" Math Solutions Online, Spring/Summer 1998. Online. Available: http://www.mathsolutions.com. June 18, 2002. National Council of Teachers of Mathematics. Principles and Standards for School Mathematics, 1989. Online. Available: http://standards.nctm.org. June 18, 2002. Richard Lee Colvin. "Formulas For Math Problems." Los Angeles Times, January 5, 1997. Online. Available: http://www.intres.com/math/Colvin.html. June 19, 2002. Jennifer K. Corvino. "Math Wars: Old vs. New." District Administrator. Online. Available: http://www.ca-magazine.org/SpecialReports/Math-Science/mathwars.html. May 17, 2002. Seymour Papert. "Child Psychologist: Jean Piaget." Time 100. Online. Available: http://www.time.com/time/time100/scientist/profile/. June 18, 2002. High school algebra participation data and David Sneeden's quote: David Klein. A Brief History of American K-12 Mathematics Education in the 20th Century, August 21, 2001. Online. Available: http://www.csun.edu/~vcmth00m/AHistory.html. June 18, 2002.
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