by Johnny W. Lott, NCTM President 2002-2004
NCTM News Bulletin, November 2002
"One of the unfortunate patterns in American response to educational innovation is a tendency to draw hard and fast battle lines between dichotomous positions" (Conference Board of the Mathematical Sciences and National Advisory Committee on Mathematical Education 1975, p. 55).
Unfortunately, this statement continues to be true today. Discussions involving change in mathematics education perpetually lead to "either/or" situations for educators. Often, those who cannot see value in using a new method or technology attempt to derail the practice and force teachers to use previous teaching methods. Two examples appeared in the news recently: "Computation skills are declining in today's youth, so we must rethink the curriculum" and "Calculator usage is destroying the ability of today's youths to compute." Both statements were printed as if true. Teachers then have to choose between either continuing the use of allegedly failing methods or returning to earlier practices.
Let's consider the first statement in light of results from the first National Assessment of Educational Progress (NAEP) in 1973:
- "The development of computation skills has not been destroyed by our current mathematics curricula" (Carpenter et al. 1978, p. 54).
Similar results are found in intervening years (cf. Carpenter et al. 1981, Lindquist 1989, Kenney and Silver 1997, Silver and Kenney 2000), and from the 2000 NAEP results (U.S. Department of Education 2001), we read:
- "Fourth-, eighth-, and twelfth-grade students had higher average scores in 2000 than in 1990, the first assessment year in which the current mathematics framework was used. Fourth- and eighth-graders showed steady progress across the decade. Twelfth-graders made gains from 1990 to 1996, but their average score declined between 1996 and 2000." (p. xiv)
- "At each grade [4, 8, and 12], the percentage of students performing at or above this [the Proficient] level was higher in 2000 than in 1990. There were gains over the decade at the Basic and Advanced levels as well. However, from 1996 to 2000, the percentage of twelfth-graders reaching the Basic level declined." (p. xiv)
Although trend data to compare recent results to past results have yet to be published for the latest NAEP study, we do know that the 1996 NAEP used trend assessment to be able to compare 1996 data with 1973 baseline data. The 1996 trend data did not allow students to use calculators but provided information on whether students' fundamental skills—including paper-and-pencil computation—changed over time. In those data the 9- and 13-year-old groups made steady progress over the 23-year span, and the 1996 level of performance was statistically greater than that in 1973. The 17-year-olds' performance declined between 1973 and 1982, but since that time they have shown an overall pattern of increased performance.
On the second issue, that of calculator use, in 2000 we find the following (U.S. Department of Education 2001):
- Eighth graders with unrestricted use of calculators had higher average scores than the students whose teachers restricted calculator use.
- Eighth graders who used calculators on class tests had higher average NAEP scores than students whose teachers did not permit calculator use on tests.
- Although frequent usage of calculators by fourth graders was associated with lower average mathematics scores than less frequent usage, for eighth and twelfth graders just the opposite was true—more frequent calculator usage was associated with higher scores.
Reports today saying the curriculum must change to emphasize computational skills are no more valid now than in 1973. The difference is that now we have NAEP results from many years to prove it. In 1996, calculator usage data reflected no loss in skills, but the 2000 trend data on fourth-grade calculator usage must be carefully examined in light of the many studies supporting calculator use. These studies include Hembree and Dessart's (1992) meta-analysis of studies on four-function calculators and Handheld Graphing Technology in Secondary Mathematics: Research Findings and Implications for Classroom Practice (Burrill et al. 2002), which synthesizes scientific research on the use of the graphing calculator. These studies found the following, respectively:
- "The preponderance of research evidence supports the fact that calculator use for instruction and testing enhances learning and the performance of arithmetical concepts and skills, problem solving, and attitudes of students." (p. 30)
- "Students who use handheld graphing technology have a better understanding of functions, of variables, of solving algebra problems in applied contexts, and of interpreting graphs than those who did not use the technology. ... No significant differences in procedural skills were found between students who use handheld graphing technology and those who do not. This indicates that extensive use of the technology does not necessarily interfere with students' acquisition of skills." (p. v)
NAEP data show that your students are better problem solvers today than ever in the past. With these data and a large body of research evidence refuting statements from the media, we should question critics. They have drawn battle lines over educational innovations that are working. Better they should erase the battle lines and think seriously about supporting teachers in mathematics classrooms.
Burrill, Gail, et al. Handheld Graphing Technology in Secondary Mathematics: Research Findings and Implications for Classroom Practice. Report prepared through a grant to Michigan State University. Dallas, Tex.: Texas Instruments, 2002.
Carpenter, Thomas, Terrence Coburn, Robert Reys, and James Wilson. Results from the First Mathematics Assessment of the National Assessment of Educational Progress. Reston, Va.: National Council of Teachers of Mathematics, 1978.
Carpenter, Thomas, Mary K. Corbitt, Henry Kepner, Jr., Mary M. Lindquist, and Robert Reys. Results from the Second Mathematics Assessment of the National Assessment of Educational Progress. Reston, Va.: National Council of Teachers of Mathematics, 1981.
Conference Board of the Mathematical Sciences and National Advisory Committee on Mathematical Education. Overview and Analysis of School Mathematics Grades K–12. Washington, DC: Conference Board of the Mathematical Sciences, 1975.
Hembree, Ray, and Donald J. Dessart. "Research on Calculators in Mathematics Education." In Calculators in Mathematics Education, 1992 Yearbook of the National Council of Teachers of Mathematics (NCTM), James T. Fey, pp. 23-32. Reston, Va.: NCTM, 1992.
Kenney, Patricia, and Edward Silver, eds. Results from the Sixth Mathematics Assessment of the National Assessment of Educational Progress. Reston, Va.: National Council of Teachers of Mathematics, 1997.
Lindquist, Mary M., ed. Results from the Fourth Mathematics Assessment of the National Assessment of Educational Progress. Reston, Va.: National Council of Teachers of Mathematics, 1989.
Silver, Edward, and Patricia Kenney, eds. Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress. Reston, Va.: National Council of Teachers of Mathematics, 2000.
U.S. Department of Education. Office of Educational Research and Improvement. National Center for Education Statistics. The Nation's Report Card: Mathematics 2000, NCES 2001-517, by J.S. Braswell, A.D. Lutkus, W.S. Grigg, S.L. Santapau, B. Tay-Lim, and M. Johnson. Washington, DC: 2001.