by Johnny W. Lott, NCTM President 2002-2004
NCTM News Bulletin, July/August 2002
NCTM's Principles and Standards for School Mathematics provides guidance for revisions to curriculum that go beyond those suggested by NCTM's 1989 Standards. Calls for reform and change in the school mathematics curriculum are not a new phenomenon. Throughout the past century, the message has been that a static mathematics curriculum is unhealthy.
At the beginning of the twentieth century, E. H. Moore in his 1902 valedictory address as president of the American Mathematical Society characterized both the school and the college curriculum as in need of change. His picture of mathematics included integration, manipulatives, group learning, and technology. Moore recognized the need for change because he saw a curriculum steeped in the algorithms of arithmetic as unconnected to the real world and not designed to be studied by all.
Throughout the ensuing decades, similar messages calling for change echoed the underlying premise that including theory in the curriculum would greatly increase both mathematics skills and understanding. In the last decade of the twentieth century, the NCTM Standards documents and reform curriculum projects have come closer to the changes proposed by Moore 100 years ago.
In all this time, mathematics curriculum has never evolved to a stage that anyone should call finished. Nonetheless, there have been segments of the mathematics community who wanted the curriculum to "go back" to an earlier era. Let us consider parts of earlier curricula.
Do we want elementary school students studying nothing but number, as in the 1907 Wentworth text entitled New Elementary Arithmetic, or number and measurement, as in the 1926 Knight, Studebaker, and Ruch textbook entitled Standard Service Arithmetics, Grade Three? Similarly, do we want high school students to study algebra from the Hawkes, Luby, and Touton book entitled First Course in Algebra (1910), in which variable and function are defined on page 259 of a 334-page book, or from a college text by Allendoerfer and Oakley entitled Fundamentals of Freshman Mathematics (1959) that has few applications?
Although these books may have been exemplary when they were written and may have contributed to the curriculum at the time, they are not books that would enable students to succeed in today's world. Simply put, both mathematics and the world have changed. To have an educated and mathematically literate populace in the future, mathematics curriculum must continue to evolve.
Today, students are entering a world that demands geometric knowledge with some understanding of a global positioning system, an understanding of pro bability and odds to make sense of lotteries, and capabilities in
data analysis to make sense of environmental problems, stock and money markets, and the mathematics found in the pages of USA Today. Even the mathematics of the 1980s did not prepare most students for today's challenges.
The reform curricula of the 1990s began addressing the perpetually changing nature of "everyday" mathematics, but are we at a place where we can finally say "We've finished" and relax? The answer is NO. We will never reach that place. As the world shrinks, the population becomes even more mobile, and worldwide communication teaches us that we do not live in isolation, we have to look beyond our borders both in a curricular sense and in a real sense if we want a mathematically literate citizenry. Trying to achieve a static curriculum or a curriculum from an earlier era is not an option.
What can we do? NCTM offered a good example for educators when it produced two sets of Standards—one in 1989 and the other in 2000. At the beginning of forthcoming decades, we must provide a snapshot of what we want students to study. As we do this, we need teachers in the classroom doing what they do best—educating the youth—and we need university professors educating prospective teachers for the future. This latter group has one of the greatest challenges—preparing those who will lead and teach a curriculum that is not yet written. We also need the general populace working with us, demanding that changes and updates continually be made in the mathematics curriculum.
As we plan the curriculum for coming decades, we must tap the best minds in mathematics, cognition, and interdisciplinary thought. We must involve people who are young and old as well as from a wide diversity of backgrounds and experiences. As we work, we must strive not to produce Edsels—models potentially way ahead of their time—but we must also strive not to produce decades of Volkswagens with no changes. The vision of mathematics education must be comparable to the original SST. It must give thought to future technology. It must be workable. And it may be ahead of its time. The production model for future decades should be of the Model T variety—useful and affordable, but never a complete vision for the future.
The possibility of reform should always be an option, whatever the model. We cannot afford to be so locked into the past that we miss the big picture of mathematics in the world around us. As the world continues to change, so must the mathematics curriculum.
Allendoerfer, Carl B., and Cletus O. Oakley. Fundamentals of Freshman Mathematics. New York: McGraw-Hill Book Co., 1959.
Hawkes, Herbert E., William A. Luby, and Frank C. Touton. First Course in Algebra. Boston: Ginn & Co., 1910.
Knight, F. B., J. W. Studebaker, and G. M. Ruch. Standard Service Arithmetics, Grade Three. Chicago: Scott, Foresman & Co., 1926.
Moore, Eliakim Hastings. "On the Foundations of Mathematics." Mathematics Teacher 60 (April 1967): 360-74. [Reprint of the 1902 address, first published in Science, 1903, and later included in A General Survey of Progress in the Last Twenty-five Years, First Yearbook of the National Council of Teachers of Mathematics, 1926.]
Wentworth, George. New Elementary Arithmetic. Boston: Ginn & Co., 1907.