At the heart of a democratic society is the ability of citizens to participate. This in turn depends not merely on the rights formally afforded by law, but on citizens' access to tools -- in our age, increasingly these are informational as well as legal -- and their capacity to interpret, understand, and analyze such information, as well as to effectively communicate information, ideas, and concepts.

Given the increasingly dominant role of technology and information in society, the centrality of what has been termed "quantitative literacy" or "numeracy" for a democratic (or indeed, functioning) society has gained attention. Verbal literacy has long been recognized as protective of the democratic fabric of society and today quantitative literacy plays a similar role; its achievement by the public is tested by whether citizens are able to "naturally use appropriate [quantitative] skills" in varied contexts (Steen, 1999).

This social framework ties together many issues in K-12 education, while providing a broader perspective with which to view such issues. If "the determination of what should be taught is a social and political enterprise..[which] cannot be neutral" (Cole, 1999), this is all the more true when one discusses how it should be taught. Rather than mourn this lack of neutrality, it is properly seen as an opportunity for society to openly discuss what constitute our educational goals and values.

The goal of nurturing students' capacities for the independent, creative thinking demanded by both industrial and civic society, and the need to function as an adapting, lifelong learner in an ever more complex world, fit hand in glove with the constructivist paradigm of human beings who are not empty vessels to be filled with knowledge, but creative agents who construct their own mental models and meanings. Producing adults who can only regurgitate memorized facts, or only perform tasks amenable to a set of learned skills which is forever fixed, is no longer "just" a loss to the individual's self-empowerment and to the democratic enterprise, but is also inadequate given the demands of the modern workplace.

This is a far cry from the educational methods and philosophies of the past, whose transformation is far from complete: "It is, in fact, nothing short of a miracle that [present] methods of instruction have not yet entirely strangled the holy curiosity of inquiry; for this delicate little plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wrack and ruin without fail." Rather than memorization of facts, the nurturing of human beings who are independent thinkers is the key: "It is not so very important for a person to learn facts. For that he [sic] does not really need [schooling]. He can learn them from books. The value of an education..is not the learning of many facts but the training of the mind to think something that cannot be learned from textbooks" (Einstein). In other words, the fostering of such capacities as independent thinking, creativity, and problem-solving skills.

In fact, it has been suggested that the NCTM Standards, and earlier work dating back to Dewey (perhaps the earliest to suggest the metaphor that education should be more like helping a flower grow rather than filling a vessel with water) are today increasingly relevant, and more likely to succeed, precisely because of these connections, and the needs of an information society which expects workers to regularly solve problems they have not previously encountered (Fleishman).

Additional connections can be drawn between the desired qualities of independent learning and adaptive problem-solving, and key areas of curricular and pedagogical reform in mathematics and the natural sciences. For example, the increased emphasis on multiple representations and perspectives, as well as the development of general purpose problem-solving skills.

What turned me into a believer in cooperative (or "collaborative") learning were the remarkable successes in terms of both student learning and my students' attitudes which I observed when I first began to implement such reforms in my courses at Cornell. Similarly, my use of long-term written projects and oral presentations expanded into a wider spectrum of assignments emphasizing communication -- a spectrum which now includes expository research papers and weekly "cover sheet" writing assignments -- precisely and simply because they worked, that is, due to the valuable introspection by students, and the student-teacher dialogue I discovered could be fostered by incorporating such activities.

This pragmatic criterion -- "does it enhance students' learning experiences?" -- is certainly not to be overlooked when educational issues are viewed within the broader social framework: it must be the cornerstone of educational policy discussions, and should be in harmony with the social, democratic, economic, and moral needs of society embodied in the broader framework.

Yet these important strands in the ongoing process of mathematics education reform, that is, written and oral communication skills and cooperative groupwork, while passing the Pragmatic Criterion, are also intimately related to the moral vision of education for democracy and the empowerment of the creative spirit of the individual. How else to educate today's children, who will find themselves in an increasingly diverse, multi-cultural, global, and information-linked "small" world?

What about technology? Properly used, it can substantially enhance the learning process, while at the same time helping prepare students for a world in which technology touches almost every facet of life. What is appropriate use of technology? It is easier to see what technology should not be: an assembly-line method for churning out all tests in multiple-choice format, or a gee-whiz form of edu-tainment, encouraging a passive observer role for students who follow a string of instructions.

What roles should technology play? For teachers, it should be a tool helping us bring mathematical ideas to life -- not just computationally, but also visually and dynamically. For students, it should foster empowerment by providing new ways to enable discovery, exploration, collaboration, and two- or multi-lateral communication.

Most exciting in mathematics education specifically is technology's ability to play the role of a "virtual laboratory", akin to the laboratory equipment available in the natural sciences. It is the extent to which we can expand and fully realize this potential for technology to bring the laboratory experience to mathematics that may ultimately determine its long-term success, both pedagogically, and in fostering the individual and collective capacities for creativity and exploration, for independence and collaborative abilities, crucial for living in a complex global environment and for contributing to a democratic society.

Thus the broader social framework of education for democracy is deeply connected to the themes and issues in mathematics education today. As we enter the next century and millennium it is perhaps worth reminding ourselves of the intimate connections between education and democracy, between how we teach and how students learn, and the social and moral responsibilities for the common good of humankind if we are to face the considerable challenges that lie ahead. Much the same lessons are echoed in these words by a thinker not usually quoted on matters of education:

"The aim [of education] must be the training of independently acting and thinking individuals who, however, see in the service to the community their highest life achievement" (Einstein).

References

Cole, Nancy S., "Determining What Is To Be Taught: The Role of Assessment," Mathematics Education Dialogues, April 1999, National Council of Teachers of Mathematics.

Einstein, Albert, various sources cited in "The Quotable Einstein," ed. Alice Calaprice, Princeton University Press, 1996.

Fleishman, Bernard A., "John Dewey, The Math and Science Standards and the Workplace," Humanistic Mathematics Network Journal #16.