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Brian Greer
Portland State University, US
Consider the way in which the National Council of Teachers of Mathematics (NCTM) begins its draft of Standards 2000. No Socrates-like character asks And shall we teach mathematics? Even if the answer is a preordained Of course, Socrates, asking the question raises a host of others: To whom shall we teach mathematics? For what ends? Mathematics of what sort? In what relation to studentss expressed needs? In what relation to our primary aims? And what are these aims?
(Noddings, 2003, p. 87).
Many answers to these questions have traditionally been, and continue to be, advanced the need to produce another generation of scholars to continue advancing the discipline of mathematics; the supply of a cadre of scientists and others such as engineers who need strong mathematical competence; as a training in logical thinking and problem solving; as part of cultural heritage as much as literature or music.
In the face of change, we need to avoid what Ubi D'Ambrosio calls "the trap of the same". Computers have changed the nature of mathematics. Technological developments have radically altered the flow of information and communication in our lives, and are creating simulated hyperrealities. The amount of systematized mathematics has increased hugely, with the result that designing a curriculum is no longer easy (if it ever was) and choices have to be made. Here is a provocative question does every student need to learn substantial amounts of mathematics (notably algebra), as is declared both possible and essential in many national documents? A short excerpt from an article by the mathematician Philip Davis, included below, questions this perceived wisdom.
Given that a small percentage of students will continue to high-level mathematics in their careers, it is appropriate to consider what might be a suitable mathematics education to prepare the majority of students for intellectual fulfillment and as future citizens. In this regard, it is surely essential to make students aware of the implications of mathematization in their societies. As argued by Gellert and Jablonka, there is a further aspect, which they label "demathematization", by which they mean the invisibility of the mathematics that has been incorporated into physical and cultural artefacts. For citizenship with critical agency, an understanding of the mechanisms and effects of these two processes is needed.
In the United States in particular, but by no means uniquely, there is more and more nationalistically phrased emphasis on the importance of mathematical training of a nation's students to maintain economic competitiveness (in the case of the US, global dominance). Such an attitude contrasts with the call by Ubi D'Ambrosio (2003) for mathematicians and mathematics educators to accept their ethical responsibilities for addressing the world's most universal problem, survival with dignity.
Within recent decades in mathematics education as a discipline there has been a fundamental shift to what may broadly be characterized as a humanistic view, manifested in numerous ways, including:
rejection of a Platonist conception of mathematics, in recognition that mathematics is a human activity
acknowledgement of cultural diversity within both academic mathematics and the diversity of other forms of mathematical practice, as emphasized in the Ethnomathematical perspective
a broadening of the influences on the field from the dominance of psychology to include a wide range of humanistic disciplines, and a related expansion of methodological tools
recognition that mathematics education is historically, culturally, socially, and politically situated
more weight in curricula on making connexions between school mathematics and people's lives. Munir Fasheh (2000, p. 5) declared that: " I cannot subscribe to a system that ignores the lives and ways of living of the social majorities in the world; a system that ignores their ways of living, knowing and making sense of the world."
teaching mathematical tools of modelling and data analysis that can be used to critique society
It is fitting at this international conference to consider the globalization of mathematics education, as discussed in the paper by Atweh. To highlight that there are exceptions to the tendency towards homogenization of curriculum and pedagogy, we consider the very special case of South Africa (see the paper by Graven and Venkat), where, following the gaining of freedom, a concerted effort has been made to design a mathematics curriculum for citizenship as well as for global competitiveness. Ths debate within South Africa exemplifies a tension evident in many post-colonial societies between teaching mathematics that valorizes diverse cultures and mathematical practices, and teaching mathematics for technical advance with the associated economic benefits.
The deliberations of scholars will remain academic if there is not a collective will to provide sufficient resources for schools, and, above all, teachers. The paper by Agudelo-Valderrama describes the situation in Colombia, but a broadly similar story could be told for many countries. We need to heed Freire's declaration (1987, p. 46):
This is a great discovery, education is politics! After that, when a teacher discovers that he or she is a politician, too, the teacher has to ask, What kind of politics am I doing in the classroom?"
However, as Apple (2000, p. 243) has pointed out:
It is unfortunate but true that there is not a long tradition within the mainstream of mathematics education of both critically and rigorously examining the connections between mathematics as an area of study and the larger relations of unequal economic, political, and cultural power.
The relationships between three aspects mathematics as a discipline, mathematics as a school subject, and mathematics as a part of people's lives need serious analysis. To promote their vision of what mathematics education should be for, mathematics educators need to engage politically.
References
Apple, M. W. (2000). Mathematics reform through conservative modernization? Standards, markets, and inequality in education. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 243-259). Westport, CT: Ablex.
D'Ambrosio, U. (2003). The role of mathematics in building up a democratic society. In Madison, B. L., & Steen, L. A. (Eds.), Quantitative literacy: Why numeracy matters for schools and colleges. Proceedings of National Forum on Quantitative Literacy, National Academy of Sciences, Washington, DC, December, 2001. Princeton, NJ: National Council on Education and the Disciplines. (http://www.maa.org/ql/qltoc.html)
Fasheh, M. (2000, September). The trouble with knowledge. Paper presented at: A global dialogue on "Building learning societies -- knowledge, information and human development. Hanover, Germany.
Freire, P. (with Shor, I.). (1987). A pedagogy for liberation. Westport, CT: Bergin & Garvey.
Noddings, N. (2003). Happiness and education [sic]. New York: Cambridge University Press.
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