Robert N. Carson

Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review of ethnomathematics

This paper is a critical review of the ethnomathematics literature and classifies ethnomathematics according to where it might stand in relation to the teaching of formal, academic mathematics. This paper investigates what it sees as four possibilities: ethnomathematics should replace academic mathematics, ethnomathematics should be a supplement to the mathematics curriculum, ethnomathematics should be used as a springboard for academic mathematics and ethnomathematics should be taken into consideration when preparing learning situations. We argue that it is only through the lens of formal, academic mathematics sensitive to cultural differences that the real value of the mathematics inherent in certain cultures and societies be understood and appreciated.

Science and the Ideals of Liberal Education

This article examines the influence of mathematics and science on theformation of culture. It then examines several definitions of liberaleducation, including the notion that languages and fields of study constitutethe substrate of articulate intelligence. Finally, it examines the linkagesbetween science, scientific culture, liberal education, and democracy, andproposes that science cannot be taught merely as a body of facts andtheories, but must be presented to students as integral with culturalstudies. The use of a contextualist approach to science education isrecommended.

Why Science Education Alone is Not Enough

Science did not come into existence independent of the other disciplines. It is one dimension of a complex culture. We err in attempting to theorize how best to teach it with little or no regard for the broader cultural matrix. How we have transformed our curriculum into its present fragmented condition is not difficult to trace. A reductionist and materialist orientation has resulted in a serious loss of coherence, of beauty, and of any real depth of meaning for the subjects we teach. In this paper, I will argue that the tendency to think of science and science education in isolation from a broad and intellectually noble cultural design is damaging, not only to the teaching of our culture in general, but also to the teaching of science. A substantial and fundamental reorientation is called for.

Our response to Adam, Alangui and Barton's ``A Comment on Rowlands & Carson `Where would Formal, Academic Mathematics stand in a Curriculum informed by Ethnomathematics? A Critical Review'''

We would like to begin by expressing our gratitude to Adam et al. (2003) for the time and effort they took to produce their comments on our article, “Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics?” (Rowlands and Carson, 2002). We do not believe that our aspirations for the education of children differ significantly from those of Adam et al. Both papers would seem to have clearly affirmed support for the dignity, uniqueness, and ingenuity of traditional and indigenous cultures, and to have expressed a clear intent to continue toward a rapprochement between the world’s standard canon of mathematics and the unique contributions one finds in the more localized forms of mathematics characteristic of traditional cultures. It is an encouraging sign of the times that our debate focuses on how best to serve the needs and interests of the children of traditional cultures and that traditional cultures are finally being understood as precious resources generally. Yet within that essentially noble set of understandings and purposes, there is room for reasonable and decent people to disagree. Our conversation does not involve simple problematics, by any means. In addition to purely mathematical issues, it involves questions of historical injury and of contemporary relationships between cultural groups whose core values are incommensurable. It is a topic that by its very nature can sometimes decay from patient reason to acrimony. Thus we wish to express our gratitude to Adam et al. for their informative and thought-provoking critique. We are disappointed with the analysis they gave, but we credit them with maintaining high standards of decorum in the process and for what we believe are honorable intentions. There is, perhaps, no more important or pressing social issue on the planet today than that of figuring out how peoples of varied cultural allegiances are to get along. Academics and educators have some part to play

A Taxonomy of Knowledge Types for Use in Curriculum Design

This article proposes the use of a taxonomy to help curriculum planners distinguish between different kinds of knowledge. Nine categories are suggested: empirical, rational, conventional, conceptual, cognitive process skills, psychomotor, affective, narrative, and received. Analyzing lessons into the sources of their resident knowledge helps the teacher proceed in a less dogmatic manner, distinguishing between categories of knowledge based upon where that knowledge originates. This taxonomy facilitates a meta-narrative on the nature of knowledge — how it is discovered, invented, decided upon, and so on — and the form that it takes in human experience and learning.