The Residual Set of a Complex on a Manifold and Related by Lefschetz S.

By Lefschetz S.

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A fundamental consideration is which knowledge interests are being served. Using a Habermasian framework (Habermas, 1963/1974), it could be argued that many official reports and semi- or fully-funded programmes are serving primarily technical or instrumental, manipulative interests, and practical or hermeneutic, communicative interests. Adults are to develop the instrumental skills, confidence, and competence to function effectively in the workplace, the home, and society — as producers and consumers of commodities and/or information.

Mathematics is, I think, quark-like for most people — difficult to grasp and certainly strange. But we are unlikely to understand how to make it useful until we acknowledge and use its truth, its beauty, and its charm. (p. 136) WHAT COUNTS AS MATHEMATICS?

Importantly it must be remembered that education as means of contributing to social and economic change does not and cannot exist in isolation from political decision-making. Yet it appears to be the case that the discourses concerning Australian school mathematics education (Ellerton & Clements, 1994), as in the VET sector, often hide the underlying complex nexus of political and economic power and resources. ’ Apple argues that this reduction in the complexity of the issues becomes an aspect of cultural reproduction — not as a conspiracy but as “a ‘logical necessity’ for the continued maintenance of an unequal social order” (p.

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