This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and employing them that reflect their appropriation to contrasting practices of mathematics teaching. Second, it examines the cultural process of instrumental evolution in which mathematical frameworks and teaching practices are adapted in response to new possibilities created by these tools, showing that such evolution remains at a relatively early stage. Third, it points to crucial prerequisites, at both classroom and systemic levels, for effective institutional adoption of such tools: explicit recognition of the interplay between the development of instrumental and mathematical knowledge, including the establishment of a recognized repertoire of tool-mediated mathematical techniques supported by appropriate discourses of explanation and justification.
New ideas for handling of loop and angular integrals in D-dimensions in QCD
