Higher order thinking skills are inevitably developed or exercised relative to some discipline. The discipline may be formal or informal, may or may not be represented in a school curriculum, or relate to a wide variety of domains. Moreover, the development or exercise of thinking skills may take place at differing levels of generality. This paper is concerned with how new uses of information technology can profoundly influence the acquisition and application of higher order thinking skills in or near the domain of mathematics. It concentrates on aspects of mathematics that relate to its representational function based on the beliefs that: (1) mathematics itself, as a tool of thought and communication, is essentially representational in nature, and (2) information technology will have its greatest impact in transforming the meaning of what it means to learn and use mathematics by providing access to new forms of representation as well as providing simultaneous access to multiple, linked representations. This report describes a few examples of novel software environments from the representation perspective, points to more novel approaches to curriculum reform in mathematics that will encourage the cultivation of higher order thinking skills and relates these to unresolved research questions and educational policy issues. (CW)