Manipulatives have been used in many mathematics classrooms across many age groups with the aim of helping students to understand abstract concepts through concrete, kinesthetic, and visual experiences. In this paper, after we provide a background for the use of physical and virtual manipulatives in teaching and learning of mathematics, we will…

The interoperability of educational systems, encouraged by the development of specifications, standards and tools related to the Semantic Web is limited to the exchange of information in domain and student models. High system interoperability requires that a common framework be defined that represents the functional essence of educational systems.…

Discusses multiple representations and multimedia learning environments; describes a functional taxonomy of MERs (multiple external representations); and considers how MERs are used to support cognitive processes in learning and problem solving with computers. (Contains 41 references.) (Author/LRW)

In this paper we describe the ways that SCoT, a Spoken Conversational Tutor, uses flexible and adaptive planning as well as multimodal task modeling to support the contextualization of learning in reflective dialogues. Past research on human tutoring has shown reflective discussions (discussions occurring after problem-solving) to be effective in…