Structure and interpretation of computer programs
Structure and interpretation of computer programs
Understanding procedures as objects
Empirical studies of programmers: second workshop
Communications of the ACM - Special issue on computer augmented environments: back to the real world
Programmable applications: interpreter meets interface
ACM SIGCHI Bulletin
Creating polyhedral models by computer
Journal of Computers in Mathematics and Science Teaching
Building curricula to shape cognitive models: a case study of higher order procedures
Building curricula to shape cognitive models: a case study of higher order procedures
Exploring rules and underlying concepts while engaged with collaborative full-body games
Proceedings of the 9th International Conference on Interaction Design and Children
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Mathematical manipulatives---tangible objects with a pedagogical purpose---have become popular tools in mathematics education. But typically, the notion of a "manipulative" carries with it a number of additional assumptions: that these objects are designed for elementary (as opposed to advanced) mathematics instruction; that they have little in the way of emotional meaning for their users; and that they are relatively simple, "low-tech" objects. In this paper we challenge these assumptions. Drawing on our experiences in two related projects in educational computing, we suggest that manipulatives may be designed for advanced mathematical topics; that they may offer creative (and thus affectively important) opportunities for students; and that they may be designed in ways that accompany or incorporate computational media.