Mini-Singularities and Learning Math
Human intelligence and computer intelligence are quite different. It is, however, common to think of a computer as a “brain” and to compare its intelligence-like capabilities to that of humans.
In the computer field, the term singularity is used in talking about the (potential, future) time when computers become more intelligent than humans. Recently I’ve written about mini-singularities—the situation in which a computer becomes much more capable than a human in a limited area. A six-function calculator satisfies my definition. More sophisticated examples are provided by a search engine such as Google, and by a graphing, equation-solving calculator.
Math educators have long made use of manipulatives such as a geoboard or number frame. These are available as physical manipulatives or as virtual manipulativesand as virtual manipulatives (including free MLC apps). A virtual manipulative is a type of mini-singularity. Its built-in “intelligence” gives it some distinct advantages over a physical manipulative.
A similar observation holds for computerized flash cards. Computer-based adaptive drill-and-practice programs that adjust to a student’s responses and incorporate relevant aspects of learning theory are now better than “old fashioned” paper/cardboard flash cards—and also better than human teachers in many situations. For example, a sophisticated modern computerized flash card system can display video, audio, and text (in many languages). It can receive and process keyboard, touchscreen, and voice input. It can keep cumulative records of a student’s performance, both over the time of a session and over a sequence of sessions.
How are you and your school handling the steadily increasing capabilities of adaptive learning systems such as the one described above, or of smartphones, tablets, and laptops? Each of these is a type of mini-singularity that even quite young students are learning to use.
If the topic intrigues you, you may be interested in these recent posts:
Technology-based mini-singularities
Education for the coming technological singularity
David Moursund is an MLC founder and current MLC board member, Professor Emeritus of the University of Oregon’s College of Education, founder of the International Society for Technology in Education (ISTE), and founder of the nonprofit company Information Age Education.
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