The three worlds also say something about conceptual development (which is how Bruner used it, as apart of his initial attempts at a theory of instruction), but which has led to a certain dogma along the lines that learners must begin with concrete manipulation (a somewhat startling metaphor when examined closely!) before being able to work with images, diagrams and thoughts, leading eventually to expressing and formalising in symbols. Instead of stretching learners to work in their imagination and to become familiar with how symbols can become less 'symbolic' and more meaningfully enactive, learners are reinforced in a simplistic version of how to learn mathematics which leads to a preference for being told what to do (procedures and practices) rather than appreciating underlying reasoning and meaning.
© ATM 2008 ● No reproduction except for legitimate academic purposes ● firstname.lastname@example.org for permissions CONFERENCE JOINED-UP REFLECTIONS: PART 1
Pages to are hidden for
"JOINED-UP REFLECTIONS: PART 1"Please download to view full document