Pedagogical, Mathematical, and Real-World Conceptual-Support Nets: A Model for Building Children's Multidigit Domain Knowledge

Abstract

A model of a conceptual-support net is exemplified in the domain of multidigit addition. This model can provide guidance in making curricular and classroom teaching choices about what kinds of conceptual supports to provide in a particular setting. An outline of a theory of children's multidigit conceptual structures and an analysis of classes of multidigit conceptual supports used in classrooms provide the background for the Conceptual-Support Net model. Issues of matches and mismatches among conceptual supports, solution methods, language of the learner, mathematics achievement level of the learner, and conceptual and procedural accessibility of various multidigit algorithms are then discussed. The presentation of the Conceptual-Support Net model specifies how this model differs from traditional instruction and from usual ways of using manipulatives in the classroom. Summaries of several different multidigit addition solution methods indicate how different quantity conceptual supports might facilitate different solutions. How to facilitate children's reflection and movement along developmental trajectories to more advanced and coherent numerical understandings and methods is then discussed. An overview of the importance of social processes in using conceptual support nets closes the paper.

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