Emergent mathematics in a grade-two classroom: A search for complex relationships.

Abstract

In light of the organically interconnected relationships of learning mathematics, a theoretical heuristic was developed to exemplify the implications of the findings of the study. Called SEARCH, the heuristic highlighted learning mathematics as a synergistic relationship constituted by an interconnectedness among social, emotional, physical, and cognitive development, each of which requires a balanced consideration in order to pursue the epistemological, ontological, and methodological paradigmatic frameworks embedded in current mathematics reform agendas. SEARCH is an acronym that stands for Social Emancipation, Active Referencing, and Creative Heuristics. SEARCH also metaphorically implies that learning mathematics is a "search" - i.e., what learners do as they endeavor to make mathematical sense. At the same time, a "search" is what teachers do in making sense of the mathematics each student constructs. It is upon such a foundation that the implications for pedagogical change engendered in contemporary mathematics education reform perspectives have been addressed.

The study employed a multiple-methods ethnographic approach incorporating the use of action research and constant comparative models, and the development of grounded theory. The findings highlighted the reflexive complementarity of a mathematics program based in the theoretical perspectives of problem-centered learning, constructivism, and positive discipline. Furthermore, the study indicated that approaches to learning mathematics advocated by current reform agendas understate the significance of learning as being as much to do with control as it does with change.

This study investigated the emergence of relationships in a grade-two classroom constituted by the contemporaneous implementation of the three theoretical perspectives of (1) problem-centered learning, (2) constructivism, and (3) positive discipline. The study explored the organic interconnectedness, evolution and creative processes of learning mathematics framed by these three theoretical perspectives from a systems theory viewpoint. The study proceeded by accounting for the epistemological, ontological, methodological, and psychological characteristics reflected in a grade-two mathematics program addressing current reform agendas in mathematics education.

While the SEARCH heuristic endeavors to provide a paradigmatic framework for addressing current mathematics reform agendas, it brings to light the potential for tension in pedagogical pragmatism as teachers seek to locate themselves in and between "intervention" (qua behaviorist) approaches and "invention" (qua constructivist) perspectives.