Big Ideas for Little People: Critical Thinking and Mathematical Concept Exploration in Elementary School

Date of Completion


Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson


An extended study of group theory was undertaken with a sixth-grade class to explore the integration of critical thinking and concept development in the mathematics curriculum. A supportive classroom environment was sustained through application of Cambourne's optimal conditions of learning and Gardner's theory of multiple intelligences. A belief in the power of play, elaborated by Armstrong and Duckworth, together with commitment to Vygotsky's distinction between 'scientific versus spontaneous' learning enabled a student-centered, active exploration of a "big idea." Big ideas were defined as: (1) concepts which are generalizable and can be explored and extended into a variety of contexts; (2) studies which begin with the intention to develop a concept; and, (3) concepts which continue to intrigue experts. Mathematical big ideas were seen as mathematical concepts which might involve application and computation, but in a broad context. It was concluded that critical thinking is what goes on naturally when learners are engaged in exploring big ideas in rich context which require and encourage substantial thinking. It is recommended that: (1) critical thinking be implemented in rich contexts, exploring big ideas; (2) classroom practice foster optimal conditions for learning; (3) multiple intelligences be recognized in classroom practice; (4) concept development be promoted through both scientific and spontaneous processes; (5) as much as one-half of the mathematics curriculum be organized around the exploration of big ideas; and (6) teachers be encouraged to trust their own practical knowledge in exploring big ideas which are also big to them.


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