The National Council of Teachers of Mathematics in Curriculum and Evaluation Standards for School Mathematics (NCTM Standards) proposed national standards defining what all children should know and do in their school development. [3] As teachers and students implement the standards, it may be useful to think of a model that acknowledges that learning is not linear and that the standards are interrelated. Building relationships and associations and applying fundamental ways of thinking and doing are key to constructing meaningful knowledge.
The Capacity Cube is a tool for helping to implement these standards. Its purpose is to focus on the interrelatedness of the standards and to frame the multidimensional aspects of mathematics instruction. The Capacity Cube (C3) is Georgia's way of representing how the three categories of learning are interrelated: The Habits of Mind, The Vehicles for Understanding and Doing, and the Big Ideas.
The C3 model highlights the mathematics that each student should under stand, appreciate, and be able to use in meaningful ways in school and in life. It is consistent with and supportive of the NCTM Standards, graphically organizing the knowledge and process areas so that fundamental connections and integrations are explicit.
Using the Capacity Cube (C3) Model
When applied to the implementation of the Learning Framework in school mathematics, the Capacity Cube model can ensure that students and teachers focus on higher-level reasoning, problem solving, and critical thinking - as well as content objectives. Learning activities should not attempt to isolate one cell or one dimension of the Capacity Cube, but should emphasize the relationships and interactions of the dimensions. While a lesson may be designed to emphasize reasoning in geometry using rubber band models, that same lesson will likely include communicating, patterns, measurement and scale, and perhaps, elements of trigonometry. This integrated approach will ensure that students are engaged in activities that are more than rote drill and practice, more than presentation of facts or rules.
The Habits of Mind of problem solving, communicating, reasoning, and making connections are ways of thinking about problems and real world situations that may be geometric, algebraic, arithmetic, or probabilistic.
The Vehicles for Understanding and Doing are meaningful ways to approach problems.
The Mathematical Big Ideas, are the culmination and refinement of mathematical thinking, and are ideas that will help students make sense of and operate in their current and future lives.
Students who are actively involved in effective learning begin to make relationships that create meaning and relevance in mathematics. When students learn to properly construct mathematical ideas, all three faces of the cube become actively involved.
