Interference in the learning of circuit theory

Commonly introductory texts on circuit theory present in tandem the loop and node formulations of the equilibrium equations, and show how these relate to each other through the duality principle. Whereas this approach understandably appeals to those already well versed in basic definitions (voltage, current, impedance, admittance, etc.), evidence exists that the early undergraduate is confused by this approach. Trying to learn at one time multiple concepts that are so very similar in some ways, but different in others, appears to increase the conceptual difficulty of the material rather strikingly. This paper reports two experiments with college sophomores. Both show that intermingling of dual concepts leads to serious interference in learning. It is suggested that students should master thoroughly one set of principles for solving circuit problems before the dual set is presented. This suggestion conforms with the approach exemplified by the older texts on circuit theory.