Abstract:
The literature has noted that some mathematical analogs are more effective than others for the teaching of fractions. This study aimed to evaluate the efficacy of seven mathematical analogs commonly used in the teaching of the partitive quotient fraction construct. A sample of twelve purposively selected Year Three children were presented with partitioning (partitive quotient) tasks in a simulated restaurant setting where they assumed the roles of waiters and waitresses serving pizzas, pancakes, pikelets, icecream bars, apple pies and licorice straps to the customers. Clinical interviews, talk-aloud protocols and non-participant observations were conducted within an interpretative methodology incorporating the Hermeneutic Dialectic Circle. The educational efficacy of the analogs was evaluated according to: (i) ecological validity, (ii) abstraction-ability, and (iii) ease of partitioning. Great variance was found in the efficacy of the seven mathematical analogs. This has significant implications for the initial teaching/learning of the partitive quotient fraction construct.