Tasks Involving Models, Tools and Representations: Making the Mathematics Explicit as We Build Tasks into Lessons

With teachers and students in Government and Catholic schools in three geographical clusters in Victoria, the Task Type and Mathematics Learning (TTML) project is investigating the best ways to use different types of mathematics tasks, particularly in Grades 5 to 8. The focus of this research is to describe in detail how the various task types contribute to mathematics learning, the features of successful exemplars of each type, constraints that teachers might experience and teacher actions that can best support students' learning. This article illustrates the process used early in the project in one of the clusters in which they used the Japanese lesson study model to explore the opportunities and constraints of using classroom tasks. Type 1 tasks involve the introduction to, or use of models, representations, tools, or explanations that elaborate or exemplify the mathematics. There is no attempt to link mathematics to its practical applications. An example of a Type 1 task, 'Colour-in Fractions', is provided.