Mathematical tasks: Clarification, classification and choice of

In this paper, the differences between mathematical tasks such as problem-solving tasks, investigative tasks, guided-discovery tasks, project work, real-life tasks, problem-posing tasks, open tasks and ill-structured tasks will be contrasted. Such clarification is important because it can affect how and what teachers teach since the diverse types of tasks have different pedagogical uses, and it can also help researchers to define more clearly the tasks that they are investigating on. A framework to characterise the openness of mathematical tasks based on task variables such as the goal, the method, the answer, scaffolding and extension will be described. The tasks are then classified according to their teaching purpose: mathematically-rich tasks, such as analytical tasks and synthesis tasks, can provide students with opportunities to learn new mathematics and to develop mathematical processes such as problem-solving strategies, analytical thinking, metacognition and creativity; and non-mathematically-rich tasks, such as procedural tasks, can only provide students with practice of procedures. Rich assessment tasks that teachers can use to assess students ’ conceptual understanding, mathematical communication and thinking processes will also be discussed. The clarification of terminologies and the classification of mathematical tasks will help teachers to understand more about the purpose and characteristics of the diverse types of tasks so that they can choose appropriate tasks to develop the different facets of their students ’ mental structures and to assess the various aspects of their learning