Maths Extending Prompts Explanation

 Enabling Prompts

Students are more likely to feel fully part of the class if teachers offer enabling prompts to allow those experiencing difficulty to engage in active experiences related to the initial goal task, rather than, for example, requiring such students to listen to additional explanations, or assuming that they will pursue goals substantially different from those of the rest of the class. 

The choice of appropriate enabling prompts is based on factors that may contribute to the complexity of a task. This complexity might be a result of the number of steps involved, the modes of communicating responses, the degree of abstraction or visualisation required, or even just the size of the numbers to be manipulated. 

It may not be clear which aspects may be contributing to a particular student’s difficulty, but by anticipating some of the factors, and preparing prompts that, for example, reduce the required number of steps, simplify the modes of representing results, make the task more concrete, or reduce the size of the numbers involved, the teacher can explore ways to give the student access to the task without the students being directed towards a particular solution strategy for the original task.

Extending Prompts 

A further planning aspect relates to anticipating that some students may complete the planned tasks quickly, and can be posed supplementary tasks that extend their thinking on that task. One of the characteristics of open-ended tasks is that they create opportunities for extension of mathematical thinking, since students can explore a range of options as well as consider forms of generalised response. The challenge for teachers is to pose prompts that extend students’ thinking in a way that does not make them feel that they are getting more of the same or being punished for completing the earlier work. They could be offered, for example, an interesting exploration or puzzle that varies the tasks contextually, that extends it mathematically in terms of proving the completeness of a set of answers or finding ways to generalise the result by describing many responses. In practice it is arguable that this is the most important and challenging of these planning steps. The key premise is that the class progresses more or less together through the lesson contributing to the sense of communal experience. Unless creative opportunities are provided for the students who have completed the tasks along the way then not only might they be bored, and so create difficulties for the teacher, but also they might not be using their time effectively or have their mathematical capabilities used to the full