Cross-posted to @NWMaths
A classic ‘extension’ activity that Maths teachers often use is to ask students to create a question on a topic when they have finished their work. It’s an easy win for teachers; they keep students busy whilst supposedly ‘stretching and challenging’ them by encouraging them to work on the so-called higher order skills required to engage in the creative process.
Creating questions is usually a more difficult skill to master than answering them, particularly when you want a ‘nice’ answer to emerge. Think for instance about the knowledge and understanding required for creating a trigonometry question giving an integer answer compared with merely answering such a question.
However, I prefer to ask certain questions and give particular prompts in order to refine this process and move it away from a ‘keep them busy’ or box-checking activity and move it towards a learning activity. For instance: “what would an easy question on this topic look like?”, “why is question a harder/easier than question b?”, “what would you expect to see in a more difficult question?”. Students can then use these prompts to create easier, medium and harder questions. They are forced to engage with the material and considering the different difficulty involved in each question really develops their metacognitive skills.
Here are some examples of the work that my year 10 class carried out on rearranging formulae:
I was especially pleased with the ‘hard’ example on the far right hand side- putting the intended subject as the denominator was a subtle but important difficulty this student grasped.
The question “can you create an easy, a medium and a hard question on this topic?” is a useful and powerful way of refining the process of students creating questions.