Following these initial thoughts about questioning, I have found myself changing how I view questioning, from being about finding the 'right' question, to viewing it as a means of promoting useful ways of thinking mathematically.
The idea of using the same questions repeatedly as a means of scaffolding, before fading them away, seems as though it must be useful. I am no longer bombarding my students with questions, or re-phrasing questions multiple times to try and find the right words. I have found that by thinking more carefully about my questioning, I am more succinct in my interactions with students, and have reduced the range of questions that I ask down to a handful. I am at times able to hypothesise which questions might be useful for a given question in advance.
Of the three questions that I initially identified as being useful, I have identified practical variants of these questions that are similar, but not quite the same, in order to suit the problem at hand.
For example, sometimes the question "Of what is this an example?" can sometimes more usefully be stated as "What does this bring to mind for me?"
Sometimes the question "What do I know?" is well followed up with "... so I also know...", or "What is another way of writing/saying what I know?"
"Can I solve a simpler problem?" may often be more specifically stated as "Can I solve this problem if [whatever is causing difficulty] wasn't there?"
There are a couple more questions I identified today as being useful, including:
- "Is there a way I can get a sense of this unfamiliar [function, sequence...]?"
- "What are the key features of this [graph, expression, ...]?"
Too many questions can be overwhelming - five is too many, I think - but too few may not suit all situations. There is a balance to be struck.