1. John Mason's questioning philosophy certainly aligns with those of inquiry-based learning. Instead of funnelling the questioning into eventually guessing what's on the teacher's mind, encouraging them to instead disclose what comes to mind inverts the funnel/allows the discussion to enter new realms. Mason had his students develop resilience and resourcefulness through experiencing various challenges so that they "will know what to do when they don't know what to do". This is precisely what inquiry-based learning preaches: the meta-cognitive process.
2. I am an advocate of creative thinking when I teach, so I will definitely try to incorporate many forms of questioning in my classes. I will be sure to change it up so that students do not become dependent on you asking the same thing repeatedly whenever a stumbling block is reached. As mathematics is all about making and justifying conjectures, asking how many ways can you find the answer versus simply finding the answer promotes creativity and gives students who approach problems differently a chance to provide their input (instead of the answer, an answer). To discourage rote memorization, ask how do you know this and have them justify their answer. Inquire about not just the question at hand, but special cases (will that always be the case/when might that be the case), shortcuts, generalizations, elegance, increased/decreased number of constraints, etc... Being wary of student answers that are actually questions when they ostensibly appear as answers (teaching by listening) is something that I will need to practice. Lastly, moderate the frequency and duration of interventions depending on the skill level/dynamics of the classroom.
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