1) Do Mason's ideas connect with inquiry-based learning in secondary school mathematics? (And why or why not?)
2) How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?
After reading John Mason's article, I think his ideas connect with inquiry-based learning in the secondary math classroom. The majority of the questions that I had often heard from my high school teachers and ask students myself are in the category of "asking as telling" which directs student attention to easier and easier answers. This type of questioning is not very helpful for student to genuinely learn to think mathematically. I was impressed by how Mason articulates the form of "teaching by listening" in that the teacher is not listening for an expected answer but listening to student's thought process and how they might justify their answers. Eventually, students internalize the metacognitive-type of questions about their own solutions so that they are capable of thinking mathematically without the teacher's verbal prompts.
In my planning for long practicum, I will try to incorporate time to interacting with students during lessons. I will write in questions such as, "How do you know...?" and "Will that always be the case?" I want to encourage students to articulate what they understand rather than being fearful of responding incorrectly to my questions. For a formative or summative assessment task, I will have students construct and solve their own problems, even ones that will challenge their peers. As a teacher, I will model the mathematical thinking myself by not immediately asking funnel-oriented questions or supplying answers but asking, "What did you do yesterday when you were stuck?"
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