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Inquiry, I am not sure that one model is more beneficial to students than…
Inquiry
Guided inquiry
Students have greater ownership, and decide haow to tackle the inquiry set
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If the topic / question is selected carefully then this model can allow students to reflect on the benefits / disadvantages or research / analysis techniques
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Feedback is really important here to ensure that students are developing effective techniques and metacognative skills to be able to transition to open inquiry
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Structured Inquiry
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Would follow on from a few confirmation inquiries. Teacher guides the question, with students tackling the inquiry with minimal input
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confirmation inquiry :
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Results are known in advance - little new knowledge generated (apart from familiarity with techniques)
This feel like the kind of task that you would set as a maths investigation in year 7/8. Highly structured, and almost like a proof. Quite common - you have found a result now prove it: models geometric / algebraic methods that can be used in the 'higher order' inquiries
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I am not sure that one model is more beneficial to students than another.
I see a continuum where you move students from a confirmation / structured approach
in lower secondary towards guided / open in IBDP
All of the approaches are appropriate in maths, and it would depend on what I was trying to achieve with a given task. The trade off between introducing / practicing skills and high order thinking / metacognition