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Curricula that promote inquiry

The most explicit reference to inquiry occurs in the International Baccalaureate's curriculum. The IB Middle Years Programme (for students aged 11-16) promotes "both inquiry and application, helping students to develop problem solving techniques that transcend the discipline and that are useful in the world beyond school." It aims to ensure students understand the principles of mathematics and its use in modelling real-life situations. As the curriculum writers explain in a subject brief, the MYP is "tailored to the needs of students, seeking to intrigue and motivate them to want to learn" by studying authentic examples that are useful and relevant to their lives.
In the Rationale for the Australian F-10 Curriculum, the designers claim the curriculum "encourages teachers to help students become self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences." While there is currently no guidance about inquiry approaches, the Australian government launched the ReSolve: Maths by Inquiry project in November 2015 to develop classroom resources.
The second aim of the National Curriculum in England is to ensure that all students "reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language." Again, there is no guidance about how this might be achieved in classrooms. However, the use of 'enquiry' suggests the curriculum planners were thinking of short discrete tasks that encompassed one or two of the processes in the list, rather than sustained 'inquiry' that could potentially combine all the processes.