A national or state curriculum can seem to be an obstacle to teachers wishing to introduce inquiry learning. A curriculum appears to close down a teacher’s options. In a 2010 survey in 12 EU countries, the most common reason maths teachers gave for not introducing inquiry was that "there is not enough time in the curriculum." Professor Raffaella Borasi in her book Learning Mathematics through Inquiry (1992) suggests that a rigid curriculum is incompatible with inquiry: "No fixed and established curriculum, however well constructed, could really respond to the needs of an instructional approach that stresses students’ independent learning" (p. 202). Open-ended inquiry, Borasi argues, requires extreme flexibility in terms of curriculum content and choices.

Flexibility was a feature of the curriculum at John Dewey’s Chicago Laboratory School, which evolved on an experimental basis in response to children’s changing interests. In Schools of Tomorrow (1915), John and Evelyn Dewey contrast their "organic curriculum" growing out of a child’s experience to a systematised and standardised curriculum that ignores the needs of individual children. However, they also praise the cross-curricular projects of Public School 45 in Indianapolis that infused the state curriculum with “intrinsic meaning and value”.

Even though the timetable hampers cross-curricular projects in most secondary (and even primary) schools today, dividing the day into separate subjects does not preclude inquiry. Indeed, the discipline of mathematics has partly developed though inquiry into its own representations, tools, forms of reasoning and language. As Artigue and Baptist acknowledge here, mathematics “creates its own objects and reality, and the questions raised by these objects have always been an essential motor of its development” (p. 5). In the same way, Inquiry Maths uses prompts internal to mathematics to generate inquiry.

Moreover, Inquiry Maths prompts are also internal to the mathematics curriculum in that they are designed to lead into pathways that are linked to national curricula. While they ‘cover’ prescribed content objectives, the order of that coverage, the time spent on different topics and the connections made between aspects of the curriculum are co-constructed with students. The order, time and connections evolve from the initial phase of questioning and noticing that students undertake when they first see the prompt. Thus, Inquiry Maths addresses the curriculum, but in a flexible way that promotes students' curiosity and initiative.