The flags prompt (right) does not feature a real flag – national or otherwise. This is very deliberate. Flags can generate debate that detracts from mathematical inquiry, leading students to argue over the nation represented or, in some cases, drawing them into emotional or political reactions. More widely, the associations that students can attach to real-life contexts might even obstruct the emergence of a mathematical understanding. As Bert van Oers says in an important paper: "It is inconceivable how the higher, abstract levels of mathematical thinking can be based on real-life situations."^{1}

There are two separate ways that real life is introduced into classrooms of mathematical inquiry. In the first way, an imaginary real-life context is used as the starting point of inquiry (such as pretending to be responsible for an initiative as a member of a company or institution). This leads to problems when students attempt to fit the hypothetical context into their everyday experience. In one study, for example, children tried to understand a bus journey mentioned in a test question by replacing it with an actual journey they had made. As Alan Schoenfeld says in this paper, real life is used in maths classrooms as a meaningless "cover story for arithmetic."

In the second way, mathematical inquiry originates in the student’s actual life experiences. Dewey argued that the inquiry process has no meaning for children unless they use materials and resources that are familiar everyday objects. However, educators have expressed concerns that mathematics "cannot be learnt directly from the everyday environment"^{2}, particularly abstract concepts. Students might develop arithmetic fluency in concrete settings, but the use of formal algebra derives from de-contextualised situations.

For that reason, the prompts on this website are designed to be as devoid of context as possible - “less to them, more in them” as one Inquiry Maths teacher commented. Each one aims to encourage students to apply their existing and new knowledge to 'fill' the prompt with meaning. In this way, students create a context of inquirythat is far more meaningful because it originates and develops through their own ideas and activity. In the case of the flags prompt, students might move on to investigate actual flags once they have learned to pose mathematical questions unhindered by real-life associations.

Andrew Blair December 2013

1. Van Oers, B. (2001). Educational Forms of Initiation in Mathematical Culture. Educational Studies in Mathematics, 46(1-3), p. 64 2. Skemp, R. R. (1971). The Psychology of Learning Mathematics. Harmondsworth: Penguin Books. p. 32