Mathematical inquiry is a process in which students respond to ill-structured, open-ended questions that reflect the authentic problems we encounter in 'real' life. This is unlike most problems we teach in mathematics, which are well-structured and close-ended. An open-ended ill-structured question has no single correct answer. It contains ambiguities in the problem or in the process of solving the problem that require students to make a number of decisions. This means that the emphasis is on the reasoning, judgements and evidence students provide rather than just on the answer (see Developing good inquiry questions on p 15).

The study we report on explores how primary children (aged 8-9) working on an inquiry-based problem draw on Game 1 and Game 2 reasoning about samples and processes (populations or mechanisms) in developing statistical arguments.

As this study is in an exploratory phase, our immediate aim is to build a foundation from which we can identify potential pathways for future research in inquiry-based statistical argumentation. In light of the theme of SRTL, we focus on three key questions:

1. To what extent does Makar & Rubin's (2009) inferential framework assist in identifying which game(s) students are playing as they conduct data-based inquiry?

2. What opportunities emerge for supporting students to stay in the [appropriate] game, when a particular pedagogical emphasis is placed on evidence in inquiry (Fielding-Wells, 2010)?

3. What role does the problem purpose play (Allmond & Makar, 2010) to assist or distract students from working in the appropriate game?

Mathematical inquiry is a process in which students respond to ill-structured, open-ended questions that reflect the authentic problems we encounter in 'real' life. This is unlike most problems we teach in mathematics, which are well-structured and close-ended. An open-ended ill-structured question has no single correct answer. It contains ambiguities in the problem or in the process of solving the problem that require students to make a number of decisions. This means that the emphasis is on the reasoning, judgements and evidence students provide rather than just on the answer (see Developing good inquiry questions on p 15).

Mathematical inquiry is a process in which students respond to ill-structured, open-ended questions that reflect the authentic problems we encounter in 'real' life. This is unlike most problems we teach in mathematics, which are well-structured and close-ended. An open-ended ill-structured question has no single correct answer. It contains ambiguities in the problem or in the process of solving the problem that require students to make a number of decisions. This means that the emphasis is on the reasoning, judgements and evidence students provide rather than just on the answer (see Developing good inquiry questions on p 15).

1. What shared and unshared perspectives do we have of mathematical inquiry?
2. What are purposes of mathematical inquiry?
3. How can mathematical inquiry be used to assess learning?
4. What signature practices characterise inquiry pedagogy in mathematics education?
5. How is mathematical inquiry similar to or different from inquiry in other content areas, such as science
6. How does the teaching of mathematical inquiry fit into the broader repertoire of pedagogies used by teachers in the course of a year?
7. What challenges do teachers and students face in adopting mathematical inquiry?
8. Does an inquiry approach benefit children with different backgrounds differently?
9. What are key benefits and drawbacks of learning mathematics through inquiry?
10. Do particular strands of mathematics fit better with inquiry?
11. Does mathematical inquiry improve learning in mathematics?
12. Is mathematical inquiry scalable?
13. How can different paradigms contribute to a diversity of insights into mathematical inquiry?
14. What key research areas are strongly tied to mathematical inquiry (e.g., argumentation, socio-mathematical norms, collaboration)?
15. What are possible programs of research for mathematical inquiry?