Seven steps to start an inquiry in maths
Last week I received an e-mail from a maths teacher who had looked over the Inquiry Maths website. She liked the ideas and wanted to carry out an inquiry: "The prompts look interesting and I can see how they could develop into inquiries, but how do I start?" The problem is that the inquiry classroom is so different from conventional maths lessons that it can seem difficult to visualise the inquiry process.
Another teacher has described using problem-solving tasks and structured investigations, but inquiry seems like "another step again." If students are setting the agenda through their questions and responses to the prompt, then teachers can become anxious about objectives and the pace of progress. Below I outline seven steps to start using the prompts on the Inquiry Maths website. The steps are meant as an adaptable framework contingent upon the progress of the inquiry, not as a rigid scaffold.
(1) Ignore content objectives in your planning; use process objectives only. Objectives could relate to students' ability to devise questions, to regulate their activity, and to justify and reason. Students will develop conceptual knowledge, but it can be a hindrance to have content objectives in mind before the inquiry starts.
(2) Choose a prompt that you would like to explore yourself (and explore it before the lesson). This is not so you can channel the inquiry into a preconceived direction, but rather to give you the opportunity to identify possible paths the inquiry might take.
(3) Prepare resources related to the prompt in case you want to close the inquiry down at any moment. If you want to use the regulatory cards, it is advisable to prepare resources anyway in case students select the card that says, for example, Practise a procedure. Knowing that resources are at hand can provide a feeling of security.
(4) Decide if you are going to teach students how to pose questions. Hand out an inquiry sheet with the prompt on so students can jot down questions and comments. You might decide to structure this phase of the inquiry with a whole-class discussion on the process of developing questions.

(5) Plan how students will communicate their questions and comments to the class. One way is to ask pairs to decide upon their best question or comment to feed back, which you record on the board. This should provide the class with enough material to start the inquiry. Allow students to "pass" if they have nothing new to add.
(6) Review the questions and statements. Look over the questions and statements with the class and classify them into groups of similar types or similar subject matter. Decide if any can be answered immediately, such as those that require a definition or a procedure that some students are able to demonstrate.
(7) Use the regulatory cards to decide what to do next. Aim to stop exploration of the prompt without first setting aims and deciding how the class will inquire. Note down the cards chosen on the board, asking students to justify their selections. Sometimes, the choice of cards allows you to run a unified class-wide inquiry; sometimes, the inquiry is diverse and multi-faceted. You decide based on the mathematical validity of the cards chosen.

Andrew Blair
April 2013