1. Orientation to the prompt: question, notice and wonder

The teacher invites pairs of students to make an observation or pose a question about the prompt, providing the class with stems (examples below) if appropriate. (Find more question stems to promote mathematical thinking here.)

2. Establish aims and plan actions

The teacher reviews the questions and observations (perhaps 'thinking aloud') and might take the opportunity to comment on possible lines the inquiry. Students participate in directing the inquiry by selecting a regulatory card- a selection that is then justified in a class discussion.

3. Exploration

Students might decide on a period of exploration when they aim to generate more examples, find a case that satisfies the condition in the prompt or test a conjecture. At the end of this period, students might have formed a generalisation through an inductive process of pattern-spotting.

4. Teacher or student explanation

Students might identify an impasse that can only be overcome with new conceptual or procedural knowledge. Their request for an explanation might lead to a whole-class episode when knowledge is shared or constructed collaboratively. Alternatively, the teacher might encourage small-group instruction (led by the teacher or a student).

5. Reason and prove

Students prove a generalisation they have made earlier in the inquiry. They reason deductively, perhaps with formal algebra or through a structural analysis of a mathematical model.

6. Present results

Students present their results in written or other forms. The teacher often calls on students to present their work in progress or suggest new ideas and directions to the class.

7. Reflect and evaluate

The teacher leads students in reflecting on the course of the inquiry, and in evaluating how successfully the class has resolved the questions posed at the beginning.

Science Activities at Partners' Schools