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Encouraging reflective thought and action

Reflective thought and action is encouraged by questioning techniques that enable students to articulate their thinking. This includes encouraging
metacognition as well as building on students’ responses by rephrasing, adding and inviting further responses from other students.

Examples of teacher actions that encourage reflective thought and action for students:

- encouraging students to develop argumentation skills
- supporting students to explain and articulate their thinking
- engaging students in evaluating different methods and strategies
- getting students to justify, compare and contrast solutions
- probing student thinking
- allowing for individual thinking time
*(BES,* p. 68)
- encouraging students to fine-tune their mathematical and statistical thinking
- supporting students to develop coherent schema.

Key questions that teachers can use:

- What do you notice?
- What does this make you wonder?
- What is the same and what is different?
- How did you get that?
- How do you know that?
- How would you approach the problem?
- How can you simplify…?
- What steps are involved in…?
- What is another way…?
- What are the pluses and minuses of...?
- What would you think if...?
- How would you describe what you were thinking when...?
- How would you define…?
- What conclusions can you draw from…?
- Do you agree or disagree with…?
- How might you explain…?
- What patterns can you find…?
- If you were going to guess…?
- Why do you think I used this teaching strategy?
- How did this teaching strategy help you to learn?
- How might we have learnt this differently?

## Specific activities

## Further information

- Fraivillig, J., Murphy, L., Fuson, K. (1999).
Advancing children’s mathematical thinking in everyday mathematics classrooms.
*Journal for Research in Mathematics Education, *Vol. 30, no. 2, pp. 148-170.
- Anthony, G., & Walshaw, M. (2009). Tools and representations (pp. 23-24).
*Effective Pedagogy in Mathematics* (PDF 320 KB). Belley: Gonnet Imprimeur.
- Anthony, G., & Walshaw, M. (2007
*). **
Effective Pedagogy in Pāngarau/Mathematics: Best Evidence Synthesis Iteration (BES)**. *Wellington: Ministry of Education.

Last updated September 5, 2018

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