“Inquiry, or investigative approach in mathematics teaching offers challenges to stimulate mathematical thinking and creates opportunities for critical reflection on mathematical concepts” (Jaworski, 1994).
Inquiry dialog (Wells, 1999) has been seen as a way of increasing the quality of school mathematics, because inquiry tasks are usually challenging and cognitively demanding. In such environment students are encouraged to conjecture, debate the conjectures, search for explanations and proofs and discuss their preferences regarding different ways of solution (Yerushalmy et al., 1990).
References:
Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer Press.
Wells, G. (1999). Dialogic Inquiry: Towards a Sociocultural Practice and Theory of Education. Cambridge: University Press.
Yerushalmy, M., Chazan, D., & Gordon, M. (1990). Mathematical problem posing: Implications for facilitating student inquiry in classrooms. Instructional Science, 19 (3), 219–245.