Rethinking Problem-Posing Situations: A Review

ABSTRACT

In research on mathematical problem posing, a broad spectrum of different situations is used to induce the activity of posing problems. This review aims at characterizing these so-called problem-posing situations by conducting three consecutive analyses: (1) By analyzing the openness of potential problem-posing situations, the concept of “mathematical posing” is concretized. (2) The problem-posing situations are assigned to the categories free, semi-structured, and structured by Stoyanova and Ellerton to illustrate the distribution of situations used in research. (3) Finally, the initial problems of the structured problem-posing situations are analyzed with regard to whether they are routine or non-routine problems. These analyses are conducted on 271 potential problem-posing situations from 241 systematically gathered articles on problem posing. The purpose of this review is to provide a framework for the identification of differences between problem-posing situations.

KEYWORDS:

• Problem posing
• problem-posing situations
• review

Notes

¹ Name of the journals and their founding year: Educational Studies in Mathematics (from 1969), Journal for Research in Mathematics Education (from 1970), For the Learning of Mathematics (from 1980), Journal of Mathematical Behavior (from 1980), Journal of Mathematics Teacher Education (from 1998), Mathematical Thinking and Learning (from 1999), ZDM Mathematics Education (from 1997), International Journal of Mathematical Education in Science and Technology (from 1970), International Journal of Science and Mathematics Education (from 2003), Mathematics Education Research Journal (from 1989), and Research in Mathematics Education (from 1999). These journals are identical to the eleven top-ranked journals in mathematics education research from the opinion-based study by Williams and Leatham (2017, p. 390).