Abstract
The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive category development, five types of activities (situation analysis, variation, generation, problem-solving, evaluation) were identified. These activities were coded in so-called episodes, allowing time-covering analyses of the observed processes. Recurring transitions between these episodes were observed, through which a descriptive phase model was derived. In addition, coding of the developed episode types was validated for its interrater agreement.
Highlights
In re mathematica ars proponendi quaestionem pluris facienda est quam solvendi. (Cantor, 1867, p. 26) Transl.: In mathematics, the art of posing a question is of greater value than solving it.In his statement, Cantor emphasizes the importance of the ability to pose substantial questions within mathematics
Problem posing is considered a central activity of mathematics (Hadamard, 1945; Halmos, 1980), and at the latest since the 1980s (Brown & Walter, 1983; Butts, 1980; Kilpatrick, 1987), it is being investigated with growing interest by mathematics education researchers
The research goal of this study is to develop a descriptive phase model for problem-posing activities based on structured situations
Summary
26) Transl.: In mathematics, the art of posing a question is of greater value than solving it. In his statement, Cantor emphasizes the importance of the ability to pose substantial questions within mathematics. Since the 1990s, it has been widely used to identify or assess mathematical creativity and abilities (Silver, 1994, 1997; Singer & Voica, 2015; Van Harpen & Sriraman, 2013; Yuan & Sriraman, 2011). A strong product orientation within research on problem posing is noticeable (Bonotto, 2013; Singer et al, 2017; Van Harpen & Sriraman, 2013); that is,
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
