Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…