Opening mathematical problems for posing open mathematical tasks: what do teachers do and feel?

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical tasks available to teachers. Additionally, we encourage teachers to pose OTs by transforming textbook mathematical problems. In this paper, we analyze teachers' skills and affective conceptions related to posing OTs and using them in teaching. Forty-four teachers with different teaching experience (years of experience-YoE) and different levels of expertise participated in a 4-h workshop that introduced them to OTs and their categorization. They were also given a homework assignment: pose OTs and solve them to demonstrate their openness. This assignment was accompanied by a 5-point Likert scale questionnaire that examined teachers' affective conceptions about engaging and teaching with OTs. We drew distinctions between different types of OTs (TOTs) posed by the teachers and the problem posing strategies they used. We found that the types of tasks and strategies that teachers use are a function of teachers' experience in terms of both the level of mathematics taught and years of teaching. In the affective dimension, we found interesting connections between conceptions regarding the difficulty of posing OTs, conceptions regarding the suitability of OTs for teaching and learning, teachers' readiness to implement OTs in their classes, and their predictions regarding teachers' and students' problem-solving behaviors.