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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.

The purpose of this paper is to advance the team dynamics and group development literatures by developing and testing a theoretical model of how affect shapes transitions in teams over time. Integrating the group transitions literature with theory and research on the mood-as-input theory, I propose that shared team mood influences the extent to which team members seek out and experiment with alternative ways of completing their work at different points in a team's life. In the first half of the team's life, when team members are relatively task-focused, I argue that team positive mood (i.e., a positively valenced affective state shared by team members at a given point in time) stimulates, whereas team negative mood (i.e., a negatively valenced affective state shared by team members) suppresses, exploratory search. At the temporal midpoint, however, when team members' focus on performance heightens, team positive mood acts as a shutoff switch for search, leading to a decline in exploratory search over the second half of the team's life. Team negative mood at the midpoint, on the other hand, leads team members to persist in exploratory search, even as a deadline draws near. A team's trajectory of exploratory search over time, I propose, influences team performance such that it is highest when teams engage in high exploratory search early in the team's life and decline in exploratory search over the second half of the team's life. The results of a longitudinal, survey-based study of teams preparing for a military competition largely support my predictions. [ABSTRACT FROM AUTHOR]