Spurred by Kilpatrick’s (1987) “Where do good problems come from?”, this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser’s attention and “triggers off” a mathematical re-action, one of the outcomes of which is a creation of a problem that gets accepted to some mathematics competition. The data were collected from 26 problem posers residing in nine countries, and who had experience in creating problems for national, regional, and international competitions. Three types of triggers emerged from the analysis: (i) Instances where the participants extracted mathematical phenomena from activities that are replete with modern elementary mathematics. These triggers were described in emotionally loaded terms that resonated with appreciation, surprise, challenge, and feeling of innovation. (ii) Cases where the participants abstracted mathematical phenomena from common everyday-life tasks in which mathematical optimization was beneficial. These situations emphasized participants’ desire to compensate for self-disappointment with an initially made decision and the value of finding a better alternative. (iii) Situations where the participants were asked to pose a problem ‘here and now’. The posers were unanimous in their dislike of such situations. They elaborated on how difficult it is to pose ‘here and now’ and highlighted the low quality of the resulting problems. The findings are situated in the body of knowledge on expert problem posing and educational literature on school students and teachers.

中文翻译：

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问题引发或数学竞赛问题从何而来？

受 Kilpatrick (1987) 的“好问题从何而来？”的启发，本研究探讨了有经验的问题提出者在数学竞赛中提出问题的触发因素。触发器被认为是注意的实例，在这种情况下，冲动会引起装腔作势者的注意并“触发”数学反应，其结果之一是创建一个被某些数学竞赛接受的问题。这些数据是从居住在 9 个国家的 26 名问题提出者那里收集的，他们有为国家、地区和国际比赛创造问题的经验。分析中出现了三种类型的触发因素： (i) 参与者从充满现代基础数学的活动中提取数学现象的实例。这些触发因素是用情感丰富的术语来描述的，与欣赏、惊喜、挑战和创新感产生共鸣。(ii) 参与者从数学优化有益的常见日常生活任务中提取数学现象的案例。这些情况强调了参与者希望通过最初做出的决定来弥补自我失望以及寻找更好选择的价值。(iii) 要求参与者“此时此地”提出问题的情况。装腔作势者一致反对这种情况。他们详细阐述了“此时此地”的姿势有多困难，并强调了由此产生的问题的低质量。