Characteristics of Students Engaged in Spontaneous Problem-Posing

Abstract

Spontaneous problem posing is a basic concept of spontaneous mathematical thinking and science learning. Students generate problems without systematic encouragement and pose problems based on the student's desire to develop their skills. As a result, they can serve as important markers of constructive mathematical and science engagement, particularly affective engagement, for problem solvers and their classroom communities. We used a qualitative approach to analyze student characteristics, especially in the affective domain, when presenting random problems. We used an observational approach and experience sampling in each class to observe students' engagement in spontaneous problem posing both individually and in groups. The findings revealed that each student showed different characteristics when presenting problems suddenly (spontaneous problem posing). The submission of the first subject problem was categorized as problem-as-exercise, satisfying the characteristics of spontaneous originality, where constructive emotional experiences impressed more on the teacher, while negative emotional experiences impressed more on oneself (self), classmates, and mathematical activities. The submission of the second subject problem is classified as a problematic problem, fulfilling the characteristics of spontaneous originality. Negative emotional experiences are more visible in me (myself), while constructive emotional experiences are more visible in teachers, classmates, and math activities