Abstract
When students solve complex mathematical problems by themselves, it is possible for them to experience and encounter some difficulties, struggles, and tensions, through which they have the chance to learn to persevere through unsuccessful attempts and impasses and eventually to achieve the essential mathematical ideas that are required to solve the problems. The existing literature, however, lacks attention to (1) how teachers might effectively support and respond to struggling students’ varying needs and (2) the kinds of professional development that could increase teachers’ awareness of their students’ struggles and could help teachers to capitalize on those struggles for their students’ productive learning of mathematics. This study attempts to fill the gap in the literature by examining the relationship between classroom instruction and students’ learning outcomes.
Using the class-video data from a two-year randomized controlled trial of professional development called Cognitively Guided Instruction (CGI), this study examines the effects of CGI intervention on struggling students’ problem-solving scores and investigates the mediation effects of CGI intervention through interactional time and instructional practices on struggling students’ problem solving.
Struggling students in the CGI classrooms received, on average, more interactional time from their teachers and had higher problem-solving scores than their counterparts from the comparison classrooms. No grade and gender moderating effects were found on the impact of CGI intervention on students’ reception of interactional time and problem-solving performance. The mediation analyses showed that the interactional time and two instructional practices (for student agency support and for extending student thinking) positively impacted struggling students’ problem solving. Two additional instructional practices (supportive strategies and encouragement of learning through/from others) showed a negative and non-significant impact on struggling students’ problem solving.