An investigation of two engagement structures in middle school mathematics classrooms

Abstract

Engagement and motivation have become increasingly important to mathematics education, particularly as concern about the educational success of students in the US grows. As a way to describe the patterns cognitive, behavioral, and affective engagement of students, Goldin, Epstein, Warner, and Schorr developed the theoretical concept of engagement structures. Engagement structures are idealized, recurring highly dynamic affective patterns inferred from behavior. This study focuses on characterizing two of these patterns of behavior: Let Me Teach You and Look How Smart I Am in the context of urban middle-school students working on a conceptually challenging problem. These structures were selected because they both are likely to focus on the mathematical content as well as require interaction between students. This dissertation reports on a qualitative study with video and audio data as well as survey responses of 55 seventh- and eighth-grade students in four classes in a large urban school district in NJ. These students worked in small groups on the same task. The students’ survey responses were compared to the findings based on the audio and video analysis. The results indicate that students appear to help one another and are often, though not always, willing to accept help from classmates. Students who attempt to impress others in some way may be trying to prove they are smarter than others or may wish to be perceived at least as smart as their classmates. Behavioral features for each engagement structure emerged from the data and describe the different behaviors that seem to be in service of the same goal. The features associated with the LMTY structure are: 1) teaching to clarify, 2) teaching procedures, 3) teaching or explaining strategies, and 4) checking for understanding. The features associated with the LHSIA structure are: 1) expressing an idea, 2) stating an answer or answers, 3) correcting others, 4) stating, “I’m smart,” or “We’re smart,” 5) keeping up with others in the group. This study, an initial investigation of two patterns of engagement, contributes to a goal of better understanding the complexity of “in the moment” engagement in the mathematics classroom.

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