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Abstract
Students participating in making mathematical connections leads to several encouraging outcomes, such as developing students’ conceptual understanding and promoting their recall of mathematical procedures. However, designing this kind of instruction is difficult for many teachers, especially novice teachers. There also remains a paucity of evidence for how teachers learn to design such instruction. In this dissertation, I conducted three studies that examined how prospective secondary mathematics teachers began to leverage and specialize the everyday practices of noticing and audience design to support students to make mathematical connections.In the first study, I examined what mathematical connections a cohort of 12 prospective secondary mathematics teachers noticed when working with secondary students in small-group instruction. Results indicated the prospective teachers attended to several kinds of connections. Further thematic analysis of the mathematical connections revealed five pedagogical considerations by prospective teachers, which led to the development of the Pedagogical Considerations of Mathematical Connections (PCMC) framework.
In the second study, I investigated how three secondary mathematics student teachers supported students to attend to, contribute, or provide reasoning for mathematical connections while they led whole-class discussions. In particular, I examined how the student teachers’ assessment of students’ expertise in the moment was evident in how they elicited, responded, facilitated, and extended students’ connection-making and reasoning. From the results, I argue that student teachers’ attention to students’ expertise in the moment mediated how the student teachers designed and coordinated their eliciting, responding, facilitating, and extending moves to support students’ participation in making connections.
In the third study, I observed how a secondary mathematics student teacher taught one lesson and then taught the same lesson again to a different class the next day. In the lesson, the student teacher intended students to make two mathematical connections through generalizing their mathematical activity. The comparison of the lesson implementations revealed that the student teacher made micro-adjustments in the second implementation to build and maintain common ground with students. By building and maintaining common ground, students were able to make the intended mathematical connections.