From noticing to knowledge : an analysis of teacher noticing and professional knowledge in one-on-one mathematics tutoring

Tutoring is a widespread educational practice that has proven to be an effective teaching approach in many domains, including the domain of mathematics. Students who have engaged in school-based tutoring programs have outperformed their peers in numerous studies, sometimes by very large margins (Bloom, 1984; Cohen, Kulik, & Kulik, 1982; Fuchs et al., 2008; Powell, Driver, & Julian, 2015; Smith, Cobb, Farran, Cordray, & Munter, 2013). In a most notable study, Bloom (1984) showed that the average student in a tutoring group performed better than 98% of the students in a conventional group. Bloom termed this outperformance of tutored students the 2 sigma problem, stating that important research should be done to determine practical ways in which the positive effects of one-on-one tutoring, "which is too costly for most societies to bear on a large scale," can be realized in classroom settings (p. 4). This Dissertation study looks to teacher noticing as an analytical framework for understanding the practice of mathematics tutoring. The knowledge that tutors build in one-on-one tutoring interactions through the process of noticing is discussed, particularly tutors’ development of knowledge of individual students, knowledge of social and practical aspects of teaching and learning, and Mathematics Knowledge for Teaching (Ball, Thames, & Phelps, 2008). A new model for Knowledge for Tutoring is constructed and the widely cited Mathematics Knowledge for Teaching model is revisited. Finally, limitations and future research are discussed