Investigating Teachers' Experiences with the History of Logarithms: A Collection of Five Case Studies

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This study investigated five secondary mathematics teachers' efforts to study and use the history of a specific topic. A professional development experience, constructed to reflect the features of effective professional development identified by Garet, Porter, Desimone, Birman, and Yoon (2001) and Smith (2001), was designed to engage teachers in the study of the historical development of logarithms. Modifications of activities found in the Exponentials and Logarithms module (Anderson, Berg, Sebrell, & Smith, 2004), as well as various print and electronic resources, were used during the professional development. Two primary research questions guided the study. First, the study addressed how teachers with different background knowledge and experiences responded to the professional development. Second, the study investigated how teachers' background variables and experience with the professional development influenced the teachers' personal mathematical knowledge and instructional practice. Exploratory case study methodology was used to describe the experiences of five participants; four teaching in a public high school and one teaching in a private day school. Data sources used in the case study included teacher background, attitudes, and content knowledge instruments; participant observation during all professional development sessions and classroom instruction (during a unit on logarithms); and semi-structured interviews. The study found that engagement during the professional development sessions was stronger on the part of participants who reported high participation in previous professional learning activities and who were able to consider alternatives for dealing with the barriers to incorporating the history of logarithms. Similarly, the extent to which participants incorporated the history of logarithms during their instruction was directly related to the extent of their engagement during the professional development. Lastly, the two teachers with the strongest professional development engagement and implementation of the history of logarithms exhibited the most improvement in content knowledge. The study conveyed important information for what Barbin (2000) indicated is essential for qualitatively analyzing "the changes that can occur when history has a place in the teaching of mathematics" (p. 66).