ALocalInstructionalTheoryfortheGuidedReinventionof.pdfVIP

A Local Instructional Theory for the Guided Reinvention of the Quotient Group Concept. Sean Larsen Portland State University Estrella Johnson Portland State University Faith Rutherford Portland State University Joanna Bartlo Portland State University Abstract In this paper, we briefly describe a local instructional theory that has resulted from a series of design experiments focused on the quotient group concept. This local instructional theory will consist of 1) a generalized instructional sequence intended to support the guided reinvention of the quotient group concept and 2) a theoretical and empirical rationale for this generalized instructional sequence. We will describe the design experiments that informed the development of the instructional sequence and, in order to illustrate and motivate the local instructional theory, we will describe key aspects of the reinvention process in terms of the participating students’ mathematical activity. Introduction This research reported here is part of a larger project that has as its goal the creation of an innovative research-based inquiry-oriented curriculum for abstract algebra. Here we will focus on the research and design work that supported the development of the quotient group unit of the curriculum. Our primary purpose will be to describe the resulting local instructional theory (Gravemeijer, 1998) for supporting the guided reinvention of the quotient group concept. It has been observed that students struggle with the quotient group concept (Dubinsky, Dautermann, Leron, and Zazkis, 1994). Burn (1996) noted that the quotient group can be seen in the elementary example of even/odd parity which suggests