The overarching goal of this dissertation research was to develop and measure the psychometric properties of an instrument to assess preservice teachers? content knowledge of the function concept embedded in contextual problems. This goal was accomplished through two research projects described in two central chapters. Chapter II reports on the collective case study that was used to pilot test the instrument and Chapter III details the rationale used in item selection and the psychometric properties of the new instrument. Unlike existing research studies that examine a broad range of function related topics using various forms of symbolic, tabular, and graphical representations as the basis for questions and problems, this study focused solely on function problems immersed in various real world contexts. Since this is not a common approach to measuring content knowledge of the function concept, the existing instruments in published studies were not found to be suitable for this specialized purpose. The psychometric measurements of the instrument did not suggest that the instrument was valid or reliable so more research will be required to validate the instrument. However, based on the preliminary results from testing, several potential suggestions can be made to teacher educations programs. Inferences drawn from the mathematical problem-solving cognition will aid in the development and validation of future instruments to assess preservice mathematics teachers? knowledge of how to connect their knowledge mathematical concept of function to a contextual setting
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