The focus of this research project was to extend existing research literature by providing insight to how prospective teachers with differing levels of mathematical knowledge developed their conceptual understanding of whole number concepts and operations. Prospective teachers of interest were enrolled in an Elementary School Mathematics Course for Teachers (in the College of Education) with a whole number concepts and operations unit set entirely in base 8. In this mixed-mode study, participants were given the MKT, a measure designed to measure teacher mathematical knowledge for teaching, before and after taking the base 8 unit. The researcher focused on two specific constructs: Common Content Knowledge (CCK) and Specialized Content Knowledge (SCK). The qualitative portion of the study involved carefully constructed student interviews which allowed the researcher to deeply explore how prospective teacher conceptual understanding changed as a result of taking the unit in base 8. Four participants with varying levels of knowledge were selected to be interviewed based upon initial scores on the MKT: 1) low CCK and low SCK, 2) low CCK and high SCK, 3) high CCK and low SCK, 4) high CCK and high SCK. Results of the interviews were used to help explain results from the MKT. Quantitative and qualitative results showed that participants did not significantly increase their CCK, but did experience an increase in their conceptual understanding (SCK) as a result of taking the unit in base 8. Most prospective teachers entering the Elementary School Mathematics Course already had high procedural knowledge of the algorithms associated with elementary mathematics, which could account for the non-significant increase in CCK. Prospective teachers all showed deeper conceptual understanding of whole number concepts and operations at varying levels by the end of the base 8 unit. Prospective teachers showed their increased understanding by way of explanations, justifications, and alternate solution strategies.
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Doctor of Philosophy (Ph.D.)
College of Education and Human Performance
Education; Mathematics Education
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Harshman, Katie, "The Influence of Instruction in Base 8 on Prospective Teachers' Mathematical Knowledge for Teaching" (2016). Electronic Theses and Dissertations. 5082.