Teacher instructional practices, student mathematical dispositions, and mathematics achievement
Kisunzu, Phillip K.
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The primary purpose of this dissertation research was to investigate the direct and indirect effects of three reform-based aspects of teacher instructional practices on four dominant aspects of middle school adolescents' mathematical dispositions: namely the confidence, flexibility, perceptive, and usefulness aspects of student mathematical dispositions. These four aspects of student mathematical dispositions were the results of exploratory and confirmatory factor analyses developed with the intended objective of testing the factorial validity of a mathematical dispositions construct for middle school adolescents, consistent with the outline provided in the National Council of Teachers of Mathematics (NCTM) framework of Evaluation Standards 6 and 10 on the aspects of student mathematical dispositions. A secondary purpose was to seek evidence as to whether these same effects, if any, were invariant across five sequential structural models controlling for a spectrum of student characteristics including gender, race and ethnicity, and socioeconomic status. The findings revealed that the often and emphasis aspects of teacher instructional practices exerted significant effects on the four aspects of student mathematical dispositions, and were significantly invariant between the base model (Model I) and the full model (Model V). The present study used a quantitative-qualitative mixed methodology wherein a multivariate analysis through the use of exploratory and confirmatory factor analyses and structural equation modeling comprised the main quantitative methodology phase, and classroom observations constituted the qualitative methodology phase. Sixteen middle school mathematics teachers were asked to respond to 17 reform-based questions about their instructional practices in a 64-item self-reporting instrument on how often and how much time students in their mathematics class took part in thirteen reform-based and four traditionally-based mathematics activities. The teachers were additionally asked to respond to 15 reform-based student objectives and were asked about how much emphasis they planned for each student objective during the school year 2006-07. Four hundred sixty-eight middle school adolescents, who were taught by eleven of the sixteen teachers, participated in this study and completed a 29-item self-reporting instrument measuring ten aspects of student mathematical dispositions as suggested in the NCTM framework of Evaluation Standards 6 and 10 on student mathematical dispositions. In an attempt to answer the research questions and investigate the potential effects and possible invariance patterns of teacher instructional practices on the aspects of student mathematical dispositions, five sets of structural equation models were developed and tested on a cross-sectional sample of 468 middle school adolescents selected from a public school district situated in a large Midwestern metropolitan region of the United States. Results from the base model (Model I) of the five structural equation models indicated that by allowing the teacher instructional practices factors of often, time, and emphasis to covary, all three factors emerged as significant sources of influence, with the most significant effects on aspects of student mathematical dispositions originating from the two exogenous factors often and emphasis. These two exogenous factors were found to exert significant direct and indirect effects on all four aspects of student mathematical dispositions, whereas the time factor was found to exert significant direct and indirect effects on two of four aspects of student mathematical dispositions. Furthermore, three of the four aspects of student mathematical dispositions were found to be statistically significant in mediating the direct effects originating from the often, time, and emphasis factors to the other aspects of student mathematical dispositions.