Abstract
Prior studies have identified the impact beliefs have on mathematics instructors’ instructional practice, such as their choice to (or not to) lecture. However, the role of instructional context role in influencing beliefs and instruction has not been thoroughly researched. This paper explores how course context and beliefs could impact mathematics instructors’ propensity to lecture by investigating two very different instructional contexts in undergraduate mathematics in the United States: Calculus and Abstract Algebra. The results of our regression analyses were significant in both data sets and, we did find beliefs in each context that predicted the amount of time spent lecturing. For instance, the more calculus instructors believed in the effectiveness of teacher-centered instructional practices, the more likely they were to lecture. Whereas the more abstract algebra instructors believed in their student’s capacity to learn the less likely they were to lecture. However, while the regression model for the abstract algebra instructors accounted for 37.8% of the variability in the reported amount of time spent lecturing, the model for Calculus instructors only accounted for 2.7% of the variability. Thus our analyses indicate that there are contextual differences, such as course coordination, student demographics, and the job security of the instructors, that may be mitigating the extent to which beliefs impact instructional practice.
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Availability of Data and Materials
The CSPCC data that support the findings of this study are available from the Mathematical Association of America, but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data from the AA survey are available from the authors upon reasonable request.
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The CSPCC elements of this paper are supported by the National Science Foundation, award #DRL-0910240. Any opinions and findings expressed in this material are of the authors’ and do not necessarily reflect the views of NSF.
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Appendix
Appendix
Plot of standardized predicted values against standardized residuals for the CSPCC data (Left) and AA data (right). For the CSPCC data, the Loess line of best fit suggests linearity was not a reasonable assumption while the spread of the data suggests homoscedasticity was met. For the AA data, the Loess line of best fit suggests linearity was a reasonable assumption while the spread of the data suggests homoscedasticity was not met
Histogram of standardized residuals (Left) and P-P plot (right) for CSPCC data. Both suggest normality may be problematic
Histogram of standardized residuals (Left) and P-P plot (right) for AA data. Both suggest normality was a reasonable assumption
Plot of centered leverage values against instructor ID for the CSPCC data (Left) and AA data (right). The distributions for both suggest some outliers, but more prominently in the CSPCC data
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Chowdhury, A.H., Mullins, S.B. & Johnson, E. Context Matters: Understanding the Relationship Between Instructor’s Beliefs and the Amount of Time Spent Lecturing. Int. J. Res. Undergrad. Math. Ed. 8, 550–580 (2022). https://doi.org/10.1007/s40753-021-00158-5
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DOI: https://doi.org/10.1007/s40753-021-00158-5