Browsing by Author "Keller, Rachel E."

Now showing 1 - 2 of 2
  • Thumbnail Image
    Individual and situational factors related to undergraduate mathematics instruction
    Johnson, Estrella; Keller, Rachel E.; Peterson, Valerie; Fukawa-Connelly, Timothy (2019-06-28)
    Background In the US, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Even with these reform initiatives, researchers continue to document that lecture remains the dominant mode of instruction in US undergraduate mathematics courses. However, we have reason to believe there is variability in teaching practice, even among instructors who self describe their teaching practice as “lecture.” Thus, our research questions for this study are as follows: what instructional practices are undergraduate mathematics instructors currently employing and what are the factors influencing their use of non-lecture pedagogies? Here, we explore these questions by focusing on instruction in algebra courses, an upper-division mathematics course that is particularly well positioned for instructional reform. Results We report the results of a survey of 219 abstract algebra instructors from US colleges and universities concerning their instructional practices. Organizing our respondents into three groups based on the proportion of class time spent lecturing, we were able to identify 14 instructional practices that were significantly different between at least two of the three groups. Attempting to account for these differences, we analyzed the individual and situational factors reported by the instructors. Results indicate that while significant differences in teaching practices exist, these differences are primarily associated with individual factors, such as personal beliefs. Situational characteristics, such as perceived departmental support and situation of abstract algebra in the broader mathematics curriculum, did not appear to be related to instructional differences. Conclusions Our results suggest that personal bounds in general, and beliefs in particular, are strongly related to the decision to (not) lecture. However, many of the commonly cited reasons used to justify the use of extensive lecture were not significantly different across the three groups of instructors. This lack of differentiation suggests that there may be relevant institutional characteristics that have not yet been explored in the literature, and a transnational comparison might be useful in identifying them.
  • Thumbnail Image
    A structural equation model looking at student’s participatory behavior and their success in Calculus I
    Keller, Rachel E.; Johnson, Estrella; DeShong, Steven (2017-11-10)
    Background Government projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates above and beyond those already projected by the year 2022. Of crucial importance to the STEM pipeline is success in Calculus I, without which continuation in a STEM major is not possible. The STEM community at large, and mathematics instructors specifically, need to understand factors that influence and promote success in order to mitigate the alarming attrition trend. Previous work in this area has defined success singularly in terms of grades or persistence; however, these definitions are somewhat limiting and neglect the possible mediating effects of affective constructs like confidence, mindset, and enjoyment on the aforementioned markers of success. Using structural equation modeling, this paper explored the effect of participation on grades in freshman college calculus and investigated whether these effects were mediated by affective variables. Results Results indicated that participation had no significant direct effect on any of the success components in the final model—a finding that was not only counterintuitive but actually contradicted previous research done on this data. Participation was however highly correlated with two other exogenous variables indicating it would be inappropriate to dismiss it as being unrelated to success. Furthermore, the results suggested a cluster of affective success components and an achievement component with confidence being the intermediary between the two. Conclusions This paper extends upon previous work with this data set in which the effect of participatory behaviors on success was investigated wherein success was measured singularly with expected course grade and affective components of success were not considered. The limited explanatory power of the model, coupled with the seemingly contradictory results, indicates that participatory behaviors alone might be insufficient to capture the complexity of the success response variable.