A structural equation model looking at student’s participatory behavior and their success in Calculus I

Abstract

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.

Problematizing teaching and learning mathematics as “given” in STEM education

“…Specifically, for these three articles published in 2016, they are all about mathematics education at either elementary school (Ding 2016;Zhao et al 2016) or university levels (Schoenfeld et al 2016). Out of the six published in 2017, three are on mathematics education (Hagman et al 2017;Keller et al 2017;Ulrich and Wilkins 2017) and the other three on either teacher professional development (Borko et al 2017;Jacobs et al 2017) or connection with engineering (Jehopio and Wesonga 2017). For the five published in 2018, two are on mathematics education (Beumann and Wegner 2018;Wilkins and Norton 2018) and the other three have close association with other disciplines in STEM (Blotnicky et al 2018;Hayward and Laursen 2018;Nye et al 2018).…”

Motivation and achievement in undergraduate STEM calculus: Applying self‐determination theory to examine the differential impact of learning environments across demographic groups

“…These findings are consistent with the Freeman et al meta‐analysis on the impact of active learning (Hedge's g = 0.5) on achievement in undergraduate STEM courses. However, Keller et al (2017) found that student participation in discussion and lecture had no impact on success measures and reported findings that contradict previous initial studies (Keller et al, 2016; Rasmussen & Ellis, 2013). Sonnert et al (2015) performed an exploratory factor analysis of attitudes toward mathematics and identified three factors related to classroom practices: “good” teaching (clarity, fairness, availability, etc.…”

From High School to College Calculus: Beliefs about Sense-Making and Mistakes

“…Prior research on the transition from high school to college calculus has conceptualized success in terms of end-of-course grades in first semester calculus courses and subsequent course taking (Bressoud et al 2015;Sadler and Sonnert 2018). These measures of achievement and persistence do not account for affective constructs of success (Keller et al 2017). This study employs a mathematical mindset theoretical framework (Boaler 2016;Dweck 2006) to describe student and instructor perceptions of in the transition from high school to college calculus.…”