## SCUDEM Participants Increase Self-Efficacy in Mathematical Modeling

In a just published article, "Building mathematics self-efficacy of STEM undergraduates through mathematical modelling," in the *International Journal of Mathematical Education in Science and Technology,* Jennifer Czocher and her colleagues, Kathleen Melhuish and Sindura Subanemy Kandasamy, the authors have found that interventions, particularly in the form of SCUDEM - SIMIODE Challenge Using Differential Equations, ". . . can promote students' mathematics self-efficacy." The article was published online on 11 July 2019.

The paper is a rich source of references on STEM education and brings out issues such as, "STEM majors do not perceive relevance of their mathematics coursework to their intended majors;" "STEM majors’mathematics proficiency (Including knowledge of applying mathematics) is critical to persistence;" "STEM majors’ mathematics-related self-efficacy mediates their interest and persistence in mathematics;" "Women’s self-efficacy contributes to differential attrition rates;" and "Mathematical modelling may ameliorate STEM major persistence." These are section headings in the article which argues that mathematical modeling in STEM courses can increase retention in STEM coursework through providing perceived relevance, particularly for women students.

The discussion on mathematical modeling in the paper goes like this, (again using section headings), "Modelling addresses the relevance paradox;" "Modelling is associated with mathematics self-efficacy in specific contexts;" "Characteristics of successful modelling interventions;" until the specifics on "Mathematical modelling competition intervention" and SCUDEM.

The authors share results of a study using pre and post-event (SCUDEM) surveys from students who participated in a recent SCUDEM offering. We quote the paper's section, "Summary of findings and their consequences:"

“Our exploratory, pre-experimental intervention study drew on theory built up by prior mathematics and STEM education research in order to address one aspect of the ‘leaky STEM pipeline:’ STEM students’ mathematics self-efficacy. Our design and analysis support the inference that some of the characteristics of successful in-class and extracurricular interventions can be replicated by the competition environment. We do not claim that any one of these characteristics of the competition directly affected gains in self-efficacy; we maintain that the combination of features like communicating one’s work, working in teams, working with a faculty mentor, revising reasoning, and working on challenging, authentic problems led to observable gains in modelling self-efficacy.

“We documented STEM majors’ gains in mathematics self-efficacy after participating in a competition to use differential equations to solve authentic and challenging real-world problems. Finding ways to re-create conditions known to increase student mathematics self-efficacy in extra-curricular settings is important because self-efficacy is strongly tied to persistence and, according to Bandura (2006), the most direct way to build self-efficacy is through powerful, positive experiences of success. Further, we know that integrating these characteristics directly into a post-secondary classroom is not always feasible. The modelling competition served to support students’ gains in mathematics self-efficacy. Our results also provide tentative evidence that extra-curricular competitions may help women strengthen their confidence to be comparable to that of their male counterparts. This thread is especially important to follow up with future research, since the women participating in our study may already have higher-than-average self-efficacy than women in the general population by virtue of choosing to participate in an advanced mathematics competition. If the hypothesis holds, it may provide a way forward for designing interventions to address the disparity in attrition between men and women.

“We also observed the greatest gains among participants who had never taken differential equations, suggesting that the positive experiences afforded by the competition environment superseded these students’ relative lack of relevant prior lack of differential equations knowledge. These are precisely the kinds of experiences that, if repeated, can lead to positive self-image and ultimately greater proficiency in mathematics. In conclusion, our data and the literature review support the idea that extra-curricular interventions based in mathematical modelling have great potential to facilitate STEM majors’ persistence through ameliorating their self-efficacy.”

The authors conclude, “The results from this study point to the potential power of extra-curricular modelling competitions to build student self-efficacy related to important skills involved in modelling real-world situations. In light of the ever-present need for STEM majors to persist in their careers, the charge is to educators to provide opportunities for students to have positive experiences with mathematics. In particular, there is a need for mathematical opportunities that are relevant to STEM majors’ coursework and career goals in order to maintain interest in studying mathematics. The modelling competition was an environment that replicated mechanisms known to encourage meaningful engagement with real-world contexts, opportunities to mathematize real-world situations, and to recognize and address the limitations of their own models. Positive experiences of this nature can then support gains in mathematical self-efficacy, a crucial factor mitigating STEM major attrition, especially among women.”