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Math anxiety is negatively correlated with student performance and can result in avoidance of further math/STEM (science, technology, engineering, and mathematics) classes and careers. Cooperative learning (i.e., group work) is a proven strategy that can reduce math anxiety and has additional social and pedagogical benefits. However, depending on the group individuals, some peer interactions can mitigate anxiety, while others exacerbate it. We propose a mathematical modeling approach to help untangle and explore this complex dynamic. We introduce a modification of the Hegselmann–Krause bounded confidence model, including both attractive and repulsive interactions to simulate how math anxiety levels are affected by pairwise student interactions. The model is simple but provides interesting qualitative predictions. In particular, Monte Carlo simulations show that there is an optimal group size to minimize average math anxiety, and that switching group members randomly at certain frequencies can dramatically reduce math anxiety levels. The model is easily adaptable to incorporate additional personal and societal factors, making it ripe for future research. 

We study a system of coupled phase oscillators near a saddle-node on invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the qualitative properties of collective dynamics. Using Ott–Antonsen reduction and geometric techniques for ordinary differential equations, we identify heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation from noncontractibile ones after bifurcation. Both families are stable for the model at hand.