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Algorithms that aid human tasks, such as recommendation systems, are ubiquitous. They appear in everything from social media to streaming videos to online shopping. However, the feedback loop between people and algorithms is poorly understood and can amplify cognitive and social biases (algorithmic confounding), leading to unexpected outcomes. In this work, we explore algorithmic confounding in collaborative filtering-based recommendation algorithms through teacher-student learning simulations. Namely, a student collaborative filtering-based model, trained on simulated choices, is used by the recommendation algorithm to recommend items to agents. Agents might choose some of these items, according to an underlying teacher model, with new choices then fed back into the student model as new training data (approximating online machine learning). These simulations demonstrate how algorithmic confounding produces erroneous recommendations which in turn lead to instability, i.e., wide variations in an item's popularity between each simulation realization. We use the simulations to demonstrate a novel approach to training collaborative filtering models that can create more stable and accurate recommendations. Our methodology is general enough that it can be extended to other socio-technical systems in order to better quantify and improve the stability of algorithms. These results highlight the need to account for emergent behaviors from interactions between people and algorithms.