Ethical principles for algorithms are gaining importance as more and more stakeholders are affected by "high-risk" algorithmic decision-making (ADM) systems. Understanding how these systems work enables stakeholders to make informed decisions and to assess the systems’ adherence to ethical values. Explanations are a promising way to create understanding, but current explainable artificial intelligence (XAI) research does not always consider existent theories on how understanding is formed and evaluated. In this work, we aim to contribute to a better understanding of understanding by conducting a qualitative task-based study with 30 participants, including users and affected stakeholders. We use three explanation modalities (textual, dialogue, and interactive) to explain a "high-risk" ADM system to participants and analyse their responses both inductively and deductively, using the "six facets of understanding" framework by Wiggins & McTighe. Our findings indicate that the "six facets" framework is a promising ap proach to analyse participants’ thought processes in understanding, providing categories for both rational and emotional understanding. We further introduce the "dialogue" modality as a valid explanation approach to increase participant engagement and interaction with the "explainer", allowing for more insight into their understanding in the process. Our analysis further suggests that individuality in understanding affects participants’ perceptions of algorithmic fairness, demonstrating the interdependence between understanding and ADM assessment that previous studies have outlined. We posit that drawing from theories on learning and understanding like the "six facets" and leveraging explanation modalities can guide XAI research to better suit explanations to learning processes of individuals and consequently enable their assessment of ethical values of ADM systems.

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