Mistaken beliefs pose a barrier to science learning. For this reason, it is important to understand the circumstances in which they emerge and change. In the current paper, we apply complexity theory to shed light on the nature of mistaken beliefs. The strength of this approach lies in conceptualizing beliefs as dynamic stabilities, a well-defined construct that can be indexed precisely. For example, Recurrence Quantification Analysis (RQA) can determine the presence of dynamic stabilities by analyzing variability in time-series data. We applied this analytical tool to probe for mistaken beliefs in a beam-balancing task, a task that is known to elicit mistaken beliefs in preschoolers. Using a case-study design with four preschoolers, we tracked children's hand position with motion sensors as they balanced various beams. The resulting time series of hand position was submitted to RQA, yielding two important results: First, we found that consistent mistakes in trying to balance the beams were not always accompanied by dynamic stability. This undermines the common assumption that overt consistency in task performance is sufficient to conclude the presence of beliefs. Second, we found strong individual differences over time, as children explored the balance beams. Applications to science education are discussed.