Humans possess a metacognitive sense of certainty which, for better or worse, influences behavior. This sense of certainty is often misleading and can leave us vulnerable to believing false information. In this dissertation, I study how humans form their sense of certainty and the types of false beliefs which we can be at times, highly certain of. This work spans across multiple domains, including concept learning, word-meaning, pseudoscience, and people’s metacognitive beliefs. Across seven experiments, I present empirical evidence that learners use heuristics over idealized model-based features when forming their sense of certainty, and that this leaves us prone to errors which can result in the adoption of misinformed beliefs as drastic as the belief that the Earth is flat.

This dissertation explores how mathematics is acquired in the mind, examining which skills are present early in development and which require cultural input to emerge. Research on mathematical cognition has traditionally been based on WEIRD (Western, Educated, Industrialized, Rich, Democratic) populations. These populations are not representative of the diversity of human thought, and can lead to inaccurate generalizations about the factors supporting mathematical understanding. This dissertation explores the origins of mathematical abilities in the Tsimane’, an indigenous group in the Bolivian Amazon. Individual Tsimane’ have variable levels of formal schooling, market experience, language for mathematical concepts, and other cultural supports. This variability helps to arbitrate between innate and environmental factors giving rise to mathematical cognition. Throughout the dissertation, a cross-cultural lens is applied to research the origins of three key mathematical abilities: counting, arithmetic, and geometry.

Numerosity perception has been studied for at least 150 years and its psychophysics have been well characterized by experimental work. However, the origins of many of its key properties remain obscure. For instance, people estimate the numerosity of small sets (up to four) much more rapidly and accurately than larger sets; people tend to underestimate larger numerosities; estimation precision and accuracy increase with exposure duration. Standard models of numerical estimation do not account for these wide ranging phenomena, with large number estimation typically characterized as a draw from Gaussian(n, w * n) where w is a person's "Weber fraction," and exact small number perception characterized separately, the result of an independent object-file system. Furthermore, the inherently perceptual nature of estimation is largely ignored in many accounts of individual differences, which are often considered evidence of disparities in innate mathematical cognition. In my dissertation, I present studies of human behavior and computational models aimed at clarifying the visual mechanisms underlying numerical estimation. Our findings help to understand, and unify, key properties of number psychophysics which have previously been explained in terms of independent mechanisms or with ad hoc modifications to existing theories. For instance, we show how the psychophysics of both small and large number estimation can be unified into a single framework with a common mechanistic origin, and in fact how myriad properties of both (including estimation precision, bias, effects of time) can be understood as downstream consequences of bounded-optimal perceptual inference.