From Piaget to the present, traditional and dual-process theories have predicted improvement in reasoning from childhood to adulthood, and improvement has been observed. However, developmental reversals--that reasoning biases emerge with development--have also been observed in a growing list of paradigms. We explain how fuzzy-trace theory predicts both improvement and developmental reversals in reasoning and decision making. Drawing on research on logical and quantitative reasoning, as well as on risky decision making in the laboratory and in life, we illustrate how the same small set of theoretical principles apply to typical neurodevelopment, encompassing childhood, adolescence, and adulthood, and to neurological conditions such as autism and Alzheimer's disease. For example, framing effects--that risk preferences shift when the same decisions are phrased in terms of gains vs. losses--emerge in early adolescence as gist-based intuition develops. In autistic individuals, who rely less on gist-based intuition and more on verbatim-based analysis, framing biases are attenuated (i.e., they outperform typically developing control subjects). In adults, simple manipulations based on fuzzy-trace theory can make framing effects appear and disappear depending on whether gist-based intuition or verbatim-based analysis is induced. These theoretical principles are summarized and integrated in a new mathematical model that specifies how dual modes of reasoning combine to produce predictable variability in performance. In particular, we show how the most popular and extensively studied model of decision making--prospect theory--can be derived from fuzzy-trace theory by combining analytical (verbatim-based) and intuitive (gist-based) processes. (Contains 2 tables and 4 figures.)