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Description: Project 1. Knowledge of Mathematical Symbols Goes Beyond Numbers: The written language of mathematics is dense with symbols and with conventions for combining those symbols to express mathematical ideas. For example, reading a factored polynomial function such as f(x)=x^2 (2x+15) requires the knowledge that parenthesis can be used to signify function notation in one context and multiplication in another. Mathematical orthography is defined as orthographic knowledge of symbolic mathematics. It entails both knowledge of discrete mathematical symbols and the conventions for combining those symbols into expressions and equations. The ability to read text written in the base-ten system, comprised of digits and conventions for combining digits to express whole and rational quantities, is an important aspect of mathematical orthography. However, success in secondary and post-secondary programs requires more advanced mathematical orthography. The goal of this research was to determine if a simple and novel measure of mathematical orthography captures individual differences in adults’ mathematical skills. Mathematical orthography was measured with a timed dichotomous symbol decision task. Adults (N = 58) discriminated between conventional and non-conventional combinations of mathematical symbols (e.g., x^2 vs. (_^2)x; |y| vs. ||y). The mathematical symbol decision task uniquely predicted individual differences in whole-number arithmetic, fraction/algebra procedures, and word problem solving. These findings suggest that the symbol decision task is a useful index of symbol associations in mathematical development and, thus, provides a tool for understanding the role of mathematical orthography in individual differences in adults’ mathematical skills. Project 2. Adults’ Knowledge of Mathematical Orthography Mathematical orthography comprises knowledge of mathematical symbols and the conventions for combining those symbols. For example, in the expression x^3+3x, the positions of the symbol “3” in each term dictate its meanings in the expression. To be successful mathematical problem solvers, people need to know these conventional orthographic patterns. In this study, mathematical orthography skills were assessed in an online format for 189 adults using a timed dichotomous symbol decision task (e.g., are these expressions conventional? (|𝑥| or ||𝑥). The symbol decision task predicted unique variance in whole-number number arithmetic, word problem solving, and algebra, controlling for verbal working memory. These results support of a role for individual differences in mathematical orthography as a predictor of advanced mathematical skills. In contrast, a written language orthography task only predicted unique variance in word problem solving, where participants read texts. The role of mathematical orthography should be considered in models of mathematical cognition.