For understanding development of quantitative thinking, the distinction between non-symbolic and symbolic thinking is fundamental. Non-symbolic quantitative thinking is present in early infancy, culturally universal, and similar across species. These similarities include the ability to represent and compare numerosities, the representations being noisy and increasing logarithmically with actual quantity, and the neural correlates of number representation being distributed in homologous regions of fronto-parietal cortex. Symbolic quantitative thinking, in contrast, emerged recently in human history, differs dramatically across cultural groups, and develops over many years. As young children gain experience with symbols in a given numeric range and associate them with non-verbal quantities in that range, they initially map them to a logarithmically-compressed mental number line and later to a linear form. This logarithmic-to-linear shift expands children's quantitative skills profoundly, including ability to estimate positions of numbers on number lines, to estimate measurements of continuous and discrete quantities, to categorize numbers by size, to remember numbers, and to estimate and learn answers to arithmetic problems. Thus, while non-symbolic quantitative thinking is important and foundational for symbolic numerical capabilities, the capacity to represent symbolic quantities offers crucial cognitive advantages.Keywords: Numerical cognition; number representation; mathematical thinking; symbols; cognitive development Quantitative thinking is central to human life. Whether the situation involves a child recalling which blocks provided her with the most candies on previous Halloweens, a Londoner telling the time by counting the tolls of Big Ben, or a candidate using polls to predict results of an upcoming election, quantitative thinking is important for learning from the past, monitoring the present, and planning for the future.Quantitative thinking plays an important role in the lives of other animals as well.To project the outcome of a future fight, prides of lionesses compare their pride-number to the number of distinct roars they hear in rival packs (McComb et al., 1994). Similarly, Development of Quantitative Thinking 2 to learn optimal foraging locations, animals in the wild encode the relative number of food items they have found previously in various locations (Davis, 1993).The existence of such quantitative abilities makes sense from an evolutionary perspective. Being deprived of a sense of how many would deprive an animal of any rationality in its judgments and decision-making. Rational choices among alternative strategies and courses of action would be rendered impossible.Given the importance of quantitative thinking, it is unsurprising that representations of quantity are a universal property of human cognition. Quantitative representations are present from early infancy Feigenson, Dehaene, & Spelke, 2004), and share striking similarities across human cultures that provide radically different cultu...