Mathematical Knowledge Developed at Work: The Contribution of Practice Versus the Contribution of Schooling

Mathematical knowledge developed independently of school instruction has been documented among children as well as adults. However, the limits and strengths of this knowledge are not yet well known, and its relationship to knowledge acquired in school remains to be clarified. This study analyzes the use and understanding of mathematical knowledge among bookies with 0 to 11 years of schooling who work in a special kind of lottery game. They were observed at work while dealing with clients and while solving modified problems based on naturalistic observations. At work, regardless of their level of instruction, bookies were always highly efficient. When solving modified problems presented by the examiner, unschooled bookies often refused to try to solve some of them; when they attempted to solve the problems, however, their proportion of correct answers was similar to that found among more schooled subjects. Number of correct answers and a more general ability to analyze and to explain verbally the relationships and the mathematical models involved in the game correlated significantly with school instruction. Schooling did not, however, influence the use of specific techniques (e.g., algorithms) for performing arithmetic operations.