Analytical framework for reasoning in algebraic problem-solving that involves unequal sharing
This text sets forth a framework for analyzing student reasoning in solving unequal sharing problems that can be used in elementary school and early secondary school. The framework is based on a consideration of two dimensions: 1) the degree of analycity of the reasoning and 2) the nature of the register of semiotic representation (Duval, 1995) used for unknowns and equations. The epistemological foundations of this analytical framework are based on a brief analysis of certain stages in the historical development of algebra. Next, the different categories of reasoning are illustrated using prototypical examples drawn from student productions.