Abstract
Number and its basic operations can be conceptualized within a general system of relationships. Children need to build a number system within which they can add, subtract, multiply, and divide any rational number. Products and quotients can be defined in terms of general relational schemes. In this study, we examine whether elementary school children can construct a number system such that multiplication and division of fractions are based on the construction of general relational schemata. Student groups are not homogeneous and children progress at different rates. For reliable assessment, teachers need methods to examine developmental and individual differences in cognitive representations of mathematical concepts and operations. A logistic regression curve offers a visualization of the learning process as a function of the average grades. Item analysis of multiplication and division of fractions shows an improvement in the probability of a correct answer, especially for students with a higher average score.
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