Investigating the mathematical equivalence of written and enacted middle school Standards-based curricula: Focus on rational numbers

Although the question of whether written curricula are implemented according to the intentions of curriculum developers has already spurred much research, current methods for documenting curricular implementation seem to be missing a critical piece: the mathematics. To add a mathematical perspective to the discussion of the admittedly controversial and conceptually complex issue of “fidelity of curricular implementation,” this study proposes a method for investigating fidelity that deals with the question of mathematical equivalence of written curricula and their enactments in the classroom. The method rests on the assumption that the curricula, both written and enacted, can be treated as discourses, and that one of the ways to judge their mathematical equivalence is to compare the mathematical objects around which these discourses evolve. As an illustration for how the method works, I analyzed a part of the written Connected Mathematics Project (CMP) curriculum and its enactment in a sixth grade classroom learning about fractions. This analysis showed that the written and enacted versions of the central mathematical objects of the two curricula, rational numbers, differed in almost every aspect: in their ontology, in the relative prominence of their realizations (i.e., symbols, icons and concrete objects) and in the importance attributed to their different properties. These differences may have an impact on the nature of students’ mathematical competence.