Using the Rasch Model to Measure Comprehension of Fraction Addition.

In this study we investigate whether transformations between different representations of mathematical objects constitute a suitable framework for the assessment of students' comprehension of fraction addition. Participants (N = 164) solved a set of 20 fraction addition problems constructed on the basis of Duval's (2017) theory of the role of representational transformations in mathematical comprehension. Using Rasch measurement theory and principal component analysis, we found that the items could be separated into three levels of difficulty based on the transformation involved. This large-scale structure was consistent across gender and across subgroups of preservice teachers and middle-grade students. On a finer scale, the production of diagrammatic representations, and the type of diagrammatic representation involved, constitute potential subdimensions of the instrument. We conclude that transformations between representations can be productive for the assessment of fraction addition comprehension as long as care is taken to curtail the potential effects of multidimensionality.