Half of One, 6/12 of Another: Understanding Relative Item Difficulties in a Fractions Assessment under Development

A strong understanding of fractions is vital to later success in mathematics. However, research has consistently shown that fractions are one of the most difficult mathematical concepts for elementary school students to master. To attempt to remedy this deficit, the authors began a project called Helping At-risk students Learn Fractions (HALF) in June of 2010. The purpose of the HALF project was to develop a technology-based learning environment that uses interactive visual representation to help students' gain conceptual understanding of fractions. The school sites whose students participated in the diagnostic assessment item pilot testing include nine different schools that represent a broad range of possible school settings in order to allow for more generalizable results. As in the selection of school sites, the authors attempted to collect data from as broad of a range of fifth- and sixth-grade students as possible; no students were systematically excluded. Of the six t tests performed, four showed a significant difference between the groups. The most striking result was the comparison between items that presented a fraction that was greater than one as an improper fraction and those presented as mixed numbers (t(27) = 7.902, p < 0.001). These findings are useful in multiple ways, for example: (1) in working to improve fractions pedagogy, they allow for making general recommendations to teachers regarding the order in which to present material; and (2) knowing that items using triangles are more challenging for students, a teacher could introduce a new topic using circle and square models and move on to triangles when the students are ready to challenge their understanding. Since instruction does not take place in a vacuum; regardless of how and in what order the theory states students should learn fractions, it is valuable to both good pedagogy and good research to understand how they actually do learn fractions. Tables and figures are appended.