Kathleen A. Cramer

Cognitive Restructuring Ability, Teacher Guidance, and Perceptual Distracter Tasks: An Aptitude-Treatment Interaction Study.

The aptitude-treatment interaction (ATI) study reported here explored the relationship between cognitive restructuring ability, as measured by the Group Embedded Figures Test (GEFT), and treatments varying in amounts of teacher guidance. It specifically investigated how these two variables affected performance on rational number tasks involving perceptual distracters. Perceptual distracter problems evolved from the work of the Rational Number Project (Behr & Post, 1981). Such problems contain visualstimulus information inconsistent with the demands of the task that must

Making sense of third-grade students’ misunderstandings of the number line

ABSTRACT Researchers collaborated with a team of third-grade teachers in an urban district in the Upper Midwest to examine misunderstandings among students when using the number line as a model for fractions. Researchers looked closely at how the number line can be used as a model to build meaning for fractions for third-grade students. This article focuses on student interviews that discuss preconstructed and blank number line tasks that indicate how and when common misunderstandings occur when using a number line model. Misunderstandings include student misinterpretations of partitioning and tick marks, misunderstanding the unit, and equivalence as it relates to the number line. With these struggles as a basis, instructional implications for using the number line as a model in the classroom are provided. Reflection is included on the role of the number line and how it enhances third graders’ understanding of fractions in ways that other models do not.