An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach.

This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in teacher-led classroom instruction with a series of six research-based lessons, and then were given a posttest. The purpose was to examine the use of discrete and continuous models and the impact on student understanding of fractions. A mixed-methods approach was utilized, with descriptive statistics discussed relative to quantitative pre/post data. Qualitative data were collected in the form of observer notes, teacher reflections, and anecdotal assessment. A case study approach was taken to examine findings within and across grade levels. Major findings include (1) students demonstrated growth in understanding of fractions with both models; (2) students generally understood fraction concepts better using discrete models, but results were mixed; (3) students were not necessarily able to express fractional ideas at a rigorous level; and (4) 3rd-graders were able to use partitioning effectively but were able to recognize equivalence more easily within the discrete model. [ABSTRACT FROM AUTHOR]