Teaching Fraction Concepts Using the Concrete-Representational-Abstract Sequence

Abstract

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence of instruction has been shown to be an effective means of teaching conceptual understanding of fractional numbers. The purpose of this study was to compare the effects of CRA with remedial multitiered systems of support (MTSS) Tier 2 instruction for teaching fraction concepts. Thirty-one fifth-grade students participated in two different Tier 2 interventions; one group received typical Tier 2 instruction with their general education teachers and the other received CRA instruction with the researchers. The researchers measured student performance using a pretest and posttest and found significant differences in progress favoring the CRA group. Results and implications are discussed.

Accuracy of Area Model and Number Line Representations of Fractions for Students with Learning Disabilities

“…Students with lower working memory capacity scored lower on the FNLE (Fuchs et al., ). Past research has also shown that students who receive explicit instruction in representing fractions on the number line during fractions intervention learn to do so with very high accuracy and significantly improve their FNLE scores (Flores et al., ). In sum, evidence may suggest that FNLE performance was less accurate than FCE performance in the present study due, in part, to the working memory demands associated with the unfamiliar number line task.…”

Is a Picture Worth 1,000 Words? Investigating Fraction Magnitude Knowledge Through Analysis of Student Representations

“…Rectangular area models are also preferable to circular models because they can better facilitate the transition to more abstract number line models. Indeed, concrete-representational-abstract (CRA) intervention research (e.g., Flores et al, 2018) has demonstrated that teaching students with LD to map bar models onto number lines can strengthen their fraction magnitude understanding.…”

“…Results from fractions intervention research also indicate a link between magnitude understanding and overall fractions performance. Interventions designed to improve fraction magnitude understanding have significantly improved performance across a variety of other fractions skills and concepts for students with, or at risk of, MD (e.g., Flores, Hinton, & Meyer, 2018; Fuchs et al, 2013). Using number line representations (i.e., measurement or length models) as the central visual representation (VR) of fractions is a common feature of successful fractions interventions focused on improving students’ magnitude understanding (e.g., Flores et al, 2018; Fuchs et al, 2013).…”

“…Interventions designed to improve fraction magnitude understanding have significantly improved performance across a variety of other fractions skills and concepts for students with, or at risk of, MD (e.g., Flores, Hinton, & Meyer, 2018; Fuchs et al, 2013). Using number line representations (i.e., measurement or length models) as the central visual representation (VR) of fractions is a common feature of successful fractions interventions focused on improving students’ magnitude understanding (e.g., Flores et al, 2018; Fuchs et al, 2013). Number lines are an important component of fractions instruction because number lines allow for clear VR of the concepts of equal, smaller, and bigger, and as a result, reinforce the idea that fractions are numbers with magnitude.…”

Teaching Multiplication to Students with Mathematical Learning Disabilities (MLD): Analysis of Preservice Teachers’ Lesson Design

“…CRA research includes mnemonic strategies; however, it is very important that students have solid conceptual understanding before moving to an emphasis on procedural knowledge and fluency [36]. Research has proven that CRA not only helps students with MLD but also neurotypical students to better develop mathematical concepts [24][25][26]37,38].…”