Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies.

Abstract

The effectiveness of an experimental middle school fraction intervention was evaluated. The intervention was centered on the number line and incorporated key principles from the science of learning. Sixth graders (N = 51) who struggled with fraction concepts were randomly assigned at the student level to the experimental intervention (n = 28) or to a business-as-usual control who received their school’s intervention (n = 23). The experimental intervention occurred over 6 weeks (27 lessons). Fraction number line estimation, magnitude comparisons, concepts, and arithmetic were assessed at pretest, posttest, and delayed posttest. The experimental group demonstrated significantly more learning than the control group from pretest to posttest, with meaningful effect sizes on measures of fraction concepts (g = 1.09), number line estimation as measured by percent absolute error (g = −.85), and magnitude comparisons (g = .82). These improvements held at delayed posttest 7 weeks later. Exploratory analyses showed a significant interaction between classroom attentive behavior and intervention group on fraction concepts at posttest, suggesting a buffering effect of the experimental intervention on the normally negative impact of low attentive behavior on learning. A number line–centered approach to teaching fractions that also incorporates research-based learning strategies helps struggling learners to make durable gains in their conceptual understanding of fractions.

Neurofunctional plasticity in fraction learning: An fMRI training study

“…Similar to previous studies applying NLE training to children, we expected the training to improve participants' conceptual knowledge of fraction magnitude on a behavioral level [20,21]. In particular, we expected significant improvements in NLE performance over the fiveday training sessions.…”

“…The aim of the present study was to investigate potential neuro-functional changes of brain activation in adult participants through a five-day consecutive NLE training on fraction magnitude. While there already exist a number of studies indicating the effectiveness of NLE training on the behavioral level [20][21][22]60] and some few studies investigating the neural correlates of fraction and proportion processing [41,42,44,45], little is still known about the neural correlates of fraction learning.…”

“…Moreover, Barbieri and colleagues [21] used a number line-based intervention to improve fraction understanding in children with poor conceptual knowledge of fractions and compared the number line intervention group to a standard mathematics curriculum group. The number line intervention group showed significantly larger learning gains than the control group.…”

Fraction Symbols and their Relation to Conceptual Knowledge

“…Importantly, math-specific language is a necessary skill that supports connecting fraction symbols and fraction representations. Students in grades 4 and 6 were compared because previous research has shown that this is a critical time period for students to consolidate their fraction knowledge (Barbieri et al, 2019;Hansen et al, 2017;Jordan et al, 2017). In addition, the students in the present research were first taught fraction symbols in grade 4; by grade 6, students were expected to have had a reasonable amount of practice using fraction symbols and thus their fraction knowledge should be more advanced.…”

Digital support principles for sustained mathematics learning in disadvantaged students

“…Yet, if prior knowledge or the capabilities and motivation to integrate new knowledge into existing knowledge structures are lacking, these cognitively activating instructional methods are unlikely to produce significant knowledge gains [ 22 ]. Instruction involving representational gestures, physical movement, and systematic feedback, for instance, has proven effective in sixth graders with mathematics difficulties [ 29 ]. Students with non-beneficial cognitive potential—i.e., with low content-specific and strategic prior knowledge, motivation, or less developed reasoning abilities—seem to particularly profit from tablet-based mathematics instruction featuring animations, adaptive tasks, and guidance during practice [ 22 , 30 ].…”