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ERIC Number: ED663016
Record Type: Non-Journal
Publication Date: 2024-Sep-21
Pages: N/A
Abstractor: As Provided
ISBN: N/A
ISSN: N/A
EISSN: N/A
A Fraction Sense Intervention Grounded in Principles from the Science of Learning for Students with Mathematics Difficulties
Nancy Dyson; Nancy Jordan; Taylor Guba; Heather Suchanec
Society for Research on Educational Effectiveness
Introduction: The 2022 NAEP Mathematics Assessment reported the "largest score declines in NAEP mathematics at grades 4 and 8 since initial assessments in 1990" (NAEP, 2022). More disturbing is that those who could least afford to lose ground lost the most. Gaps based on race, gender, and disability remain virtually unchanged from year to year, making this lack of proficiency in math a matter of equity. Even students who might not pursue math-intensive fields increasingly need mathematics proficiency to contribute to the workforce and perform daily tasks. Fractions, in particular, represent a crucial component of mathematics proficiency, especially in trades and mathematics for daily life. Fractions are often needed for correct measurement when cooking, making home improvements, and even when dispensing medication. However, fractions are difficult for both students and teachers alike. Several studies have shown that both preservice and in-service elementary teachers struggle with fractions (Olanoff, 2014). Even if teachers are proficient at fraction procedures, they have trouble explaining why fraction procedures work (Copur-Gencturk, 2021). Special education teachers have shown themselves to be particularly weak in fraction conceptual understanding and have difficulty even explaining why a common denominator is necessary for the addition of fractions (Copur-Gencturk, 2021). Those responsible for teaching fraction understanding to students who struggle with math must have proven, effective approaches for developing fraction understanding. This instruction must give students the ability to perform simple operations with fractions without depending on easily misapplied rote procedures. Furthermore, those who prepare math educators must be familiar with such validated approaches to be able to equip preservice teachers with a means of breaking the cycle of failure in these students. The goal of this presentation is to show how approaches from the science of learning can be used effectively by classroom teachers to develop fraction sense in students who struggle with math in general and fractions in particular. Preliminary results from a multi-year RCT will be presented. The Fraction Sense Intervention: To address the need for an effective fraction intervention, we developed a user-friendly intervention with funding from an IES Development and Innovation grant. This intervention seeks to build fraction sense in students whose approach to fractions has previously been nonsensical and wrought with misapplication of rote procedures. The Fraction Sense Intervention (FSI) has been shown to be effective when taught by researchers to small (Dyson et al., 2018) and larger-sized groups (Barbieri et al., 2019). Designed specifically for students who have not responded to conventional instruction in fractions, the FSI is intended for supplemental use as an intervention in an MTSS (Multi-Tiered Support System) classroom. However, the approaches can also be used in general education classrooms as a universal approach to developing deep fraction understanding in all students. The goal of the intervention is to improve students' understanding of fractions as numbers with magnitudes, fraction equivalence and ordering, and fraction arithmetic. This is accomplished by building a deep understanding of the meaning of the numerator and denominator and how they work together to determine the magnitude of the fraction. The fraction concepts are taught with a limited number of denominators (2,4,8,3,6,12), ones that are commonly encountered in daily life. This approach allows students to think deeply about fraction concepts without overwhelming them with too many changing denominators. The fraction intervention connects familiar representations (e.g., fraction bars) to the number line while emphasizing fraction magnitude, equivalency, and arithmetic concepts. (See examples of representations in the appendix). The Current Study: Supported by funding from an IES Efficacy Grant, the current study examines the efficacy of the FSI when being implemented by classroom teachers. The intervention lessons are presented as animated PowerPoint slides which are both engaging and effective in presenting fraction concepts. The lesson script appears on the PowerPoint slides, enabling the teachers to draw student attention to the slides and to provide visual and verbal representations side by side. Grounded in Principles from the Science of Learning: To maximize effectiveness or, in other words, to help learning "stick" (Brown et al., 2014), the FSI employs principles derived from research in the cognitive and learning sciences. These principles include use of physical movements or gestures to promote learning (Alibali, Nathan, & Fujimore, 2011); concreteness fading to help students integrate concrete and symbolic representations (Fyfe & Nathan, 2019; Uttal et al., 2013); integrated visual and verbal models to reduce attention splitting (Ayres, & Sweller, 2005), and side by side comparisons of solution methods (Rittle-Johnson, Star & Durkin, 2009; Richland, Stigler, & Holyoak, 2012). The intervention also provides challenging retrieval practice that is spaced out over time and interleaves different types of problems (Rohrer, Dedrick, & Burgess, 2014) to enhance retention, understanding, and transfer (Carpenter et al., 2012; Dunlosky et al., 2013). Corrective and process-oriented feedback is always provided after students complete practice (Brown et al., 2014). Finally, the intervention is anchored in meaningful contexts (Bottge et al., 2014) that center on visual number lines and fraction bars (Bottge et al., 2014). Procedures and Results: We will be presenting results from our ongoing RCT which is examining the impact of the fraction intervention, and the conditional (mediators and moderators) effects of student-level factors as well as treatment fidelity (see Figure 1). Data are being collected from 5 large school districts that serve a socioeconomically and ethnically diverse population of students. Using multi-level modeling, data collected from our first and second cohorts show promising (see Table 1). Descriptive analyses showed that at pretest, many students exhibited conceptual misunderstandings and relied on inappropriate fraction procedures leading to nonsensical solution. For example, for a simple problem such as 2+3/8, students responded with answers less than 1, such as 5/8 or 5/10. After participating in the FSI, most FSI students understood that this addition problem results in a number greater than its parts. The findings show that students who are far behind their peers in mathematics can learn to interpret and operate with fractions. We will have data from our third cohort incorporated into the analysis in time for the conference in September.
Society for Research on Educational Effectiveness. 2040 Sheridan Road, Evanston, IL 60208. Tel: 202-495-0920; e-mail: contact@sree.org; Web site: https://www.sree.org/
Publication Type: Reports - Research
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED)
Authoring Institution: Society for Research on Educational Effectiveness (SREE)
IES Funded: Yes
Grant or Contract Numbers: N/A