Does an integrated focus on fractions and decimals improve at-risk students’ rational number magnitude performance? [Fractions intervention with decimal magnitude instruction vs. control]

Findings

Rational Numbers Computation outcomes—Statistically significant positive effect found for the domain

Outcome measure	Comparison	Period	Sample	Intervention mean	Comparison mean	Significant?	Improvement     index	Evidence tier
Fraction calculations from the fraction battery-revised	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	18.52	8.69	Yes	44

Rational Numbers Knowledge outcomes—Substantively important positive effect found for the domain

Outcome measure	Comparison	Period	Sample	Intervention mean	Comparison mean	Significant?	Improvement     index	Evidence tier
National Assessment of Educational Progress (NAEP) selected items	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	14.99	13.77	No	--

Rational Numbers Magnitude Understanding/Relative Magnitude Understanding outcomes—Statistically significant positive effect found for the domain

Outcome measure	Comparison	Period	Sample	Intervention mean	Comparison mean	Significant?	Improvement     index	Evidence tier
0-2 Fraction Number Line	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	-0.37	-0.52	Yes	32
0-1 Decimal Number Line Task (Malone, Kelley, & Fuchs, 2014, adapted from Siegler et al., 2011)	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	-0.27	-0.31	Yes	19
Decimal Magnitude Assessment—similar items only (Malone et al., 2019)	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	0.65	0.19	No	--
Decimal Magnitude Assessment—dissimilar items only (Malone et al., 2019)	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	0.20	0.19	No	--

Rational Numbers Word Problems/Problem Solving outcomes—Statistically significant positive effect found for the domain

Outcome measure	Comparison	Period	Sample	Intervention mean	Comparison mean	Significant?	Improvement     index	Evidence tier
Fraction word problems from the fraction battery-revised	Targeted Math Intervention vs. Business as usual	1 Month	Fraction Magnitude + Decimal Magnitude intervention vs. Control group contrast; 152 students	11.04	8.97	Yes	22

Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.

Study Details

Setting

Participants were drawn from 58 fourth-grade classrooms in 12 schools in a large United States city.

Study sample

In this contrast, the intervention group (fraction magnitude + decimal magnitude) was 42% male. The racial and ethnic breakdown of the intervention group was 38% African American, 15% white non-Hispanic, and 24% Hispanic. The race/ethnicity for the other 23% of students in this group was not specified. 12% of students in the intervention group were receiving special education services, and of these, 67% had a learning disability. 22% of students in the intervention group were classified as English learner students. 89% of the students in the intervention group qualified for free or reduced price lunch. The comparison group (the business as usual control group) was 46% male. The racial and ethnic breakdown of the comparison group was 46% African American, 18% white non-Hispanic, and 26% Hispanic. The race/ethnicity for the other 10% of students in this group was not specified. 13% of students in the comparison group were receiving special education services, and of these, 60% had a learning disability. 20% of students in the comparison group were classified as English learner students. 87% of the students in the comparison group qualified for free or reduced price lunch (p. 3).

Intervention Group

For this review, the intervention condition is the Fraction Magnitude + Decimal Magnitude group. Lessons, which lasted 35-minutes, were taught to student dyads, three times per week for 12 weeks (36 lessons). Each lesson had the same structure: warm-up, training (tutors model new ideas), relay (guided practice, with students providing reasoning for their problem solving thinking), sprint (fluency building skills), and individual contest (students complete problems independently and are given feedback). The lessons used the Fraction Face-Off! program, which includes a self-regulation component. The lessons focus on fraction magnitude understanding, particularly by comparing fractions to benchmark fractions like 1/2. Tutors teach students about comparing and ordering fractions, finding equivalent fractions, and placing fractions on 0-1 and 0-2 number lines. Sessions use manipulatives (fraction tiles and fraction circles) and number lines. In the warm-up portion of the session beginning in lesson 7, the fraction magnitude + decimal magnitude group received the decimal magnitude portion of the intervention. In these sessions, instruction integrated fraction magnitude and decimal magnitude. Lessons 7-12 focused on writing decimal-fraction equivalencies with tenths, and Lessons 13-15 compared decimal tenths and fraction tenths. Lessons 16-18 focused on placing decimal tenths on a number line, Lessons 19-21 focused on decimal-fraction equivalencies with hundredths, Lessons 22-30 mixed tenths and hundredths, Lessons 31-33 involved ordering decimals (tenths and hundredths), and Lessons 34-36 were review.

Comparison Group

In this contrast, the comparison condition was business-as-usual math instruction. The district’s fourth-grade math program was envisionMATH, which addresses fractions in two units: Understanding Fractions and Adding/Subtracting Fractions. The authors administered a questionnaire to district teachers, and results indicated that five of the 39 math teachers reported using only the Common Core Math Standards, one reported using only enVisionMATH, and 33 reported using a combination of the Common Core Math Standards, enVisionMATH, and the state standards. Researchers found that students in the comparison group focused more on part-whole understanding with respect to fractions and relied more on procedural methods when comparing fractions. Intervention group students, on the other hand, focused more on conceptual and magnitude understanding and emphasized more strongly the assessment of fraction and decimal magnitude with number lines. Additionally, intervention group activities restricted fraction denominators to 12, whereas comparison group activities included denominators to 100. Also, almost a third of teachers did not integrate decimal and fraction concepts, and when they did, they did not tend to include manipulatives and real-life applications or emphasis comparing, ordering, and number line placement strategies (as did the intervention tutors). Lastly, comparison group instruction utilized picture-drawing and the identification of key words, whereas the intervention instruction focused on identifying word problem types. Students across conditions (both intervention conditions and the comparison condition) received similar amounts of math instruction.

Support for implementation

Tutors were trained in two phases. The first phase, which was 20 hours in duration, focused on the manualized intervention. After practice delivering lessons with peers and achieving 95% implementation accuracy, tutors could begin working with the student participants. The second phase of training involved weekly meetings for additional support on upcoming teaching content. (page 6) The researchers conducted frequent live observations during intervention sessions and audio-recorded all sessions to monitor implementation fidelity and provide feedback.