Improving At-Risk Learners' Understanding of Fractions
Fuchs, Lynn S.; Schumacher, Robin F.; Long, Jessica; Namkung, Jessica; Hamlett, Carol L.; Cirino, Paul T.; Jordan, Nancy C.; Siegler, Robert; Gersten, Russell; Changas, Paul (2013). Journal of Educational Psychology, v105 n3 p683-700 . Retrieved from: https://eric.ed.gov/?id=EJ1054396
-
examining143Students, grade4
Practice Guide
Review Details
Reviewed: May 2026
- Practice Guide (findings for Targeted Math Intervention)
- Randomized Controlled Trial
- Meets WWC standards without reservations because it is a randomized controlled trial with low attrition.
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
2010 Fraction Battery: Fraction Calculations |
Targeted Math Intervention vs. Business as usual |
1 Week |
Full sample;
|
9.07 |
7.51 |
Yes |
|
|
|
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 Week |
Full sample;
|
12.20 |
11.36 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
National Assessment of Educational Progress - Part-Whole questions |
Targeted Math Intervention vs. Business as usual |
1 Week |
Full sample;
|
5.79 |
5.36 |
Yes |
|
||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
2010 Fraction Battery: Comparing Fractions |
Targeted Math Intervention vs. Business as usual |
1 Week |
Full sample;
|
12.73 |
7.06 |
Yes |
|
|
|
|
Fraction Number Line |
Targeted Math Intervention vs. Business as usual |
1 Week |
Full sample;
|
-0.20 |
-0.32 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
National Assessment of Educational Progress - Measurement questions |
Targeted Math Intervention vs. Business as usual |
1 Week |
Full sample;
|
5.62 |
4.68 |
Yes |
|
||
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
10% English language learners -
Female: 48%
Male: 52% -
Race Black 62% Other or unknown 4% White 44% -
Ethnicity Hispanic 19% Not Hispanic or Latino 81%
Study Details
Setting
Sample Alignment: Study participants are students who scored below the 35th percentile on an assessment of skill in whole-number calculation. A previous version of the study looked at students who were between the 0th and 17th percentiles and students who were between the 17th and 34th percentiles. Age or grade range: Students are in fourth grade. Location: Study participants are in 13 schools, presumably in the U.S.
Study sample
Percentages were provided for intervention and control conditions separately. Respectively, intervention and control: 50% and 54% male; 12% and 9% EL; 81% and 83% FRL, 5% each recieved special education; 51% and 54% African American; 26% and 24% White; 19% and 19% Hispanic; 4% and 3% other. (all Hispanic students were White). According to the author, groups were demographically comparable (all ps .05).
Intervention Group
The intervention was small-group tutoring (3 pupils per instructor) on fractions, conducted for 30 minutes at a time, 3 times a week, for 12 weeks. The tutoring was in addition to students' regular math courses and used the fraction program Fraction Challenge. Fraction Challenge emphasizes the conceptualization of fractions on a number line from 0 to 1 over the conceptualization of fractions as a part of a whole (e.g. 3/4 of a pie).
Comparison Group
The comparison condition was regular classroom instruction using Houghton Mifflin Math, which emphasizes the part-whole conceptualization of fractions. Part-whole conceptualization interprets fractions as representing a part of an object. Many of the students also attended a remediation course provided by the schools three times a week.
Support for implementation
Training for tutors consisted of participation in a 2-day workshop. Over the course of the intervention, tutors participated in biweekly, hour-long meetings for ongoing support. The tutors received a script for each lesson but was not expected to memorize or read the script during the tutoring session.
Practice Guide
Review Details
Reviewed: May 2026
- Practice Guide (findings for Fraction Face-Off! with multiplicative word problems)
- Randomized Controlled Trial
- Meets WWC standards without reservations because it is a randomized controlled trial with low attrition.
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Fraction Calculations |
Fraction Face-Off! with multiplicative word problems vs. Fraction Face-Off! with additive word problems |
1 Week |
Multiplicative Word Problem Intervention vs. Additive Word Problem Intervention ;
|
19.67 |
21.40 |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! with multiplicative word problems vs. Fraction Face-Off! with additive word problems |
1 Week |
Multiplicative Word Problem Intervention vs. Additive Word Problem Intervention;
|
15.20 |
14.70 |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Fraction Number Line |
Fraction Face-Off! with multiplicative word problems vs. Fraction Face-Off! with additive word problems |
1 Week |
Multiplicative Word Problem Intervention vs. Additive Word Problem Intervention;
|
0.17 |
0.19 |
No |
-- |
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Multiplicative Word Problems from the 2012 Fraction Battery |
Fraction Face-Off! with multiplicative word problems vs. Fraction Face-Off! with additive word problems |
1 Week |
Multiplicative Word Problem Intervention vs. Additive Word Problem Intervention;
|
13.48 |
8.31 |
Yes |
|
|
|
Additive Word Problems from the Fraction Battery–2012 |
Fraction Face-Off! with multiplicative word problems vs. Fraction Face-Off! with additive word problems |
1 Week |
Multiplicative Word Problem Intervention vs. Additive Word Problem Intervention;
|
13.49 |
15.31 |
No |
-- |
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
17% English language learners -
Female: 54%
Male: 46% -
Race Black 58% Other or unknown 6% White 14% -
Ethnicity Hispanic 23% Not Hispanic or Latino 78%
Study Details
Setting
The sample includes 143 at-risk 4th grade students from 45 general education classrooms in 14 schools.
Study sample
The sample consisted of at-risk students. The authors defined risk as performance below the 35th percentile at the start of fourth grade on a broad-based calculations test (Wide Range Achievement Test–4 [WRAT]; Wilkinson & Robertson, 2006). They sampled half the at-risk students from the 15th percentile and the other half between the 15th and 34th percentiles. Two-subtests of the Wechsler Abbreviated Scales of Intelligence (WASI; Wechsler, 1999) were administered to students who met the risk criterion and 18 students with T-scores below the 9th percentile on both subtests were excluded. The sample of 143 students includes 54% females, 17% English learners, 89.5% free/reduced lunch, 17% receiving special education, 57.5% African American, 14% White, 22.5% Hispanic, and 6% Other.
Intervention Group
The Multiplicative Word Problem (M-WP) condition included 36 lessons from the Fraction Face-Off! intervention program (Fuchs, Schumacher, Malone, & Fuchs, 2015). Each lesson was 35 minutes long and was delivered to students in groups of 2 by tutors hired by the research team. A focus of the lessons was the measurement interpretation of fractions, which involved comparing, ordering, placing fractions on a number line, equivalencies, and the use of manipulatives. Two multiplicative word problems were taught: "splitting" and "grouping." The M-WP condition limited the denominators to 2, 3, 4, 5, 6, 8, 10, and 12 and the pool of equivalent fractions and reducing activities to 1/2, 1/3, 1/4, 1/5, and 1/1. It focused on using words to explain thinking, identifying problems as belonging to word problem types, and representing the structure of word problems using arrays.
Comparison Group
The Additive Word Problem (A-WP) condition included 36 lessons from the Fraction Face-Off! intervention program (Fuchs, Schumacher, Malone, & Fuchs, 2015). Each lesson was 35 minutes long and was delivered to students in groups of 2 by tutors hired by the research team. A focus of the lessons was the measurement interpretation of fractions, which involved comparing, ordering, placing fractions on a number line, equivalencies, and the use of manipulatives. Two additive word problems were taught: "increase" and "decrease." The A-WP condition limited the denominators to 2, 3, 4, 5, 6, 8, 10, and 12 and the pool of equivalent fractions and reducing activities to 1/2, 1/3, 1/4, 1/5, and 1/1. It focused on using words to explain thinking, identifying problems as belonging to word problem types, and representing the structure of word problems using a number sentence.
Support for implementation
The authors conducted follow-up trainings for tutors biweekly for 1 hour to provide opportunities for (a) dynamic feedback as the fraction lessons progressed in difficulty and (b) solving problems related to students’ challenging behavior and skill-level differences in dyads.
Fraction Face-Off! Intervention Report - Primary Mathematics
Review Details
Reviewed: April 2024
- Randomized Controlled Trial
- Meets WWC standards without reservations because it is a randomized controlled trial with low attrition.
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Please see the WWC summary of evidence for Fraction Face-Off!.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 5;
|
14.83 |
12.36 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
14.41 |
11.35 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: conceptual group;
|
14.64 |
12.07 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
14.88 |
12.68 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: combined fluency and conceptual groups;
|
14.44 |
12.07 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: fluency group ;
|
14.25 |
12.07 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
14.45 |
12.68 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: fraction-decimal magnitude group;
|
16.03 |
13.29 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
14.66 |
12.68 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: combined word problems requiring addition and subtraction and fraction-decimal magnitude groups;
|
15.61 |
13.29 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: combined multiplicative word problems and additive word problems groups;
|
15.03 |
13.21 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: multiplicative word problems group;
|
15.38 |
13.21 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 3: low performing students;
|
12.74 |
10.08 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group;
|
15.20 |
13.29 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: additive word problems group;
|
14.68 |
13.21 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 3: multiplicative word problems group vs. additive word problems group;
|
15.38 |
14.68 |
No |
-- | ||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 2: fluency group vs. conceptual group;
|
14.25 |
14.64 |
No |
-- | ||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
14.45 |
14.88 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Face-Off! vs. Fraction Face-Off! |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group vs. fraction-decimal magnitude group;
|
15.20 |
16.03 |
No |
-- | ||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Magnitude comparison |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
6.21 |
4.59 |
Yes |
|
|
|
|
Magnitude explanation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
6.10 |
1.14 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
Magnitude comparison |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
6.47 |
4.59 |
Yes |
|
||
|
Magnitude explanation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
9.10 |
1.14 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) - Measurement subscale |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
7.02 |
4.66 |
Yes |
|
||
|
Magnitude explanation |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
9.10 |
2.93 |
Yes |
|
||
|
Magnitude comparison |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
5.94 |
4.59 |
Yes |
|
||
|
Magnitude explanation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
2.93 |
1.14 |
Yes |
|
||
|
Magnitude comparison |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
6.47 |
5.94 |
Yes |
|
||
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|
|---|---|---|---|---|---|---|---|---|---|
|
Fraction calculation |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 5;
|
19.30 |
8.68 |
Yes |
|
|
|
|
Additive word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: combined multiplicative word problems and additive word problems groups;
|
14.48 |
7.94 |
Yes |
|
|
|
|
Fraction number line |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 5;
|
0.23 |
0.33 |
Yes |
|
|
|
|
Fraction word problems |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: combined word problems requiring addition and subtraction and fraction-decimal magnitude groups;
|
11.51 |
8.79 |
Yes |
|
|
|
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohorts 3 to 4;
|
10.35 |
6.93 |
Yes |
|
|
|
|
Compare fractions |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
12.73 |
7.06 |
Yes |
|
|
|
| Show Supplemental Findings | |||||||||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group;
|
18.54 |
8.45 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: fraction-decimal magnitude group;
|
20.85 |
8.45 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
17.60 |
7.50 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
20.42 |
8.89 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
21.75 |
8.89 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
21.07 |
8.89 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: additive word problems group;
|
21.39 |
11.43 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: combined word problems requiring addition and subtraction and fraction-decimal magnitude groups;
|
19.67 |
8.45 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: conceptual group;
|
17.84 |
8.16 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: fluency group ;
|
17.43 |
8.16 |
Yes |
|
||
|
Additive word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: additive word problems group;
|
15.08 |
7.94 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: combined fluency and conceptual groups;
|
17.63 |
8.16 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: combined multiplicative word problems and additive word problems groups;
|
20.51 |
11.43 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: multiplicative word problems group;
|
19.64 |
11.43 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
13.61 |
6.49 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
0.20 |
0.32 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: fluency group ;
|
0.19 |
0.27 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: conceptual group;
|
0.20 |
0.27 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 2: combined fluency and conceptual groups;
|
0.19 |
0.27 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: multiplicative word problems group;
|
13.89 |
7.37 |
Yes |
|
||
|
Additive word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: multiplicative word problems group;
|
13.88 |
7.94 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: multiplicative word problems group;
|
0.18 |
0.26 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: combined multiplicative word problems and additive word problems groups;
|
0.18 |
0.26 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 3: low-performing students;
|
16.11 |
7.21 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group;
|
0.37 |
0.52 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: fraction-decimal magnitude group;
|
0.36 |
0.52 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 3: multiplicative word problems group vs. additive word problems group;
|
13.89 |
8.21 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: additive word problems group;
|
0.19 |
0.26 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: combined word problems requiring addition and subtraction and fraction-decimal magnitude groups;
|
0.37 |
0.52 |
Yes |
|
||
|
Fraction word problems |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: fraction-decimal magnitude group;
|
12.08 |
8.79 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: word problems group;
|
0.20 |
0.26 |
Yes |
|
||
|
Fraction word problems |
Fraction Face-Off! vs. enVisionMATH |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group;
|
10.97 |
8.79 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: combined multiplicative word problems and additive word problems groups;
|
11.07 |
7.37 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
0.21 |
0.26 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
0.21 |
0.26 |
Yes |
|
||
|
Compare fractions |
Fraction Face-Off! vs. Business as usual |
2 Weeks |
Student cohorts 1 to 3: low-performing students;
|
11.36 |
7.67 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: combined explaining and word problems groups;
|
9.64 |
6.49 |
Yes |
|
||
|
National Assessment of Educational Progress (NAEP) - Part-whole subscale |
Fraction Face-Off! vs. Houghton Mifflin Mathematics |
2 Weeks |
Student cohort 1;
|
5.79 |
5.36 |
Yes |
|
||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 3: additive word problems group;
|
8.21 |
7.37 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 3: multiplicative word problems group vs. additive word problems group;
|
0.18 |
0.19 |
No |
-- | ||
|
Fraction number line |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 2: fluency group vs. conceptual group;
|
0.19 |
0.20 |
No |
-- | ||
|
Fraction calculation |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 2: fluency group vs. conceptual group;
|
17.43 |
17.84 |
No |
-- | ||
|
Fraction number line |
Fraction Face-Off! vs. Fraction Face-Off! |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group vs. fraction-decimal magnitude group;
|
0.37 |
0.36 |
No |
-- | ||
|
Multiplicative word problems |
Fraction Face-Off! vs. enVisionMATH |
2 Weeks |
Student cohort 4: explaining group;
|
5.88 |
6.49 |
Yes |
|
||
|
Fraction number line |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
0.21 |
0.20 |
No |
-- | ||
|
Fraction calculation |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
20.42 |
21.75 |
Yes |
|
||
|
Fraction word problems |
Fraction Face-Off! vs. Fraction Face-Off! |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group vs. decimal-fraction magnitude group;
|
10.97 |
12.08 |
No |
-- | ||
|
Fraction calculation |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 3: multiplicative word problems group vs. additive word problems group;
|
19.64 |
21.39 |
Yes |
|
||
|
Additive word problems |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 3: multiplicative word problems group vs. additive word problems group;
|
13.88 |
15.08 |
Yes |
|
||
|
Fraction calculation |
Fraction Face-Off! vs. Fraction Face-Off! |
1 Month |
Student cohort 5: word problems requiring addition and subtraction group vs. decimal-fraction magnitude group;
|
18.54 |
20.85 |
No |
-- | ||
|
Multiplicative word problems |
Fraction Face-Off! vs. Fraction Face-Off! |
2 Weeks |
Student cohort 4: explaining group vs. word problems group;
|
5.88 |
13.61 |
Yes |
|
||
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
15% English language learners -
Female: 55%
Male: 45% -
Race Black 52% Other or unknown 29% White 19% -
Ethnicity Hispanic 23% Not Hispanic or Latino 77%
Study Details
Setting
The study took place in multiple classrooms and schools within a single school district over a 5-year period. Each year of the study, the study involved a new cohort of approximately 250 fourth-grade students from 50 classrooms in 14 elementary schools. The location of the schools was not specified.
Study sample
Study students were fourth-grade students considered at-risk in mathematics, which the authors defined as scoring below the 35th percentile on a computation test. Among students who met the definition of at-risk within study classrooms, the authors sampled three to nine students per class for inclusion in the study. Averaging across the five student cohorts, approximately 52% of students were African American, 19% were White, 23% were Hispanic, and 6% were another race or ethnicity. Approximately 55% of students were female, 15% English learners, 88% were eligible for free or reduced-price lunch, and 10% were in special education classrooms.
Intervention Group
Fraction Face-Off! is a supplemental math program designed to support fourth-grade students who need assistance solving fraction problems. Teachers use program materials with individual students or small groups to promote understanding of the magnitude of fractions, to compare two fractions, to put three fractions in order, and to place fractions on a number line. The program includes 36 lessons, each with four activities: a warm-up problem, group work, a speed game to build fluency, and a worksheet to check students’ understanding. These lessons are designed to be taught three times a week for 12 weeks. Within each study class, the Fraction Face-Off! intervention was delivered by one teacher to small groups (three-to-one ratio) three times per week for 12 weeks between September/October and early February. Each teacher was responsible for two to four groups. Depending on each regular classroom teacher’s scheduling preference, the teacher delivered the intervention to the study students through pull-out tutoring sessions that took place during one of the three school instructional periods: 1) students' math block (typically 50 minutes), 2) math center time (typically 20 minutes), or 3) the school's intervention period (typically 45 minutes). Study teachers were graduate students funded by the research grant; some were licensed teachers, but most were not licensed. Each of the 36 lessons varied in length between 30 and 35 minutes, and included four to six activities. In year 1, there was one intervention group, and each lesson included four activities: introduction of concepts or skills (8–12 minutes), group work (8–12 minutes), the speed game (1 minute), and individual work (8 minutes). In years 2 through 5, when there were two Fraction Face-Off! intervention groups, 25 minutes of each session were the same across the two intervention conditions. Instructional methods differed for the remaining 5 to 7 minutes of each session. For year 2, the activities for 5 minutes of each session differed between the two intervention conditions; students either completed activities to build fluency with measurement topics or they completed activities to consolidate conceptual understanding of the same measurement topics. In year 3, the activities for 7 minutes of each session differed between groups; one intervention condition focused on multiplicative word problems, while the other intervention condition focused on additive word problems. In year 4, the activities for 7 minutes of each session differed, during which teachers taught students to provide high quality explanations when comparing fraction magnitudes or solve fraction word problems. In year 5, the 7-minute warm-up activity differed between the two intervention conditions, during which teachers implemented the decimal magnitude or fraction applications component. In addition to Fraction Face-Off!, students in the intervention group also used their regular district math curriculum, Houghton Mifflin Math (Greenes et al., 2005) in year 1 and enVisionMATH (Scott Foresman-Addison Wesley, 2011) in years 2 through 5.
Comparison Group
The comparison group used the regular district curriculum, Houghton Mifflin Math in year 1 and enVisionMATH in years 2 through 5. Houghton Mifflin Math included lessons on conceptual understanding and procedural calculations and focused on understanding parts of a whole. The conceptual lessons included vocabulary instruction, connections across multiple curricula (including social studies, music, and writing), guided practice, independent work, and connections to real life. The procedural calculations included calculations with proper and improper fractions and mixed numbers. The enVisionMATH curriculum included two units: 1) Understanding Fractions, and 2) Adding and Subtracting Fractions. The Understanding Fractions unit focused on understanding parts of a whole by using manipulatives and drawings to illustrate the concept, and the Adding and Subtracting Fractions unit focused on procedures with fractions. The delivery of the enVisionMATH curriculum in the comparison condition covered some more advanced topics than its delivery in the intervention condition and did not restrict the range of denominators, whereas the intervention conditions limited the range of denominators to 2, 3, 4, 5, 6, 8, 10, and 12 and the range of equivalent fractions and reducing activities to 1/2, 1/3, 1/4, 1/5, and 1/1.
Support for implementation
The study teachers were full- or part-time graduate student employees of the research grant and included some licensed teachers. They were trained by experienced Fraction Face-Off! professional staff through a weeklong initial workshop followed by 1-hour follow-up trainings every other week. Follow-up trainings provided teachers with feedback and included problem solving about students’ challenging behavior and skill-level differences. Teachers received lesson guides for each of the 36 lessons and were expected to review, but not memorize, the guides. Before implementation, teachers practiced delivering the lesson to other teachers.
Additional Sources
In the case of multiple manuscripts that report on one study, the WWC selects one manuscript as the primary citation and lists other manuscripts that describe the study as additional sources.
-
Fuchs, L. S., Fuchs, D., Compton, D. L., Wehby, J., Schumacher, R. F., Gersten, R., & Jordan, N. C. (2015). Inclusion versus specialized intervention for very-low-performing students: What does access mean in an era of academic challenge?. Exceptional Children, 81(2), 134-157.
-
Fuchs, Lynn S.; Malone, Amelia S.; Schumacher, Robin F.; Namkung, Jessica; Hamlett, Carol L.; Jordan, Nancy C.; Siegler, Robert S.; Gersten, Russell; Changas, Paul. (2016). Supported Self-Explaining during Fraction Intervention. [Fractions intervention with instruction in providing explanations vs. control]. Journal of Educational Psychology, v108 n4 p493-508.
-
Fuchs, L. S., Malone, A. S., Schumacher, R. F., Namkung, J., & Wang, A. (2017). Fraction intervention for students with mathematics difficulties: Lessons learned from five randomized controlled trials. Journal of Learning Disabilities, 50(6), 631-639.
-
Fuchs, Lynn S.; Schumacher, Robin F.; Sterba, Sonya K.; Long, Jessica; Namkung, Jessica; Malone, Amelia; Hamlett, Carol L.; Jordan, Nancy C.; Gersten, Russell; Siegler, Robert S.; Changas, Paul. (2014). Does Working Memory Moderate the Effects of Fraction Intervention? An Aptitude-Treatment Interaction. [Fractions knowledge intervention with fluency building activities vs. control]. Journal of Educational Psychology, v106 n2 p499-514.
-
Fuchs, Lynn S.; Schumacher, Robin F.; Long, Jessica; Namkung, Jessica; Malone, Amelia S.; Wang, Amber; Hamlett, Carol L.; Jordan, Nancy C.; Siegler, Robert S.; Changas, Paul. (2016). Effects of Intervention to Improve At-Risk Fourth Graders' Understanding, Calculations, and Word Problems with Fractions. Elementary School Journal v116 n4 p625-651.
-
Fuchs, L. S., Sterba, S. K., Fuchs, D., & Malone, A. S. (2016). Does evidence-based fractions intervention address the needs of very low-performing students?. Journal of Research on Educational Effectiveness, 9(4), 662-677.
-
Malone, Amelia S.; Fuchs, Lynn S.; Sterba, Sonya K.; Fuchs, Douglas; Foreman-Murray, Lindsay. (2019). Does an Integrated Focus on Fractions and Decimals Improve At-Risk Students' Rational Number Magnitude Performance?.
Improving At-Risk Learners' Understanding of Fractions
Review Details
Reviewed: August 2013
- Single Study Review (109 KB) (findings for Fraction Challenge)
- Randomized Controlled Trial
- Meets WWC standards without reservations
This review may not reflect the full body of research evidence for this intervention.
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Findings
|
Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
|
Fraction Calculations |
Fraction Challenge vs. Business as usual |
Posttest |
At-risk students;
|
17.57 |
7.50 |
Yes |
|
|
|
Comparing Fractions |
Fraction Challenge vs. Business as usual |
Posttest |
At-risk students;
|
12.91 |
7.07 |
Yes |
|
|
|
Fraction Number Line |
Fraction Challenge vs. Business as usual |
Posttest |
At-risk students;
|
-0.21 |
-0.32 |
Yes |
|
|
|
National Assessment of Educational Progress (NAEP) selected items |
Fraction Challenge vs. Business as usual |
Posttest |
At-risk students;
|
14.36 |
11.35 |
Yes |
|
|
Evidence Tier rating based solely on this study. This intervention may achieve a higher tier when combined with the full body of evidence.
Sample Characteristics
Characteristics of study sample as reported by study author.
-
11% English language learners -
Female: 48%
Male: 52% -
Race Black 53% Other or unknown 3% White 25% -
Ethnicity Hispanic 19% Not Hispanic or Latino 81%
An indicator of the effect of the intervention, the improvement index can be interpreted as the expected change in percentile rank for an average comparison group student if that student had received the intervention.
For more, please see the WWC Glossary entry for improvement index.
An outcome is the knowledge, skills, and attitudes that are attained as a result of an activity. An outcome measures is an instrument, device, or method that provides data on the outcome.
A finding that is included in the effectiveness rating. Excluded findings may include subgroups and subscales.
The sample on which the analysis was conducted.
The group to which the intervention group is compared, which may include a different intervention, business as usual, or no services.
The timing of the post-intervention outcome measure.
The number of students included in the analysis.
The mean score of students in the intervention group.
The mean score of students in the comparison group.
The WWC considers a finding to be statistically significant if the likelihood that the finding is due to chance alone, rather than a real difference, is less than five percent.
The WWC reviews studies for WWC products, Department of Education grant competitions, and IES performance measures.
The name and version of the document used to guide the review of the study.
The version of the WWC design standards used to guide the review of the study.
The result of the WWC assessment of the study. The rating is based on the strength of evidence of the effectiveness of the intervention. Studies are given a rating of Meets WWC Design Standards without Reservations, Meets WWC Design Standards with Reservations, or >Does Not Meet WWC Design Standards.
A related publication that was reviewed alongside the main study of interest.
Study findings for this report.
Based on the direction, magnitude, and statistical significance of the findings within a domain, the WWC characterizes the findings from a study as one of the following: statistically significant positive effects, substantively important positive effects, indeterminate effects, substantively important negative effects, and statistically significant negative effects. For more, please see the WWC Handbook.
The WWC may review studies for multiple purposes, including different reports and re-reviews using updated standards. Each WWC review of this study is listed in the dropdown. Details on any review may be accessed by making a selection from the drop down list.
Tier 1 Strong indicates strong evidence of effectiveness,
Tier 2 Moderate indicates moderate evidence of effectiveness, and
Tier 3 Promising indicates promising evidence of effectiveness,
as defined in the
non-regulatory guidance for ESSA
and the regulations for ED discretionary grants (EDGAR Part 77).