WWC review of this study

Improving At-Risk Learners' Understanding of Fractions

Fuchs, L. S., Schumacher, R. F., Long, J., Namkung, J., Hamlett, C. L., Cirino, P. T., Jordan, N. C., Siegler, R., Gersten, R., & Changas, P. (2013). Journal of Educational Psychology, 105(3), 683–700 Retrieved from: https://eric.ed.gov/?id=EJ1054396

  • Randomized Controlled Trial
     examining 
    259
     Students
    , grade
    4

Reviewed: February 2020

At least one finding shows strong evidence of effectiveness
At least one statistically significant positive finding
Meets WWC standards without reservations
Rational Numbers Computation outcomes—Statistically significant positive effects found
Outcome
measure
Comparison Period Sample Intervention
mean
Comparison
mean
Significant? Improvement
    index
ESSA
rating

2010 Fraction Battery: Fraction Calculations

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

9.07

7.51

Yes

 
 
49
 
Rational Numbers Knowledge outcomes—Statistically significant positive effects found
Outcome
measure
Comparison Period Sample Intervention
mean
Comparison
mean
Significant? Improvement
    index
ESSA
rating

National Assessment of Educational Progress (NAEP) selected items

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

12.20

11.36

Yes

 
 
32
 
More Outcomes
Show Supplemental Findings

National Assessment of Educational Progress - Part-Whole questions

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

5.79

5.36

Yes

 
 
11
Rational Numbers Magnitude Understanding/Relative Magnitude Understanding outcomes—Statistically significant positive effects found
Outcome
measure
Comparison Period Sample Intervention
mean
Comparison
mean
Significant? Improvement
    index
ESSA
rating

2010 Fraction Battery: Comparing Fractions

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

12.73

7.06

Yes

 
 
47
More Outcomes

Fraction Number Line

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

-0.20

-0.32

Yes

 
 
36
Show Supplemental Findings

National Assessment of Educational Progress - Measurement questions

Targeted Math Intervention vs. Business as usual

1 Week

Full sample;
259 students

5.62

4.68

Yes

 
 
36

Characteristics of study sample as reported by study author.


  • 10% English language learners

  • 82% Free or reduced price lunch

  • Female: 48%
    Male: 52%
  • Race
    Black
    62%
    Not specified
    4%
    White
    44%
  • Ethnicity
    Hispanic
    19%
    Not Hispanic
    81%

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.

Reviewed: August 2013

At least one finding shows promising evidence of effectiveness
At least one statistically significant positive finding
Meets WWC standards without reservations
General Mathematics Achievement outcomes—Statistically significant positive effects found
Outcome
measure
Comparison Period Sample Intervention
mean
Comparison
mean
Significant? Improvement
    index
ESSA
rating

Fraction Calculations

Fraction Challenge vs. Business as usual

Posttest

At-risk students;
259 students

17.57

7.50

Yes

 
 
49
 
More Outcomes

Comparing Fractions

Fraction Challenge vs. Business as usual

Posttest

At-risk students;
259 students

12.91

7.07

Yes

 
 
47
 

Fraction Number Line

Fraction Challenge vs. Business as usual

Posttest

At-risk students;
259 students

-0.21

-0.32

Yes

 
 
35
 

National Assessment of Educational Progress (NAEP) selected items

Fraction Challenge vs. Business as usual

Posttest

At-risk students;
259 students

14.36

11.35

Yes

 
 
32
 

Characteristics of study sample as reported by study author.


  • 11% English language learners

  • 83% Free or reduced price lunch

  • Female: 48%
    Male: 52%
  • Race
    Black
    53%
    Not specified
    3%
    White
    25%
  • Ethnicity
    Hispanic
    19%
    Not Hispanic
    81%
 

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