Putting Fractions Together [Practice estimating fraction sums]
Braithwaite, David W.; Siegler, Robert S. (2021). Journal of Educational Psychology, v113 n3 p556-571. Retrieved from: https://eric.ed.gov/?id=EJ1291033
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examining103Students, grades5-6
Single Study Review
Review Details
Reviewed: October 2022
- Single Study Review (findings for Practice estimating fraction sums—Braithwaite et al., 2021)
- 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 |
|---|---|---|---|---|---|---|---|---|
|
Researcher-developed number line estimation of unequal denominator fraction sums |
Practice estimating fraction sums—Braithwaite et al., 2021 vs. Practice estimating whole number sums |
0 Days |
Full sample;
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12.20 |
17.80 |
Yes |
|
|
|
Researcher-developed fraction sum magnitude comparison |
Practice estimating fraction sums—Braithwaite et al., 2021 vs. Practice estimating whole number sums |
0 Days |
Full sample;
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78.60 |
80.50 |
Yes |
|
|
|
Researcher-developed fraction sum magnitude comparison with think-aloud protocols |
Practice estimating fraction sums—Braithwaite et al., 2021 vs. Practice estimating whole number sums |
0 Days |
Full sample;
|
83.70 |
81.60 |
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.
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Female: 58%
Male: 41%
Other or unknown: 1% -
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Florida, Pennsylvania
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Race Black 27% Other or unknown 19% White 54% -
Ethnicity Hispanic 17% Other or unknown 83% -
Eligible for Free and Reduced Price Lunch Free or reduced price lunch (FRPL) 36% No FRPL 64%
Study Details
Setting
The study took place in two schools: a middle school in Pittsburgh, Pennsylvania and a school in Tallahassee, Florida. The study authors did not report the grade level of the Florida school.
Study sample
A total of 103 students in grades 5 and 6 were included in the study. Approximately 41% of the students were male and 36% were eligible for free or reduced-price lunch. Fifty-four percent were White, 27% were Black, and 19% either were another race or did not report race. Seventeen percent of students were Hispanic or Latino.
Intervention Group
The intervention is a computer program intended to provide students with practice estimating the magnitude of fraction sums. Researchers implemented the intervention one-on-one with individual students in a single session. A researcher first gave the student a tutorial on using fraction strips to visually represent unit fractions (that is, fractions with a numerator of one, ranging from 1/2 to 1/10) and positioning the fractions strips on a number line that ranged from zero to one to show the size of a fraction. For example, to show the size of 2/4, the student would place two 1/4 strips on the number line, starting at zero. After the student followed this procedure to show the size of three fractions, the researcher gave the student a tutorial in putting together unit fraction strips to determine the location on the 0–1 number line corresponding to the sum of two fractions (for example, for the sum 3/9 + 1/2, place three 1/9 strips on the number line, followed by a 1/2 strip). The student then played a computer game in which each trial involved attempting to capture a monster by correctly showing on the number line the size of the fraction sum. If the size indicated by the student was sufficiently close to the correct size of the fraction sum, the monster was caught in a cage; otherwise, the monster escaped. The game had three phases, with students completing as many trials as they could during each phase. In the first phase, which lasted 4 minutes, the unit fraction strips appeared on the computer screen and students could move the strips onto the number line; the researcher provided feedback if the student used the strips incorrectly. In the second phase, which lasted 5 minutes, the unit fraction strips appeared on the screen but could not be moved; the researcher encouraged the student to imagine moving the strips onto the number line. In the third phase, which lasted 6 minutes, the unit fraction strips did not appear on the screen. Within each phase, the accuracy required to capture the monster increased as the student estimated fraction sums correctly. The two fractions in a given sum always had different denominators and summed to a value less than one. Students completed a total of 51 trials, on average.
Comparison Group
Students in the comparison group played a computer game intended to provide them with practice estimating the magnitude of whole number sums. Researchers used a computer to implement the practice one on one with individual students in a single session. A researcher first gave the student a tutorial on using whole number strips that visually represented 1, 5, 10, 20, 50, 100, 200, and 500 and showing the location of a given number on a number line that ranged from zero to 1,000 by positioning on the number line the strips that stood for the hundreds digit, tens digit, and units digit of the number. After the student followed this procedure to show the location of three whole numbers on the number line, the researcher gave the student a tutorial in putting together whole number strips to determine the location on the 0–1,000 number line corresponding to the sum of two whole numbers (for example, 598 + 145). The student then played a computer game in which each trial involved attempting to capture a monster by correctly showing on the number line the size of the number sum. The game had the same three phases and the same increases in required accuracy within each phase as the game played by the intervention group. The whole numbers in the sums were roughly equivalent to the fractions used in the intervention group, multiplied by 1,000; for example, the fraction sum 3/5 + 1/7 could become the numbers sum 598 + 145, with 598 being used instead of 600 to decrease the likelihood of the student computing the exact sum. Students completed 47 trials, on average.
Support for implementation
The researchers conducting the interventions followed scripts that specified the instructions and feedback to give the students in each session.
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.
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