Putting Fractions Together [Practice estimating individual fractions and fraction sums]
Braithwaite, David W.; Siegler, Robert S. (2021). Journal of Educational Psychology v113 n3 p556-571. Retrieved from: https://eric.ed.gov/?id=ED612394
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examining63Students, grades4-5
Single Study Review
Review Details
Reviewed: October 2022
- Single Study Review (findings for Practice estimating individual fractions and 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
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Outcome measure |
Comparison | Period | Sample |
Intervention mean |
Comparison mean |
Significant? |
Improvement index |
Evidence tier |
|---|---|---|---|---|---|---|---|---|
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Researcher-developed number line estimation of unequal denominator fraction sums |
Practice estimating individual fractions and fraction sums—Braithwaite et al., 2021 vs. Practice estimating individual fractions |
0 Days |
Full sample;
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8.30 |
13.90 |
Yes |
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|
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Researcher-developed number line estimation of equal-denominator fraction sums |
Practice estimating individual fractions and fraction sums—Braithwaite et al., 2021 vs. Practice estimating individual fractions |
0 Days |
Full sample;
|
8.90 |
9.90 |
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: 59%
Male: 38%
Other or unknown: 3% -
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Pennsylvania
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Race Black 2% Other or unknown 3% White 95% -
Ethnicity Other or unknown 100% -
Eligible for Free and Reduced Price Lunch Free or reduced price lunch (FRPL) 39% No FRPL 61%
Study Details
Setting
The study took place in one middle school in the Pittsburgh, Pennsylvania area.
Study sample
A total of 63 students in grades 4 and 5 were included in the study. Approximately 38% of the students were male and 39% were eligible for free or reduced-price lunch. Ninety-five percent were White, 2% were Black, and 3% were another race.
Intervention Group
The intervention is a computer program intended to provide students with practice estimating the magnitude of fractions and fraction sums. Researchers implemented the intervention one-on-one with individual students over two sessions. In session one, 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. The student then played a computer game in which each trial involved attempting to capture a monster by correctly clicking the point on a 0–1 number line that corresponded to the size of a target fraction. If the point clicked by the student was sufficiently close to the correct point, the monster was caught in a cage; otherwise, the monster escaped. After the student clicked on the number line, the unit fraction strips corresponding to the target fraction displayed on the number line. The game had three phases of 4.5 minutes each, with students completing as many trials as they could during each phase. In the first phase, the unit fraction strips appeared on the computer screen and students could move the strips onto the number line (for example, move two 1/3 strips onto the number line to determine the size of 2/3); the researcher provided feedback if the student used the strips incorrectly. In the second phase, 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, 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 sizes correctly. Students completed an average of 74 trials in session one. Session two proceeded similarly as session one but with a focus on fraction sums instead of individual 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 the line the size of the fraction sum. The game had the same three 4.5-minute phases and the same increases in required accuracy within each phase as the game in session one. The two fractions in a given sum always had different denominators and summed to a value less than one. Students completed an average of 49 trials in session two. The time between sessions ranged from 1 to 6 days.
Comparison Group
Students in the comparison group played a computer game intended to provide them with practice estimating the magnitude of individual fractions but not fraction sums. Researchers implemented the practice one-on-one with individual students over two sessions. Session one was the same as session one for the intervention group, as described above. Students completed 67 trials of the game, on average. In session two, the researcher reviewed with the student how to use unit fraction strips to estimate the size of fractions on a number line, and the student followed the procedure for three fractions. The student then played the same game as played in session one. Students completed 82 trials, on average. The time between sessions ranged from 1 to 6 days.
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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