Emphasize measurement and number line interpretations of fractions in instruction to build fraction magnitude understanding¶

Strategy · All strategies
Evidence · 3 claims (3 for) · 2 studies (1 review, 1 associational), q3 · 1 of 2 report an effect size · 3 claims rest on one study

Description¶

Because fraction magnitude understanding is central to mathematics achievement, the authors argue that interventions improving magnitude understanding may be effective in the fraction domain. They cite evidence that activities mapping numbers onto space, such as feedback interventions and numerical board games for whole numbers, and card games focusing on the "representation and manipulation of fractions in terms of their magnitudes", improved students' fraction magnitude understanding. An intervention putting greater emphasis on measurement and number line interpretations of fractions was more effective than one emphasizing part-whole interpretations, and gains in magnitude understanding mediated gains in other outcome measures.

Design Implications¶

Context¶

Requirements¶

• Interventions require sustained practice; the cited studies ran 10 weeks and 12 weeks with multiple 30-minute sessions per week.

Constraints¶

• The cited interventions combined a variety of instructional techniques, learner activities, and fraction representations, so the active ingredients are not yet isolated; the authors state subsequent research must clarify if, when, how, and for whom such interventions work and whether gains transfer.

Target Learners¶

• Elementary school students, including children with mathematics learning difficulties and children from low-income households

Target Learning Goals¶

• Fraction magnitude understanding
• Fraction arithmetic proficiency

Affordances¶

• Integrated Theory Numerical Development Fractions

Claims¶

• Fraction magnitude understanding, measured by number line estimation, predicts general mathematics achievement beyond fraction arithmetic skill in 5 of 6 Belgian, Chinese and U.S. grade samples, though not among Chinese 8th graders [+M]
• The relation between fraction magnitude understanding and mathematics achievement is a general cognitive characteristic, not attributable to specifics of the U.S. educational system, though instruction quality may strengthen or weaken it [+W]
• Number line estimation and numerical magnitude comparison correlate with mathematics achievement (r = .24 to .44), with number line estimation more strongly related in older children [+M]

Related Strategies¶

Examples¶

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Key Sources¶

• Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the Gap: Fraction Understanding is Central to Mathematics Achievement in Students from Three Different Continents. Learning and Instruction. https://doi.org/10.1016/j.learninstruc.2014.03.002