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Developing an understanding of fractions is critical and is an educational focus, as reflected in national standards and principles. This study conducted a quantitative synthesis of 22 experimental studies to investigate the overall efficacy of previously conducted fraction interventions compared to standard instruction. Instruction type and achievement level were used to examine variations of the effect sizes. The results indicated that intervention was more effective than standard instruction only in problem‐solving domains, and the effects were differentiated by instruction type and achievement level. This study provides a diagnostic view of the current state of U.S. mathematics education on fractions, along with insights for future directions in fraction instruction, particularly focusing on students with mathematics difficulties. Educational implications and limitations are discussed.

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We consider a class of multidimensional conservation laws with vanishing nonlinear diffusion and dispersion terms. Under a condition on the relative size of the diffusion and dispersion coefficients, we show that the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation law. Our proof is based on methodology developed in [S. Hwang, A.E. Tzavaras, Kinetic decomposition of approximate solutions to conservation laws: Applications to relaxation and diffusion-dispersion approximations, Comm. Partial Differential Equations 27 (2002) 1229-1254] which uses the averaging lemma.