Academically talented students have precocious reasoning abilities and are ready for advanced math earlier than when it is typically offered. This study examined above-grade-level abstract reasoning abilities of 150 students ranging from 2nd-6th grades. Based on chi-square analyses, the distribution of students' scores on the Arlin Test of Formal Reasoning (Arlin, 1982, 1984) was not significantly different from distributions for a normative group of students four grade levels higher. An Age Level by Gender MANOVA revealed that understanding of various abstract concepts varied by age for only 4 of 8 subscales or concepts: Probability, Proportion, Momentum, and Frames of References. Performance varied widely within age level for the understanding of Volume, Correlation, Combination, and Mechanics. There may not be one age at which children acquire abstract reasoning and are ready for advanced mathematics.
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