ABSTRACT
The study reported in detail in this volume is an extension of Alexander, White, and Daugherty (1997) in the very interesting and innovative book edited by English. The earlier (1997) study with 4-and 5-year-olds revealed that their analogical reasoning ability, assessed by conventional A:B::C:? form items, was significantly correlated with their ability to extend patterns, but not with three other measures of mathematical learning. Age was a significant determinant of mathematical learning but not of analogical reasoning. The present study was a longitudinal one that traced children from preschool to the end of the second grade. The children, from both the United States and Australia, were tested with a new instrument that is allegedly a measure of mathematical reasoning (the Mathematical Reasoning Test for Young Students [MRTYS]) as well as the same classical measure of analogical reasoning (the Test of Analogical Reasoning for Children [TARC]) used in the 1997 study. The children were tested a few times, so the relationships between these two measures could be investigated developmentally. The MRTYS consisted primarily of three components, Attributions and Patterning, Quantification–Relations, and Quantification–Numbers. It covered a wide range of the products of mathematical learning: Some items were concerned with mathematical reasoning, whereas others tapped requisite knowledge, like the meaning of terms used in mathematics.
