Judith Wylie

Children’s knowledge of the ordinal relations among number symbols is related to their mathematical learning. Ordinal knowledge has been measured using judgment (i.e., decide whether a sequence of three digits is in order) and ordering tasks (i.e., order three digits from smallest to largest). However, the question remains whether performance on these two ordinal tasks tap into similar cognitive processes. Canadian children (N = 87; Age M = 8.7 years, Grade 3) completed symbolic number tasks (i.e., number comparison, ordering, and order judgment) and measures of arithmetic fluency (i.e., addition and subtraction) and working memory (i.e., digit span backward). For both ordinal tasks, there was a reverse distance effect for ordered sequences such that children responded faster to adjacent than to non-adjacent sequences (e.g., 2 3 4 vs. 4 7 9) and a canonical distance effect for unordered sequences such that children responded faster to non-adjacent than to adjacent sequences (e.g., 4 2 3 vs. 4 9 7). Working memory and number comparison each predicted unique variance in the ordinal measures (ordering, order judgment, and a latent ordinal factor based on the two measures). Furthermore, ordinal skills superseded the role of number comparison as the key predictor of arithmetic, controlling for children’s gender and working memory skills. In summary, although both ordering and order judgment tasks index ordinal knowledge, a latent factor that excludes task-specific error may be a better index than either task separately.

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All families were English-speaking, and parent education levels ranged from high school to postgraduate, with a median of community college. In Grade 2, children completed general cognitive tasks (i.e., receptive vocabulary, working memory, nonverbal reasoning, and inhibitory control). In both grades, children completed single-digit addition and complementary subtraction problems. In Grade 3, they completed single-digit multiplication problems and measures of applied mathematics, specifically, word-problem solving, algebra, and measurement. We found that addition and subtraction were reciprocally related (controlling for cognitive skills). Subtraction fluency predicted multiplication in Grade 3, whereas addition fluency did not. In Grade 3, both subtraction and multiplication fluency were predictors of applied mathematics, with multiplication partially mediating the relation between subtraction and applied mathematics performance. These findings support the view that learning arithmetic associations is a hierarchical process. As students practice each new skill, individual differences reflect the integration of the novel component into the developing associative network. (PsycInfo Database Record (c) 2021 APA, all rights reserved).