Children’s subtraction by addition strategy use and their subtraction-related conceptual knowledge

This study is the first to examine the associations between the occurrence, frequency, and adaptivity of children’s subtraction by addition strategy use (SBA; e.g., 712 − 346 = ?; 346 + 54 = 400, 400 + 300 = 700, 700 + 12 = 712, and 54 + 300 + 12 = 366) and their underlying conceptual knowledge. Specifically, we focused on two rarely studied components of conceptual knowledge: children’s knowledge of the addition/subtraction complement principle (i.e., if a + b = c, then c − b = a and c − a = b) and their knowledge of different conceptual subtraction models (i.e., understanding that subtraction can be conceived not only as “taking away” but also as “determining the difference”). SBA occurrence was examined using a variability on demand task, in which children had to use multiple strategies to solve a subtraction. SBA frequency and strategy adaptivity were investigated with a task in which children could freely choose between SBA and direct subtraction (e.g., 712 − 346 = ?; 712 − 300 = 412, 412 − 40 = 372, and 372 − 6 = 366) to solve 15 subtractions. We measured both children’s knowledge of the addition/subtraction complement principle, and whether they understood subtraction also as “determining the difference.” SBA occurrence and frequency were not related to conceptual knowledge. However, strategy adaptivity was related to children’s knowledge of the addition/subtraction complement principle. Our findings highlight the importance of attention to conceptual knowledge when teaching multi-digit subtraction and expand the literature about the relation between procedural and conceptual knowledge.