Using non-verbal methods to study the flexible use of the subtraction by addition strategy

Over the past 30 years, extensive research has been conducted on the strategies that are used to mentally solve symbolically presented subtraction problems (M - S = .). One way to classify these strategies is by looking at the operation that underlies the solution process. In this way, two types of strategies can be distinguished: (1) direct subtraction strategies, in which the subtrahend is directly subtracted from the minuend (e.g., 75 - 43 = . by doing 75 - 40 = 35, 35 - 3 = 32), and (2) subtraction by addition strategies, in which one determines how much needs to be added to the subtrahend to get to the minuend (e.g., 75 - 43 = . by doing 43 + 30 = 73 and 73 + 2 = 75, so the answer is 30 + 2 = 32). Several studies have shown that adults report the subtraction by addition strategy frequently and use it efficiently and flexibly, whereas children hardly report using it. A closer inspection of reaction time data of earlier studies suggests, however, that children sometimes used subtraction by addition while reporting direct subtraction. In this doctoral thesis, we therefore used two non-verbal methods to study the use of subtraction by addition: we compared performance on problems in different presentation formats, and used linear regression models that represented different strategy use patterns. With these methods, we investigated the flexible use of subtraction by addition in both large single-digit and multi-digit subtraction, first in adults (presented in Chapters 1 and 2), then in both typically achieving children (presented in Chapters 3 and 4) and children with MLD (presented in Chapter 5). In all five studies, we focused on whether participants switched between the direct subtraction and the subtraction by addition strategy, and, if so, whether they based their strategy choice on the relative size of the subtrahend. Based on previous work in the fields of cognitive psychology and mathematics education, we hypothesized that this task characteristic would influence the strategy choice process: Problems with a relatively small subtrahend (such as 12 - 3 = . or 81 - 2 = .) can be solved very fast and easy by taking away the subtrahend from the minuend, whereas for problems with a relatively large subtrahend (such as 12 - 9 = . or 81 - 79 = .) it would be faster and easier to determine the difference by adding on to the subtrahend to get to the minuend.In four of the five studies, participants indeed based their strategy choices on the relative size of the subtrahend (studies presented in Chapters 1, 2, 4, and 5). However, a different result was found for the study presented in Chapter 3, in which typically developing children solved large single-digit subtraction problems. The reports of the five studies are preceded by an introductory chapter, and followed by a final chapter wherein we provide an overview of the conclusions of these studies, together with some limitations, future research directions, and educational implications.

Jaar van publicatie:2013