Working memory and domain-specific precursors predicting success in learning written subtraction problems
The study aimed to identify individual differences predicting competence in solving written subtractions with borrowing in second-grade schoolchildren. A group of 68 second-graders was tested at three different sessions. Domain-general precursors, including four working memory (WM) tasks, were analyzed during the first session. The tasks distinguished between simple-storage and complex-span WM tasks. Domain-specific mathematical abilities tested were knowledge of symbols, arithmetical fact retrieval, understanding of the positional value of digits, and alignment skills. During the second and third sessions, children were taught written subtraction algorithms, first without and then with borrowing procedures, and were then immediately assessed on their acquired competences. Path analysis models were run, and the final model showed that performance in written subtractions with borrowing was predicted by both visuospatial WM and specific mathematical skills. The results are discussed for their theoretical and educational implications.
Acquiring written calculation skills is a fundamental goal of the primary school arithmetic curriculum, and it represents a difficult point of transition essential to learning more complex mathematical skills at higher education levels. The goal of the present study was to analyze the factors that can predict the successful acquisition of a specific written arithmetic algorithm, i.e. multi-digit subtraction with borrowing, that is typically taught in second grade. Learning this algorithm represents not only one of the main goals of the arithmetic classes for this age group, but also one of the crucial difficulties encountered by primary school children.
A sizable body of research has shown that a number of domain-general competences may predict success in learning at school, particularly in arithmetic. In the present study, we focused on the case of working memory (WM), which has already emerged as an essential aspect of numerical cognition. The concept of WM refers to a set of processes or structures that are intimately associated with many arithmetic processes. In the present research, we distinguished between simple-storage and complex WM span tasks, which are considered as distinct constructs. Simple storage tasks only involve storing information, while complex WM span tasks entail both storing and processing information.
We also distinguished between verbal and visuospatial WM processes because an increasing amount of research has shown that different WM components are associated with arithmetic at different ages. Visuospatial WM appears to be crucially implicated in the mathematical performance of younger children who are still learning basic arithmetic skills. Learning and Individual Differences xxx (2014) xxx–xxx
The present study concentrated on the period when children learn multi-digit written subtraction with borrowing. This stage can be clearly identified in the life of a primary school class and it requires explicit teaching. It is a stage that may be associated with potentially different predictors from those relating to other aspects of arithmetic. In fact, a number of experimental studies have shown that the role of WM components in calculation depends on several factors, such as the type of algorithm required, the presentation format, or the involvement of carrying/borrowing procedures.
During their formal education, children gradually learn procedures for using multi-digit algorithms. The mathematics curricula in many countries conventionally distinguish between three main arithmetic approaches: written standard algorithms, written informal algorithms, and mental arithmetic, or the strategic approach. Multi-digit arithmetic is still taught mainly with paper-and-pencil written standard algorithms. A mathematics curriculum for teaching arithmetic that is based on the written standard approach requires that children in grade 1 consolidate their counting skills and start learning the principles of adding and subtracting, while the procedures for solving written additions and subtractions are taught in grade 2.
It is worth noting here that, when children perform calculations, they allocate their cognitive abilities differently, not only according to the type of algorithm required, but also to the problem's complexity. They may use specific strategies, and the role of WM components in calculation depends on several factors, such as the type of algorithm required, the presentation format, or the involvement of carrying/borrowing procedures. The verbal WM component seems to be involved in addition and multiplication problems, while the visuospatial one seems to relate to subtractions, though this may be mediated by cultural effects. Other studies found that operations with carrying or borrowing procedures increased the demands on WM, prompting a selective involvement of WM components.
