There is a renewed debate about whether educated adults solve simple addition problems (e.g., 2 + 3) by direct fact retrieval or by fast, automatic counting-based procedures. Recent research testing adults' simple addition and multiplication showed that a 150-ms preview of the operator (+ or ×) facilitated addition, but not multiplication,…

Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

Developing high levels of mathematical skills in students is a concern for teachers worldwide, since most of the fastest growing occupations require significant mathematics or science preparation. Teachers need to be prepared to teach mathematics successfully. If teachers are not fluent in simple mathematical calculations, they may not feel…

The effectiveness of two instructional interventions was investigated in the context of teaching Arithmetic Combinations (ACs) of multiplication and division to students with Learning Disabilities (LD) or Mild Intellectual Disability (MID). The intervention for the control group (LD = 20, MID = 10) was based on principles of effective instruction,…

PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

A variety of experimental evidence indicates that the memory representation for multiplication facts (e.g., 6 [times] 9 = 54) incorporates bidirectional links with a forward association from factors to product and a reverse association from product to factors. Surprisingly, the authors did not find evidence in Experiment 1 of facilitative…

The aim of this study was twofold. First, it evaluated the developmental changes on frequency of use, efficiency, and choice of counting strategies from childhood to adulthood. Second, it determined the adaptation of the counting strategies to the structural features of the task. Participants in seven age groups ranging from 5-year-old to…