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…

Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As…

This study examined whether counting and rapid automatized naming (RAN) could operate as significant predictors of both later arithmetic calculation and reading fluency. The authors also took an important step to clarify the cognitive mechanisms underlying these predictive relationships by controlling for the effect of phonological awareness and…

We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…