Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

This research pursued a fine-grained analysis of the acquisition of a procedural skill. In two experiments (n = 29 and n = 27), adults practiced 12 alphabet arithmetic problems (e.g., C + 3 = C D E F) in two sessions with 20 practice blocks in each. If learning reflected speed up of a counting algorithm, response time (RT) speed up should be…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

We performed a meta-analysis of dual-task experiments to assess the robustness of the effects of conducting working memory secondary tasks on arithmetic performance. Four hundred effect sizes from 21 studies from 1,049 participants were analyzed across a variety of specifications. Results revealed that increases in working memory load resulted in…

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,…

Higher working memory capacity (WMC) improves performance on a range of cognitive and academic tasks. However, a greater ability to control attention sometimes leads individuals with higher WMC to persist in using complex, attention-demanding approaches that are suboptimal for a given task. We examined whether higher WMC would hinder insight…

Several types of converging evidence have suggested recently that skilled adults solve very simple addition problems (e.g., 2 + 1, 4 + 2) using a fast, unconscious counting algorithm. These results stand in opposition to the long-held assumption in the cognitive arithmetic literature that such simple addition problems normally are solved by fact…

A focus of early mathematics education is to build fluency through practice. Several models of skill acquisition have sought to explain the increase in fluency because of practice by modeling both the learning mechanisms driving this speedup and the changes in cognitive processes involved in executing the skill (such as transitioning from…

Determining adults' and children's strategies in mental arithmetic constitutes a central issue in the domain of numerical cognition. However, despite the considerable amount of research on this topic, the conclusions in the literature are not always coherent. Therefore, there is a need to carry on the investigation, and this is the reason why we…

The purpose of the present study was to examine factors that influence strategic flexibility in computational estimation for Chinese- and Canadian-educated adults. Strategic flexibility was operationalized as the percentage of trials on which participants chose the problem-based procedure that best balanced proximity to the correct answer with…

In two experiments, participants studied two types of word lists. Direct lists were taken from the Deese-Roediger-McDermott (DRM) paradigm (e.g., "water", "bridge", "run") and contained words directly related to a nonpresented critical item (CI; e.g., "river", Roediger & McDermott, 1995). Mediated lists (e.g., "faucet", "London", "jog") contained…

In the present study, the authors tested the effects of working-memory load on math problem solving in 3 different cultures: Flemish-speaking Belgians, English-speaking Canadians, and Chinese-speaking Chinese currently living in Canada. Participants solved complex addition problems (e.g., 58 + 76) in no-load and working-memory load conditions, in…