Imbalances in problem distributions in math textbooks have been hypothesized to influence students' performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Here, we assess whether quantity representations are influenced by the perceptual biases hypothesized to manifest in depressive individuals. In contrast to this clinical model, several prominent models of numerical cognition assume that quantity representations are abstract, and therefore are independent of the items that are being quantified. If…

Learning fractions poses a challenge for many elementary school students, including applying fraction knowledge in novel contexts. For instance, there are substantial individual differences in students' tendency of spontaneous focusing on quantitative relations (SFOR), which is related to the development of rational number knowledge. In this…

Exact arithmetic abilities require symbolic numerals, which constitute a precise representation of quantities, such as the Arabic digits. Numerical thinking, however, also engages an intuitive non-linguistic number sense, the Approximate Number System (ANS). The ANS allows us to discriminate quantities, approximate arithmetic transformations, and…

What is the foundational knowledge that children rely on to provide meaning as they construct an exact symbolic number system? People and animals can quickly and accurately distinguish small exact quantities (i.e., 1 to 3). One possibility is that children's ability to map small quantities to spoken number words supports their developing exact…

The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children.…

We explored the multi-dimensionality of mathematics and working memory (WM) by examining the differential relationships between different areas of mathematics with visual, spatial, and verbal WM. Previous research proposed that visuospatial WM is a unique predictor of mathematics, but neuroimaging and cognitive research suggest divisions within…

In Asia, some children are taught a calculation technique known as the 'mental abacus'. Previous research indicated that mental abacus experts can perform extraordinary feats of mental arithmetic, but it disagrees as to whether the technique improves working memory. The present study extended and clarified these findings by contrasting performance…

Neuropsychological case-studies suggested that dates and encyclopedic numbers may be processed differently than unknown numbers. However, this issue was seldom investigated in healthy participants. Therefore, it is unclear whether known dates are read like words (as lexical items), or like numbers (each position strictly defines digits' values in…

For a significant number of students, attitudes towards mathematics decrease notably during secondary education. Thus, there is an urgent need to improve students' mathematics attitudes because attitudes may negatively affect conceptual understanding of mathematics or mathematics performance. However, without a clear unified construct of…

This study investigated the effects of: (1) proximal grouping of numbers; (2) problem-solving goals to make 100; and (3) prior knowledge on students' initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state.…

In three experiments, we used a masked prime in a verification task to investigate the processing stages occurring during multiplication fact retrieval. We aimed to investigate the retrieval process by overlapping its execution with the processing of a masked prime consisting of a number. Participants evaluated the correctness of multiplication…

Algebraic thinking and strategy flexibility are essential to advanced mathematical thinking. Early algebra instruction uses 'missing-operand' problems (e.g., x - 7 = 2) solvable via two typical strategies: (1) direct retrieval of arithmetic facts (e.g., 9 - 7 = 2) and (2) performance of the inverse operation (e.g., 2 + 7 = 9). The current study…

Several working memory processes have been hypothesized to influence different arithmetic operations. Working memory has been compartmentalized into a number of different sub-processes, such as phonological memory and visuospatial memory that are believed to have unique contributions to the performance of two distinct arithmetic operations:…