Longitudinal changes in young children's 0-100 to 0-1000 number-line error signatures

Numerical Estimation and Mathematical Learning Methodology in Preschoolers

One of the means for representing quantities/magnitudes is the mental number line. It is still a nonsolved question as to whether the method of learning mathematics in the early years could improve this type of estimating. A total of 233 students, aged four and five years, who learned mathematics with a new method called Open Algorithm Based on Number or the more traditional Closed Based on Ciphers approach, were evaluated with a reliable estimation on the number line test. Results revealed significant differences in participants' estimation functions based on the learning method used. Students who learned mathematics through the Open Algorithm Based on Number method used a linear representation more efficiently than those who were taught with the Closed Based on Ciphers methodology. This group exhibited a logarithmic function in their approach. We discussed whether these differences can be attributed to a recurrent practice in estimation tasks at school, characterized by the Open Algorithm Based on Number methodology.

Empirical Sample Size Guidelines for Use of Latent Difference Score Mediation

Mediation models are commonly used to identify the mechanisms through which one variable influences another. Among longitudinal mediation methods, latent difference score mediation stands out due to its unique ability to capture non-linear change over time. However, there is limited information regarding sample size demands to achieve adequate power with this method, resulting in few applications of latent difference score mediation. To address this limitation, the current study presents empirically supported sample size guidelines for 10 common latent difference score mediation structural models and 9 unique population models. The results of this study offer researchers with a set of representative sample estimates that may be used when designing studies or seeking funding.

The Use of Local and Global Ordering Strategies in Number Line Estimation in Early Childhood

A lot of research has been devoted to number line estimation in primary school. However, less is known about the early onset of number line estimation before children enter formal education. We propose that ordering strategies are building blocks of number line estimation in early childhood. In a longitudinal study, children completed a non-symbolic number line estimation task at age 3.5 and 5 years. Two ordering strategies were identified based on the children's estimation patterns: local and global ordering. Local ordering refers to the correct ordering of successive quantities, whereas global ordering refers to the correct ordering of all quantities across the number line. Results indicated a developmental trend for both strategies. The percentage of children applying local and global ordering strategies increased steeply from 3.5 to 5 years of age. Moreover, children used more advanced local and global ordering strategies at 5 years of age. Importantly, level of strategy use was related to more traditional number line estimation outcome measures, such as estimation accuracy and regression fit scores. These results provide evidence that children use dynamic ordering strategies when solving the number line estimation task in early stages of numerical development.

Variability in Single Digit Addition Problem-Solving Speed Over Time Identifies Typical, Delay and Deficit Math Pathways

We assessed the degree to which the variability in the time children took to solve single digit addition (SDA) problems longitudinally, predicted their ability to solve more complex mental addition problems. Beginning at 5 years, 164 children completed a 12-item SDA test on four occasions over 6 years. We also assessed their (1) digit span, visuospatial working memory, and non-verbal IQ, and (2) the speed with which they named single numbers and letters, as well the speed enumerating one to three dots as a measure of subitizing ability. Children completed a double-digit mental addition test at the end of the study. We conducted a latent profile analysis to determine if there were different SDA problem solving response time (PRT) variability patterns across the four test occasions, which yielded three distinct PRT variability patterns. In one pattern, labeled a typical acquisition pathway, mean PRTs were relatively low and PRT variability diminished over time. In a second pattern, label a delayed pathway, mean PRT and variability was high initially but diminished over time. In a third pattern, labeled a deficit pathway, mean PRT and variability remained relatively high throughout the study. We investigated the degree to which the three SDA PRT variability pathways were associated with (1) different cognitive ability measures, and (2) double-digit mental addition abilities. The deficit pathway differed from the typical and delayed pathway on the subitizing measure only, but not other measures; and the latter two pathways also differed from each other on the subitizing but not other measures. Double-digit mental addition problem solving success differed between each of the three pathways, and mean PRT variability differed between the typical and the delayed and deficit pathways. The latter two pathways did not differ from each other. The findings emphasize the value of examining individual differences in problem-solving PRT variability longitudinally as an index of math ability, and highlight the important of subitizing ability as a diagnostic index of math ability/difficulties.

Culture-Independent Prerequisites for Early Arithmetic

In numerate societies, early arithmetic development is associated with visuospatial working memory, executive functions, nonverbal intelligence, and magnitude-comparison abilities. To what extent do these associations arise from cultural practices or general cognitive prerequisites? Here, we administered tests of these cognitive abilities (Corsi Blocks, Raven’s Colored Progressive Matrices, Porteus Maze) to indigenous children in remote northern Australia, whose culture contains few counting words or counting practices, and to nonindigenous children from an Australian city. The indigenous children completed a standard nonverbal addition task; the nonindigenous children completed a comparable single-digit addition task. The correlation matrices among variables in the indigenous and nonindigenous children showed similar patterns of relationships, and parallel regression analyses showed that visuospatial working memory was the main predictor of addition performance in both groups. Our findings support the hypothesis that the same cognitive capacities promote competence for learners in both numerate and nonnumerate societies.

Innate or Acquired? - Disentangling Number Sense and Early Number Competencies

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.