Symbolic and non-symbolic predictors of number line task in Italian kindergarteners.

The number line estimation task (NLE) is often used as a predictor for broader measures of mathematical achievement. In spite of its popularity, it is still not clear whether the task is based on symbolic or non-symbolic numerical competence. In particular, there is only a very limited amount of studies investigating the relationship between NLE performance and symbolic vs. non-symbolic math skills in children who have not yet begun formal schooling. This study investigates the strength of the association between NLE performance and symbolic and non-symbolic tasks in young kindergarteners. Ninety two 5-year-old children completed the NLE task (range 0-100) and a battery of early numerical competence tests including symbolic-lexical tasks, symbolic semantic tasks, and non-symbolic semantic tasks. The relationship between symbolic and non-symbolic early numerical competence and NLE performance was analyzed using a regression model based on the Bayesian Information Criterion (BIC). Results show that only symbolic semantic tasks are significant predictors of NLE performance. These results suggest that symbolic numerical knowledge is involved in number line processing among young children, whilst non-symbolic knowledge is not. This finding brings new data to the debate on the relationship between non-symbolic numeral knowledge and symbolic number processing and supports the evidence of a primary role of symbolic number processing already in young kindergarteners.

The Morra Game as a Naturalistic Test Bed for Investigating Automatic and Voluntary Processes in Random Sequence Generation.

Morra is a 3,000-years-old hand game of prediction and numbers. The two players reveal their hand simultaneously, presenting a number of fingers between 1 and 5, while calling out a number between 2 and 10. Any player who successfully guesses the summation of fingers revealed by both players scores a point. While the game is extremely fast-paced, making it very difficult for players to achieve a conscious control of their game strategies, expert players regularly outperform non-experts, possibly with strategies residing out of conscious control. In this study, we used Morra as a naturalistic setting to investigate the necessity of attentive control in generation of sequence of items and the ability to proceduralize random number generation, which are both a crucial defensive strategy in Morra and a well-known empirical procedure to test the central executive capacity within the working memory model. We recorded the sequence of numbers generated by expert players in a Morra tournament in Sardinia (Italy) and by undergraduate students enrolled in a course-based research experience (CRE) course at Lawrence Technological University in the United States. Number sequences generated by non-expert and expert players both while playing Morra and in a random number generation task (RNGT) were compared in terms of randomness scores. Results indicate that expert players of Morra largely outperformed non-experts in the randomness scores only within Morra games, whereas in RNGT the two groups were very similar. Importantly, survey data acquired after the games indicate that expert players have very poor conscious recall of their number generation strategies used during the Morra game. Our results indicate that the ability of generating random sequences can be proceduralized and do not necessarily require attentive control. Results are discussed in the framework of the dual processing theory and its automatic-parallel-fast vs. controlled-sequential-slow polarities.

Visual and Spatial Working Memory Abilities Predict Early Math Skills: A Longitudinal Study.

This study aimed to explore the influence of the visuospatial active working memory subcomponents on early math skills in young children, followed longitudinally along the first 2 years of primary school. We administered tests investigating visual active working memory (jigsaw puzzle), spatial active working memory (backward Corsi), and math tasks to 43 children at the beginning of first grade (T1), at the end of first grade (T2), and at the end of second grade (T3). Math tasks were selected according to the children's age and their levels of formal education: the "Battery for the evaluation of numerical intelligence from 4 to 6 years of age" (BIN 4-6) at T1 to test early numerical competence and the "Test for the evaluation of calculating and problem-solving abilities" (AC-MT 6-11) to test math skills at T2 and T3. Three regression models, in which the predictors were identified through a backward selection based on the use of the Bayesian information criterion (BIC) index, were performed to study the relationship between visual and spatial working memory and math ability at the three points in time. The results show that spatial working memory influences early numerical performance at T1, while early numerical performance is the unique predictor of math performance at T2. At the end of the second grade, the regression model reveals a relationship between math performance and both visual and spatial working memory and the attenuation of the importance of domain-specific predictors. The study depicts the different implications of visual and spatial working memory predictors over the children's development periods and brings additional evidence to the debate on the relationship between visuospatial working memory and math ability in young children.