Preschool predictors of mathematics in first grade children with autism spectrum disorder

AbstractUp till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5–6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6–7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed

Mapping kindergartners’ quantitative competence

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 304). A confirmatory factor analysis showed that the four-factor structure fitted the empirical data from the Netherlands. For the Cyprus data a one-factor structure was found to have a more adequate fit. Regarding the effect of country on performance, a comparison at item level showed that the kindergartners in the Netherlands outperformed those in Cyprus in the majority of quantitative competence items. Analyses of variance revealed for each country a significant effect of kindergarten year on performance, with children in K2 (second kindergarten year) outperforming those in K1 (first kindergarten year). A statistical implicative analysis at item level revealed that in both countries the relevant implicative chain, showing what successful solving of an item implies for correct solving of another item, reflects by and large the sequential steps mostly followed in teaching kindergartners early number. This sequence starts with counting and subitizing, then continues with additive reasoning and finally multiplicative reasoning. These implicative chains also clearly show that the development of early quantitative competence is not linear. There are many parallel processes and cross-connections between the components of quantitative competence.publishedVersionPaid Open Acces

Training mathematical skills in school children: Some preliminary results.

The present study is a further development of an earlier research on school failure. The aim is to develop sound, simple, effective evaluation and training procedures for children with difficulties to learn mathematics. A review of research on mathematical knowledge reveals some confusion in using terms and a lack of empirical studies on intervention strategies. Nevertheless, some progress has been done in defining the necessary skills for children to solve mathematical problems. In the current study, two cases of primary school children (ISCED 1) with difficulties to learn mathematics are presented. They were trained to acquire a set of pre-mathematical or mathematical skills. The core of the intervention procedures is Behavior Skills Training (BST), a highly effective technique for teaching individuals with different disabilities a wide variety of skills. Evaluation of the training is carried out by comparing the percentage of attained objectives before (pre-test) and after training (post-test). Future developments of this research are explaine

Prospective Early Childhood Teachers’ Evolving Conceptions of Using a Mathematics Learning Trajectory to Guide Intentional Teaching

This qualitative, phenomenological study investigated how fifteen early childhood preservice teachers’ (PSTs) mathematical knowledge needed for teaching and early mathematics learning trajectory knowledge impacted the intentionality of instructional decision-making. The central research question asked: In what ways do early mathematics learning trajectories inform prospective early childhood teachers’ instructional decisions in ways that are likely to advance student learning on the subitizing trajectory? The literature review revealed numerous studies focused on the usefulness of learning trajectory knowledge on prospective elementary and inservice teachers’ mathematical knowledge for teaching, lesson planning, instruction, and assessment, but no studies were found regarding early childhood pre-service teachers’ understanding of an early mathematics learning trajectory to guide intentional instructional decision-making. A semi-structured interview protocol with stimulus texts was designed to elicit early childhood PSTs’ understanding of subitizing, the subitizing trajectory, and the influence of each on their instructional decision-making. Five themes emerged from the analysis of this data offering insights into the intentionality of early childhood PSTs’ decision-making to advance student learning: (1) demonstrates an understanding of subitizing, (2) recognizes and validates the importance of subitizing for young children, (3) articulates learning trajectory progression through dot arrangements, (4) demonstrates an awareness of the developmental nature of children’s mathematical thinking, and (5) centers instructional decisions on children’s thinking. Findings from this study suggest early childhood PSTs (a) demonstrated a keen interest in understanding children’s thinking and were capable of crafting instructional opportunities that aligned with the subitizing learning trajectory, (b) developed a complex and nuanced understanding of the subitizing trajectory, and (c) engaged in a cycle of instructional decision-making highlighting an intricate relationship between subject matter knowledge, pedagogical content knowledge, and learning trajectory knowledge

Developing number sense with Fingu: a preschooler’s embodied mathematics during interactions with a multi-touch digital game

Early number sense, including subitizing and composition, is a foundation for mathematics, and bodies, especially fingers, are integral to number sense. Multi-touch technology offers innovative opportunities for developing and studying number sense, especially using conceptually congruent gestures that match the mathematics. However, there have been few investigations of the development of early number sense, particularly in embodied forms. Therefore, this mixed-methods study explores a preschooler’s development of early number sense during a month of interactions with the multi-touch digital mathematics game Fingu. Key findings related to the development of early number sense include relevance of configuration and quantity, relationships among gestures and quantities, and development of estimation and precision. This research adds new perspectives to our understandings of early number sense research and practice, calling for consideration of embodiment and conceptually congruent gestures

Creature Counting: The Effects of Augmented Reality on Perseverance and Early Numeracy Skills

Augmented reality (AR) and mobile devices show promise for promoting mathematics practices and an increase in perseverance. Using an experimental pre-/posttest comparable condition group design, this study investigated (a) whether differences exist in students’ number sense outcome scores based upon the type of board game they played with (augmented reality version versus traditional) and (b) find whether students’ perseverance levels based upon the type of board game they played were different. Using a classroom observation protocol designed to measure perseverance and a pre-/posttest on subitizing and approximate number system, the study used a 2x2 mixed repeated measures ANOVA, one-way ANOVA, and linear regression models to analyze these assessments. The early number sense scores of students playing an AR version of the researcher designed game called Creature Counting (n=30) was compared with students who played a traditional board game version of the same game (n=26).Results of this empirical study show students who participated in the AR version of Creature Counting had growth in number sense scores. Findings from the study showed that students in both groups improved between the pre-/posttest on the subitizing assessment, with the AR group making greater improvement. The findings also showed that students in both groups improved between the pre-/posttest on the approximate number systems assessment. However, there was no statistically significant difference in improvement when comparing children in the intervention group to children in the comparison group. Additionally, for children in the intervention group, perseverance scores collected did not predict number sense scores after playing Creature Counting. Implications for these findings are discussed