Longitudinal study of low and high achievers in early mathematics

Background. Longitudinal studies allow us to identify, which specific maths skills are weak in young children, and whether there is a continuing weakness in these areas throughout their school years. Aims. This 2-year study investigated whether certain socio-demographic variables affect early mathematical competency in children aged 5–7 years. Sample. A randomly selected sample of 127 students (64 female; 63 male) participated. At the start of the study, the students were approximately 5 years old (M = 5.2; SD = 0.28; range = 4.5–5.8). Method. The students were assessed using the Early Numeracy Test and then allocated to a high (n = 26), middle (n = 76), or low (n = 25) achievers group. The same children were assessed again with the Early Numeracy Test at 6 and 7 years old, respectively. Eight socio-demographic characteristics were also evaluated: family model, education of the parent(s), job of the parent(s), number of family members, birth order, number of computers at home, frequency of teacher visits, and hours watching television. Results. Early Numeracy Test scores were more consistent for the high-achievers group than for the low-achievers group. Approximately 5.5% of low achievers obtained low scores throughout the study. A link between specific socio-demographic characteristics and early achievement in mathematics was only found for number of computers at home. Conclusions. The level of mathematical ability among students aged 5–7 years remains relatively stable regardless of the initial level of achievement. However, early screening for mathematics learning disabilities could be useful in helping low-achieving students overcome learning obstacles.This material is based on work supported by the Spanish Ministry of Science & Technology grant no. SEJ2007-62420/EDUC and Junta de Andalucia grant no. P09-HUM-4918

Readiness-based differentiation in primary school mathematics: expert recommendations and teacher self-assessment

The diversity of students’ achievement levels within classrooms has made it essential for teachers to adapt their lessons to the varying educational needs of their students (‘differentiation’). However, the term differentiation has been interpreted in diverse ways and there is a need to specify what effective differentiation entails. Previous reports of low to moderate application of differentiation underscore the importance of practical guidelines for implementing differentiation. In two studies, we investigated how teachers should differentiate according to experts, as well as the degree to which teachers already apply the recommended strategies. Study 1 employed the Delphi technique and focus group discussions to achieve consensus among eleven mathematics experts regarding a feasible model for differentiation in primary mathematics. The experts agreed on a five-step cycle of differentiation: (1) identification of educational needs, (2) differentiated goals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation of progress and process. For each step, strategies were specified. In Study 2, the Differentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate how teachers  self-assess their use of the strategies recommended by the experts. While teachers (N = 268) were moderately positive about their application of the strategies overall, we also identified areas of relatively low usage (including differentiation for high-achieving students) which require attention in teacher professional development. Together, these two studies provide a model and strategies for differentiation in primary mathematics based on expert consensus, the DSAQ which can be employed in future studies, and insights into teachers’ self-assessed application of specific aspects of differentiation

Two sides of the same coin? How are neural mechanisms of cognitive control, attentional difficulties and creativity related?

Creativity has been associated with increased distractibility, but at the same time - and seemingly paradoxically- also with increased focused attention. Therefore, this study focused on the attentional processes involved in creativity and attentional difficulties. Healthy primary school children (N = 62) between 9 and 13 years old performed a selective attention paradigm while electrophysiological measures were recorded that measured the neural mechanisms of cognitive control (P300), conflict monitoring (N200), and subconscious attentional shifts (Mismatch Negativity). Attentional difficulties were measured with a parental questionnaire and creativity was measured with a divergent mathematical creativity task and a creative drawing task. We found that more creativity was related to decreased neural mechanisms of cognitive control and conflict monitoring (i.e. less negative N200 and smaller P300 amplitudes), however without affecting task performance. In addition, attentional difficulties were related to less negative N200 amplitudes on the attended and non-attended standard trials of the selective attention paradigm, as well as reduced task performance. Tentatively, the current findings suggest that original responses are associated with decreased cognitive control, possibly by promoting remote associations. Furthermore, our data shows that attentional difficulties are associated with a lack of selective attention and impaired information processing. Hence, although less cognitive control is often referred to in a negative way, it might facilitate certain aspects of creative thinking without affecting task performance

Cognitive predictors of children’s development in mathematics achievement: a latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children’s individual differences in mathematics achievement. However, research into the predictors of children’s individual growth rates, i.e., between-person differences in within-person change, in mathematics achievement is scarce. We assessed 334 children’s domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the 1st and 2nd grade of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children’s starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children’s initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children’s individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one’s mathematical success. We argue the need for more research focus on explaining children’s individual growth rates in mathematics achievement

Cell signalling: Control of free calcium

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Early numerical competencies in 5- and 6-year-old children with autism spectrum disorder

Research Findings: To date, studies comparing the mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are scarce, and results remain inconclusive. In general, studies on this topic focus on mathematical abilities learned from elementary school onward, with little attention for possible precursors at younger ages. The current exploratory study focused on the important developmental period of preschool age, investigating 5 early numerical competencies in 30 high-functioning children with ASD and 30 age-matched control children: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Children were examined at 5 or 6 years of age, attending the 3rd and final year of preschool. Overall, rather similar early number processing was found in children with and without ASD, although marginally significant results indicated a weaker performance of children with ASD on verbal subitizing and conceptual counting. Practice or Policy: Given the pervasiveness and impact of ASD on other domains of functioning, it is important to know that no general deficits in early numerical competencies were found in this study. However, some downward trends in mathematics performance were identified in children with ASD, which can serve as the basis for additional research in this field

Early number and arithmetic performance of Ecuadorian 4-5-year-olds

This study aimed at (a) constructing a reliable and valid test to assess Ecuadorian 4–5-year olds’ number and arithmetic skills; (b) providing empirical data on Ecuadorian 4–5-year olds’ number and arithmetic skills; and (c) confronting these children’s actual performances with the performances expected by national experts in this domain. We administered the Test of Early Number and Arithmetic (TENA), developed on the basis of the Ecuadorian mathematics standards to 86 Preschoolers and 127 Kindergartners and asked 10 experts to evaluate TENA’s validity and predict children’s performances on it. Results supported the overall reliability and validity of the TENA. Furthermore, we observed differences in number and arithmetic competencies between and within Preschoolers and Kindergartners, but not between boys and girls. Finally, experts overestimated children’s performances on the test. The scientific and practical implications of these results are discussed

Aequorin-based measurements of intracellular Ca(2+)-signatures in plant cells

Due to the involvement of calcium as a main second messenger in the plant signaling pathway, increasing interest has been focused on the calcium signatures supposed to be involved in the patterning of the specific response associated to a given stimulus. In order to follow these signatures we described here the practical approach to use the non-invasive method based on the aequorin technology. Besides reviewing the advantages and disadvantages of this method we report on results showing the usefulness of aequorin to study the calcium response to biotic (elicitors) and abiotic stimuli (osmotic shocks) in various compartments of plant cells such as cytosol and nucleus