The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development.

https://www.onlinelibrary.wiley.com/doi/pdf/10.1111/desc.12395

Magnitude Knowledge: The Common Core of Numerical Development.

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of shapes). Children who received sequential training showed near transfer to a number ordering task and far transfer to a number line task. Furthermore, these children showed more improvement on the version of the number line task where a midpoint reference was presented (i.e., at 5) than on the version without a midpoint. Before the training, the midpoint reference did not enhance performance. In contrast, although children who received non-numerical spatial training showed near transfer to a 2-D mental transformation task, they did not show transfer to number ordering or number line tasks, even though spatial skills were correlated with performance on these tasks. These results support the view that knowledge of sequential relations among successive numbers is an important aspect of children's early numeracy knowledge in tasks that require ordinal understanding of numbers from 1 to 10 and support the educational importance of developing numerical activities that enhance children's understanding of these relations. (PsycINFO Database Record

Training young children on sequential relations among numbers and spatial decomposition: Differential transfer to number line and mental transformation tasks.

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In this study, we used verbal protocols to identify whether adults spontaneously apply quartile-based strategies or whether they need additional external support to use these strategies when solving a 0–1,000 number line estimation (NLE) task. Participants were assigned to one of three conditions based on the number of external benchmarks provided on the number line. In the bounded condition only the origin and endpoint were indicated, the mid-point condition included an additional external benchmark at 50%, and in the quartile condition three additional external benchmarks at 25%, 50%, and 75% were specified. Firstly, participants in the bounded condition reported to spontaneously apply quartile-based strategies to calibrate their estimates. Moreover, participants frequently relied on the external benchmarks for creating internal benchmarks at the mid-point, quartiles, and even octiles of the number line. Secondly, overall estimation accuracy improved as the number of external benchmarks increased, and target numbers close to external benchmarks were estimated more accurately and with less variability. Thirdly, the use of a larger variety in benchmark-based strategies was positively related to NLE accuracy. In summary, this study provides evidence that the NLE task induces more sophisticated strategy use in participants than initially anticipated.

Benchmark-based strategies in whole number line estimation.

Sense of proportion

As a special kind of handwriting with a brush, Chinese calligraphic handwriting (CCH) requires a large amount of practice with high levels of concentration and emotion regulation Previous studies have showed that long-term CCH training has positive effects physically (induced by handwriting activities) and psychologically (induced by the state of relaxation and concentration), the latter of which is similar to the effects of meditation The aim of this study was to investigate the long-term CCH training effect on anxiety and attention, as well as brain structure Participants were 32 individuals who had at least five years of CCH experience and 44 controls Results showed that CCH training benefited individuals' selective and divided attention but did not decrease their anxiety level Moreover, the VBM analysis showed that long-term CCH training was mainly associated with smaller grey matter volumes (GMV) in the right precuneus/posterior cingulate cortex (PCC) No brain areas showed larger GMV in the CCH group than the control group Using two sets of regions of interest (ROIs), one related to meditation and the other to handwriting, ROI analysis showed significant differences between the CCH and the control group only at the meditation-related ROIs, not at the handwriting-related ROIs Finally, for the whole sample, the GMV of both the whole brain and the PCC were negatively correlated with selective attention and divided attention The present study was cross-sectional and had a relatively small sample size, but its results suggested that CCH training might benefit attention and influence particular brain structure through mental processes such as meditation

/pdf/long-term-chinese-calligraphic-handwriting-reshapes-the-4p95pena5v.pdf

Long-term Chinese calligraphic handwriting reshapes the posterior cingulate cortex: A VBM study.

https://escholarship.org/content/qt0k55w5td/qt0k55w5td.pdf?t=nq79pl

Development of numerical estimation in Chinese preschool children

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Long-term Chinese calligraphic handwriting reshapes the posterior cingulate cortex: A VBM study.

Development of numerical estimation in Chinese preschool children