The relationship between numerical mapping abilities,maths achievement and socioeconomic status in 4- and 5-year-old children

Background

Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances.

Aims

The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance.

Sample

Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds.

Method

The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks.

Results

The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks.

Conclusion

The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.     

Dynamic equilibrium on a cyclic-interval schedule with a ramp

Five human subjects pressed a panel for money on a cyclic-interval schedule that arranged recurring periods of linearly increasing reinforcement rates (ramps). Response rate versus time functions for all subjects showed recurring periods of linearly increasing response rates. The responding of four of the five subjects was in phase with the reinforcement input. The remaining subject showed a two-minute phase shift. These results suggest that organisms may act like simple amplifiers on cyclic-interval schedules, that is, the form of the input signal is not changed by the organism, but is returned with amplification. By analogy with the variable-interval case, the controlling variable on cyclic-interval schedules with rate ramps may be the constant reinforcement acceleration that is arranged by the schedule.     

Reforming mathematics instruction: The role of curriculum materials

The crisis in mathematics education is likely to grow. One of the targets for reform is the math textbook, which largely defines the math curriculum. Several aspects of math textbooks that strongly influence student learning are explained: the organization of lessons, the use of time, the rate of introducing new concepts, the quality of instructional activities, the nature of the examples, and the provision of guided and independent practice. Excerpts from math texts illustrate these factors. Research findings on an alternative to basais, represented by the Direct Instruction math curriculum, illustrate how conceptual understanding and proficiency can be developed for a full spectrum of students.     

数学焦虑个体近似数量加工的神经机制:一项EEG研究

近似数量加工是对大数目物体数量在不依赖逐个数数前提下的估计。行为学研究提示高数学焦虑人群近似数量加工能力下降, 但神经机制未明。本研究探讨高数学焦虑个体近似数量加工的神经机制, 比较高低数学焦虑脑电活动的差异:(1)行为上无显著组间差异; (2)高数学焦虑组的P2p成分波幅增加; (3) δ频段ERS及β频段ERD无显著数量比例效应, 而低数学焦虑组在上述指标的数量比例效应显著。本研究为高数学焦虑人群近似数量加工能力下降提供了电生理学的证据。     

The academic outcomes of working memory and metacognitive strategy training in children: A double‐blind randomized controlled trial

Working memory training has been shown to improve performance on untrained working memory tasks in typically developing children, at least when compared to non‐adaptive training; however, there is little evidence that it improves academic outcomes. The lack of transfer to academic outcomes may be because children are only learning skills and strategies in a very narrow context, which they are unable to apply to other tasks. Metacognitive strategy interventions, which promote metacognitive awareness and teach children general strategies that can be used on a variety of tasks, may be a crucial missing link in this regard. In this double‐blind randomized controlled trial, 95 typically developing children aged 9–14 years were allocated to three cognitive training programmes that were conducted daily after‐school. One group received Cogmed working memory training, another group received concurrent Cogmed and metacognitive strategy training, and the control group received adaptive visual search training, which better controls for expectancy and motivation than non‐adaptive training. Children were assessed on four working memory tasks, reading comprehension, and mathematical reasoning before, immediately after, and 3 months after training. Working memory training improved working memory and mathematical reasoning relative to the control group. The improvements in working memory were maintained 3 months later, and these were significantly greater for the group that received metacognitive strategy training, compared to working memory training alone. Working memory training is a potentially effective educational intervention when provided in addition to school; however, future research will need to investigate ways to maintain academic improvements long term and to optimize metacognitive strategy training to promote far‐transfer. A video abstract of this article can be viewed at https://youtu.be/-7MML48ZFgw     

Synchronicity and the I Ching: Jung, Pauli, and the Chinese woman

The capacity of the human mind to discover and invent both imagistic analogies and mathematical structures to represent reality is strikingly juxtaposed in the ancient Chinese text of the I Ching. Its emphasis on containing all sorts of opposites and its plastic appeal to multi-valenced experience has kept it alive through millennia and across cultures. Jung was introduced to its Taoist wisdom by the Sinologist Richard Wilhelm. The Nobel Laureate quantum physicist Wolfgang Pauli became familiar with its philosophy and mathematics through his reading of Schopenhauer and Leibniz. In their correspondence about the nature of the unconscious and synchronicity, Pauli and Jung also exchanged their musings on Pauli's dreams of a Chinese woman, her role in his psyche and his scientific theories(1).     

Academic Self-Schemas and their Self-Congruent Learning Patterns: Findings Verified with Culturally Different Samples

This paper reported two studies investigating high school students’ academic self-schemas in learning mathematics and their self-congruent learning engagement patterns. Using cluster analyses, Study 1 located two contrasting groups of students holding positive and negative self-schemas in learning mathematics among Chinese participants. MANOVA analyses showed that these two groups of Chinese schematic students differed from each other in the use of achievement goals, approaches to learning, and expected levels of performance. These findings were validated and extended in Study 2 using a culturally different sample, Australian students. Again, cluster analyses successfully classified Australian participants into positive and negative schematic clusters. It was also found that these two groups of schematic students approached learning mathematics in a self-congruent manner similar to those found in Study 1. The converging results in both studies lent empirical support to the theoretical formulation of positive and negative schematic students and the validity of using the self-schema concept to investigate motivation and learning. The differences in their learning engagement patterns were discussed in terms of students’ different academic self-schemas in learning mathematics.     

Analysis of precurrent skills in solving mathematics story problems

We conducted an analysis of precurrent skills (responses that increase the effectiveness of a subsequent or "current" behavior in obtaining a reinforcer) to facilitate the solution of arithmetic word (story) problems. Two students with developmental disabilities were taught four precurrent responses (identifying the initial value, change value, operation, and resulting value) in a sequential manner. Results of a multiple baseline design across behaviors showed that the teaching procedures were effective in increasing correct performance of each of the precurrent behaviors with untaught problems during probes and that once the precurrent behaviors were established, the number of correct problem solutions increased.     

Theories of Types and Names with Positive Stratified Comprehension

We introduce a certain extension of -calculus, and show that it has the Church-Rosser property. The associated open-term extensional combinatory algebra is used as a basis to construct models for theories of Explict Mathematics (formulated in the language of "types and names") with positive stratified comprehension. In such models, types are interpreted as collections of solutions (of terms) w.r. to a set of numerals. Exploiting extensionality, we prove some consistency results for special ontological axioms which are refutable under elementary comprehension.