学前儿童近似数量系统敏锐度与符号数学能力的关系

选取杭州市122名学前儿童(3~6岁)为被试,以点数比较任务及点数异同任务测量幼儿的近似数量系统敏锐度,以数数测验、基数测验、符号数字知识测验及简单计算来测量幼儿的符号数学能力,以此考察学前儿童近似数量系统敏锐度的发展及与符号数学能力的关系。结果发现:(1)随年龄增长,学前儿童的近似数量加工的敏锐度逐渐提高;(2)点数比较任务与点数异同任务均适合测量学前儿童近似数量系统敏锐度,但儿童完成点数比较任务的正确率要高于点数异同任务的正确率;(3)在抑制控制、短时记忆、工作记忆和言语测验成绩被控制后,根据点数比较任务计算的韦伯系数能显著预测学前儿童的基数和符号数字知识测验分数,总正确率能显著预测学前儿童的数数、基数、符号数字知识测验分数;(4)点数异同任务中只有点数不同试次下的正确率能显著预测学前儿童的符号数字知识测验分数。     

近似数量系统敏锐度与数学能力的关系

近年来,来自认知发展、比较认知、跨文化认知和神经生物学的研究证据都表明近似数量系统的存在,并且相较于一般认知能力,它更可能是决定个体数学能力差异最为重要的因素。本文综述了有关近似数量系统敏锐度与数学能力相互关系的横断研究、纵向研究、训练研究及认知神经科学的研究成果,分析了影响二者关系的因素,包括个体年龄、数学能力高低、抑制控制等,并总结了多种理论对二者间显著正相关关系的解释。未来研究需要在确定更具信效度的测量范式的基础上探讨近似数量系统与数学能力各维度的关系,以及这种相互关系背后的原因,并将研究结论运用于数学教学及计算障碍个体的干预。     

个体近似数量系统与其数学能力之间的关系：发展研究的证据

近似数量系统在个体数学能力的发展中起着重要的作用, 二者之间的关系受到年龄因素的影响。主要表现为, 随着年龄的增长, 相关程度逐渐减弱, 二者之间关系的作用机制可能由基数知识中介转变为多种中介变量的共同作用。未来可采用更严格的实验设计和多种研究方法考察各年龄段儿童近似数量系统与不同数学能力之间关系的发展趋势、因果方向、关键转折点和潜在机制, 以更好地理解近似数量系统在个体数学能力发展中所起的作用。     

心算形式对不同近似数量系统敏锐度儿童心算表现的影响

选取112名二年级小学生,以点阵比较任务测量近似数量系统敏锐度,同时以工作记忆测验成绩为协变量,探究了不同心算形式（视算、读算）对不同近似数量系统敏锐度儿童心算表现的潜在影响。结果显示：（1）心算形式显著影响心算的正确率,读算形式下儿童的心算表现最好;（2）控制工作记忆影响后,心算形式与近似数量系统敏锐分组均对心算正确率影响显著。总体来讲,读算可能是提高小学儿童简单心算表现的有效形式,并能提高低近似数量系统敏锐度儿童的心算表现。     

青少年抑制控制与同伴拒绝:身体攻击、关系攻击的中介作用

选取1589名青少年(平均年龄15.22±0.36岁)为被试,考察身体攻击、关系攻击在抑制控制与同伴拒绝间的中介作用。结果发现,(1)抑制控制与身体攻击、关系攻击、同伴拒绝之间均存在显著负相关,身体攻击、关系攻击与同伴拒绝之间存在显著正相关;(2)身体、关系攻击在抑制控制与同伴拒绝之间发挥中介作用;相比关系攻击,身体攻击的中介效应更强。该结果表明抑制控制对于同伴拒绝的作用既存在直接效应,又可通过身体攻击、关系攻击的中介效应实现,身体攻击、关系攻击的中介效应存在差异。     

数学焦虑影响儿童数学任务表现的作用机制探析

研究设计了心算加法和图形旋转/平移两类数学任务,同时采用《儿童数学焦虑问卷》、工作记忆和抑制任务,以探讨数学焦虑影响儿童数学任务表现的作用机制.213名小学五年级儿童参与研究,其中89人参与正式实验.结果发现:(1)数学焦虑与数学成绩呈显著负相关;(2)高数学焦虑组在工作记忆和两类数学任务中的得分均显著低于低数学焦虑组,而两组在抑制任务指标上差异不显著;(3)言语工作记忆和视空间工作记忆是数学焦虑影响心算加法任务的完全中介变量;视空间工作记忆是数学焦虑影响图形旋转/平移任务的完全中介变量,言语工作记忆是二者关系的调节变量.研究结果支持了加工效能理论.     

结果预期对青少年攻击性行为的影响：中介效应与调节效应

采用攻击性问卷、关系攻击行为量表、结果预期量表、移情量表和自我控制能力问卷对720名中学生进行调查,考察了结果预期与青少年攻击性行为的关系,以及自我控制在其中的中介作用和移情在其中的调节作用。结果发现:(1)结果预期与青少年的攻击性行为(外部攻击和关系攻击)存在显著负相关;(2)自我控制在结果预期与青少年攻击性行为之间起着完全中介作用;(3)在结果预期对青少年外部攻击行为的预测中,移情发挥了调节作用。在高移情个体中,结果预期并不预测外部攻击行为,而在低移情个体中,结果预期显著地反向预测外部攻击行为;(4)自我控制在结果预期与青少年外部攻击行为之间的中介作用受到移情的调节,高水平的移情能力可以有效地缓解青少年因低自我控制而导致的高攻击性。     

父母行为控制、心理控制与青少年早期攻击和社会退缩的关系

考察父母行为和心理控制与青少年早期攻击和社会退缩有无特异性联系、是否存在非线性关系、是否以情绪调节策略(认知重评和表达抑制)作为中介。694名青少年(平均年龄13.67岁)完成了父母控制问卷、情绪调节量表、青少年攻击以及社会退缩量表。结果表明:(1)行为控制和心理控制均与两类结果有关,未表现出"一对一"的特异性联系;(2)行为控制与两类结果呈倒U型曲线关系,心理控制与两类结果呈线性关系;(3)认知重评在心理控制与攻击之间具有部分中介作用,表达抑制在心理控制与社会退缩之间具有部分中介作用。     

大学生依恋焦虑与抑郁的关系:恋爱中关系攻击和关系质量的序列中介作用

浪漫关系中的关系攻击指通过操纵或损害关系以达到伤害浪漫关系伴侣的行为。本文以628名处于恋爱关系中的大学生为被试,探讨了依恋焦虑与抑郁之间的关系,并考察了恋爱中的关系攻击和恋爱关系质量在其中的序列中介作用。结果表明:(1)大学生依恋焦虑对抑郁有显著的正向预测作用;(2)关系攻击和关系质量在大学生依恋焦虑与抑郁之间分别发挥着单独中介作用;(3)关系攻击和关系质量在大学生依恋焦虑与抑郁之间发挥着序列中介作用。研究结果验证了依恋焦虑个体在关系中的“自我实现预言”模型,同时能够为大学生心理健康教育提供实践指导。     

父母严厉管教与儿童焦虑的关系：家庭亲密度的中介作用

以605名小学生为被试,采用问卷调查法考察家庭亲密度在父母严厉管教(心理攻击和体罚)与儿童焦虑间的中介作用,以及儿童性别对这一中介效应的调节作用。结果发现:(1)父亲和母亲严厉管教与家庭亲密度均呈显著负相关,与儿童各焦虑症状均呈显著正相关,家庭亲密度与儿童各焦虑症状均呈显著负相关;(2)家庭亲密度在父亲心理攻击、母亲心理攻击和母亲体罚与儿童焦虑之间均存在显著的中介作用;(3)家庭亲密度的中介作用存在显著的儿童性别差异。     

ANS acuity and mathematics ability in preschoolers from low‐income homes: contributions of inhibitory control

Recent findings by Libertus, Feigenson, and Halberda (2011) suggest that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling. The present study examined the generalizability and validity of these findings in a sample of preschoolers from low‐income homes. Children attending Head Start (N = 103) completed measures to assess ANS acuity, mathematics ability, receptive vocabulary, and inhibitory control. Results showed only a weak association between ANS acuity and mathematics ability that was reduced to non‐significance when controlling for a direct measure of receptive vocabulary. Results also revealed that inhibitory control plays an important role in the relation between ANS acuity and mathematics ability. Specifically, ANS acuity accounted for significant variance in mathematics ability over and above receptive vocabulary, but only for ANS acuity trials in which surface area conflicted with numerosity. Moreover, this association became non‐significant when controlling for inhibitory control. These results suggest that early mathematical experiences prior to formal schooling may influence the strength of the association between ANS acuity and mathematics ability and that inhibitory control may drive that association in young children.     

Differences in the acuity of the Approximate Number System in adults: The effect of mathematical ability

It is largely admitted that processing numerosity relies on an innate Approximate Number System (ANS), and recent research consistently observed a relationship between ANS acuity and mathematical ability in childhood. However, studies assessing this relationship in adults led to contradictory results. In this study, adults with different levels of mathematical expertise performed two tasks on the same pairs of dot collections, based either on numerosity comparison or on cumulative area comparison. Number of dots and cumulative area were congruent in half of the stimuli, and incongruent in the other half. The results showed that adults with higher mathematical ability obtained lower Weber fractions in the numerical condition than participants with lower mathematical ability. Further, adults with lower mathematical ability were more affected by the interference of the continuous dimension in the numerical comparison task, whereas conversely higher-expertise adults showed stronger interference of the numerical dimension in the continuous comparison task. Finally, ANS acuity correlated with arithmetic performance. Taken together, the data suggest that individual differences in ANS acuity subsist in adulthood, and that they are related to mathematical ability.     

Concurrent validity of approximate number sense tasks in adults and children

Reasoning with non-symbolic numerosities is suggested to be rooted in the Approximate Number System (ANS) and evidence pointing to a relationship between the acuity of this system and mathematics is available. In order to use the acuity of this ANS as a screening instrument to detect future math problems, it is important to model ANS acuity over development. However, whether ANS acuity and its development have been described accurately can be questioned. Namely, different tasks were used to examine the developmental trajectory of ANS acuity and studies comparing performances on these different tasks are scarce. In the present study, we examined whether different tasks designed to measure the acuity of the ANS are comparable and lead to related ANS acuity measures (i.e., the concurrent validity of these tasks). We contrasted the change detection task, which is used in infants, with tasks that are more commonly used in older children and adults (i.e., comparison and same-different tasks). Together, our results suggest that ANS acuity measures obtained with different tasks are not related. This poses serious problems for the comparison of ANS acuity measures derived from different tasks and thus for the establishment of the developmental trajectory of ANS acuity.     

Preschool acuity of the approximate number system correlates with school math ability

Previous research shows a correlation between individual differences in people's school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and with non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants' ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children's math ability and vocabulary size prior to the onset of formal math instruction. We found that children's ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life.     

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate. The findings reported in the literature are actually inconsistent; some studies emphasized the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the coefficient of variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially, however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and non-numerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.     

The Acuity for Numerosity (but Not Continuous Magnitude) Discrimination Correlates with Quantitative Problem Solving but Not Routinized Arithmetic

Approximate number sense (ANS) acuity refers to the ability to non-symbolically recognize, estimate and operate upon large numerosities. ANS acuity has been reported to be correlated with math achievement in children and adolescents. However, reports of this relationship in adults have been inconsistent. The present study aimed to resolve the inconsistency in the relationship between adults’ ANS acuity and math achievement by contrasting between different kinds of mathematical problem solving. We hypothesized that the correlation between ANS acuity mathematical performance would be stronger when deep quantitative processing is required during problem solving. In Experiment 1, ANS acuity was correlated with Mathematical Reasoning but not Directed Calculation performance. In Experiment 2, ANS acuity was correlated with Two-digit Subtraction (but not Addition) performance only when Regrouping (i.e., borrowing) was required. The results from two experiments demonstrated that ANS acuity was correlated with mathematical performance only when problem solving involved effortful, quantitative processing that goes beyond automatized, routinized arithmetic. In addition, ANS acuity was distinguishable from Area acuity regarding its unique relationship with math achievement, which was unconfounded by the influence of demographic variables and fluid intelligence. Overall, the present results help resolve the inconsistency in previous reports of the correlation between ANS acuity and math achievement in adults.     

Infants’ sense of approximate numerosity: Heritability and link to other concurrent traits

The ability to perceive approximate numerosity is present in many animal species, and emerges early in human infants. Later in life, it is moderately heritable and associated with mathematical abilities, but the etiology of the Approximate Number System (ANS) and its degree of independence from other cognitive abilities in infancy is unknown. Here, we assessed the phenotypic specificity as well as the influence of genetic and environmental factors on the ANS in a sample of 5-month-old twins (N = 514). We found a small-to-moderate but statistically significant effect of genetic factors on ANS acuity (heritability = 0.18, 95% CI: 0.02, 0.33), but only when differences in numerosity were relatively large (1:4 ratio). Non-verbal ability assessed with the Mullen Scales of Early Learning (MSEL) was found to be heritable (0.47; 95% CI: 0.34, 0.57) and the phenotypic association between ANS acuity and non-verbal ability performance was close to zero. Similarly, we found no association between ANS acuity and general attention during the task. An unexpected weak but statistically significant negative association between ANS acuity and scores on the receptive language scale of the MSEL was found. These results suggest that early ANS function may be largely independent from other aspects of non-verbal development. Further, variability in ANS in infancy seems to, to some extent, reflect genotypic differences in the population.

Highlights

• Assessing 514 infant twins with eye tracking, we found that infants' sense of approximate numerosity is heritable and not positively associated with concurrent attentional, cognitive or motor abilities.
• These results have implications for our understanding of development of mathematical ability and the link between cognitive abilities early in postnatal life.

     

青少年未来取向三种测试途径的比较

考察未来取向测试新方法（作品分析法）有效性及对比已有测量方法(自陈问卷法、行为测试法)的优缺点。结果发现,问卷法测得青少年未来取向水平随年龄增长逐渐降低,行为测试法和作品分析法测得青少年未来取向水平随年龄增长逐渐提高;问卷法测得未来取向与学校投入相关密切,行为测试法测得未来取向与学业成绩相关密切,作品分析法测得未来取向与学校投入、学业成绩均相关。作品分析法是一种有效测量青少年未来取向的新途径。