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1.
Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children’s numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.  相似文献   

2.
Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the Number-to-Position task as a measure of estimation, and completed standardised assessments of arithmetical and mathematical reasoning. Deaf students performed significantly more poorly on all measures, including making less accurate number-line estimates. For deaf students, there was also a strong relationship showing that those more accurate in making number-line estimates achieved higher scores on the math achievement tests. No such relationship was apparent for hearing students. Further insights into the estimation abilities of deaf individuals should be made, including tasks that require symbolic and non-symbolic estimation and which address the quality of estimation strategies being used.  相似文献   

3.
Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (Mage = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance.  相似文献   

4.
It has been hypothesized that developmental dyscalculia (DD) is either due to a defect of the approximate number system (ANS) or to an impaired access between that system and symbolic numbers. Several studies have tested these two hypotheses in children with DD but none has dealt with adults who had experienced DD as children.This study aimed to compare these two hypotheses in an adult population in order to investigate which deficits still persist at that age. To that aim, numerical estimation tasks were given to adults who had or had not experienced DD as a child. Three of the estimation tasks required a mapping between the ANS and symbolic numbers: participants had to estimate the number of same or different-sized dots presented by producing the corresponding Arabic number or, conversely, to produce the number of dots corresponding to a presented Arabic number. A fourth task did not require any processing of symbolic numbers; participants had to produce a collection of dots of the same numerosity as another one previously presented.Consistently, in all the four numerical tasks and irrespective of whether the tasks used symbolic numbers or not, the estimates of DD participants were less accurate than those of the control participants. These results indicate that adults who had experienced DD as children continue to demonstrate a less precise magnitude representation.  相似文献   

5.
The contribution of intentionality understanding to symbolic development was examined. Actors added colored dots to a map, displaying either symbolic or aesthetic intentions. In Study 1, most children (5–6 years) understood actors' intentions, but when asked which graphic would help find hidden objects, most selected the incorrect (aesthetic) one whose dot color matched referent color. On a similar task in Study 2, 5- and 6-year-olds systematically picked incorrectly, 9- and 10-year-olds picked correctly, and 7- and 8-year-olds showed mixed performance. When referent color matched neither symbolic nor aesthetic dot colors, children performed better overall, but only the oldest children universally selected the correct graphic and justified choices with intentionality. Results bear on theory of mind, symbolic understanding, and map understanding.  相似文献   

6.
First- and second-grade children were successfully taught symbolic multi-digit addition and subtraction procedures by first doing the procedures with a physical embodiment of the first four places of the base-ten system. Relationships between the embodiment and the numerical symbols were supported by close linking of the physical and the symbolic procedures and by the use of base-ten, named-value (standard English), and embodiment-name words. Most children successfully extended the procedures to ten-digit symbolic problems done without the embodiment. For many children who made procedural errors on delayed tests, the mental representation of the procedure with the physical embodiment was strong enough for them to use it to selfcorrect their symbolic procedure. The physical embodiment also seems to support the learning of various other concepts related to place value.  相似文献   

7.
Before one can understand or use any symbol, one must first realize that it is a symbol, that is, that it stands for or represents something other than itself. This article reports 4 studies investigating very young children's understanding of 2 different kinds of symbolic stimuli--scale models and pictures. The data replicate previous findings that 2.5-year-old children have great difficulty appreciating the relation between a scale model and the larger space it represents, but that they very readily appreciate the relation between a picture and its referent. This result is interpreted in terms of the dual orientation hypothesis. Models are difficult for young children because they require a dual representation--a child must think about a model both as an object itself and as a representation of something else. Because pictures are not salient as real objects, they do not require a dual representation. Several kinds of evidence supporting the dual orientation hypothesis are presented. An additional result was the occurrence of a transfer effect: Prior experience with a picture task led to better performance on a subsequent model task. This finding suggests that experience with a symbolic medium they understand can help young children figure out a different, unfamilar medium that they would otherwise not understand.  相似文献   

8.
Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation.  相似文献   

9.
Developmental dyscalculia (DD) is a mathematical learning disability that occurs in around 5%–7% of the population. At present, there are only a handful of screening tools to identify children that might be at risk of developing DD. The present study evaluated the classification accuracy of one such tool: The Numeracy Screener, a 2‐min test of symbolic (Arabic numerals) and nonsymbolic (dot arrays) discrimination ability. A sample of 222 children who demonstrated persistent deficits (n = 55), inconsistent deficits (n = 51), or typical performance (n = 116) on standardized tests of math achievement over multiple observations was tested. The Numeracy Screener correctly classified children in all three groups. Notably, the symbolic condition has greater sensitivity in discriminating children with persistent DD from the other two groups. Screening tools that assess early numeracy skills may be promising for identifying children at risk for developing severe mathematical difficulties.  相似文献   

10.
The study sought out to extend our knowledge regarding the origin of mathematical learning disabilities (MLD) in children by testing different hypotheses in the same samples of children. Different aspects of cognitive functions and number processing were assessed in fifth- and sixth-graders (11–13 years old) with MLD and compared to controls. The MLD group displayed weaknesses with most aspects of number processing (e.g., subitizing, symbolic number comparison, number-line estimation) and two cognitive functions (e.g., visual–spatial working memory). These findings favor the defective approximate number system (ANS) hypothesis, but do not fit well with the access deficit hypothesis. Support is also provided for the defective object-tracking system (OTS) hypothesis, the domain general cognitive deficit hypothesis and to some extent the defective numerosity-coding hypothesis. The study suggests that MLD might be caused by multiple deficits and not a single core deficit.  相似文献   

11.
2 experiments were carried out to clarify the process by which children encode briefly presented spatial positions. The task in both experiments was judging whether a test dot occupied the same position on a card as any 1 of a number of dots which had been presented tachistoscopically. Subjects were first, third, and fifth graders. In the first experiment, performance improved with grade level for stimulus arrays composed of more than 1 dot. The finding contrasts with an earlier report of only minimal developmental change in position encoding, but the procedures of the earlier study appear to have permitted a confounding of position and configural encoding. In the second experiment, position encoding was found to improve with increasing pattern goodness at all age levels. The finding attests to a powerful influence of pattern information on the perceptual system and further suggests that position information is encoded within configural information.  相似文献   

12.
The present study compared Argentine (N = 39) and U.S. (N = 43) children and their mothers on exploratory, symbolic, and social play and interaction when children were 20 months of age. Patterns of cultural similarity and difference emerged. In both cultures, boys engaged in more exploratory play than girls, and girls engaged in more symbolic play than boys; mothers of boys engaged in more exploratory play than mothers of girls, and mothers of girls engaged in more symbolic play than mothers of boys. Moreover, in both cultures, individual variation in children's exploratory and symbolic play was specifically associated with individual variation in mothers' exploratory and symbolic play, respectively. Between cultures, U.S. children and their mothers engaged in more exploratory play, whereas Argentine children and their mothers engaged in more symbolic play. Moreover, Argentine mothers exceeded U.S. mothers in social play and verbal praise of their children. During an early period of mental and social growth, general developmental processes in play may be pervasive, but dyadic and cultural structures are apparently specific. Overall, Argentine and U.S. dyads utilized different modes of exploration, representation, and interaction--emphasizing "other-directed" acts of pretense versus "functional" and "combinatorial" exploration, for example--and these individual and dyadic allocentric versus idiocentric stresses accord with larger cultural concerns of collectivism versus individualism in the two societies.  相似文献   

13.
Visual perspective-taking skills in children   总被引：1，自引：0，他引：1  
The present study evaluated the effects of stimulus complexity and rule usage on a visual perspective-taking task. Preschoolers, first, third, and fifth graders, and adults were shown arrays of dolls and performed a series of perspective-taking tasks. Errors decreased with age, and more errors occurred with the more complex visual arrays. A significant number of errors were made in self-view trials, especially by the preschoolers, showing that the ability to relate an array to a pictorial representation of it is not perfect. A conditional probability analysis showed that most egocentric errors were not due to an inability to relate the array to pictorial representations, but rather to a lack of mastery of Flavell's different positions--different views rule. When the array was covered, however, even first graders showed almost perfect mastery of this rule. There were also task effects on the use of Flavell's same position--same view rule: children performed better for a task involving self and other than for 2 others. Response latencies and effects for the observer's relative position provided evidence for a new rule: opposite positions--opposite views. In addition, front and back views of the dolls were significantly easier than the side views, which suggests a role of labeling or stimulus-discrimination skills.  相似文献   

14.
数量表征是人类重要的基础心理能力,包括了符号和非符号两种表征系统。非符号数量表征是个体不需要依赖符号知识对视觉、听觉或跨通道呈现的实物或实物记号的数量刺激进行表达和运算的过程,具有一定的种系进化基础,先于语言发生。在未接受正式数学教育之前,儿童在一定程度上就能在平面空间和三维空间内表征非符号数量,并表现出了在视觉-听觉跨通道条件下的抽象非符号数量表征能力。个体早期即可能拥有两种特点不同的离散量表征系统:对非符号小数量的精确表征和对大数量的近似表征,但对其产生机制还存在不同的理论解释。在符号系统出现后,非符号数量表征和符号数量表征在行为及神经机制既有区别又有联系,并可能通过映射过程在头脑内部相互转换。与符号数量表征相互作用发展成为个体高级数能力的重要基础。  相似文献   

15.
Pigeons were trained in a forced choice task with four alternatives to categorize arrays consisting of 1, 3, 5, or 8 dots. Before the pigeons chose a comparison stimulus, they were required to peck each dot sequentially. A single peck to a dot, which was defined as an indicating response, changed the color of the dot so that it was differentiated from those that remained to be counted. The pigeons successfully learned to categorize the numerical arrays and then displayed transfer to novel arrays consisting of two, four, six, or seven dots, in a manner according to the order of 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8. Subsequent tests revealed that the pigeons discriminated the stimuli by relying on the number of indicating responses. They also utilized multiple information (surface area, time, and other confounded events), but this was of minor significance, and after training, the pigeons were able to disregard these cues.  相似文献   

16.
The effects of three routine classroom tasks upon heart rate reactivity were investigated with a sample of 30 typical fifth-grade children. Instructions for a mental arithmetic task, the mental arithmetic task itself, and silent reading were administered under standardized conditions, with a reward being offered for performance on the mental arithmetic task to enhance competition. Heart rate was individually monitored each second during these tasks, and data were collected on mental arithmetic performance and reading ability. Results indicated that some children showed large increases in their heart rates during the three tasks, and that these children should be considered as at-risk in terms of their cardiac health.  相似文献   

17.
To investigate the symbolic quality of preschoolers' gestural representations in the absence of real objects, 48 children (16 3-, 4-, and 5-year-olds) performed 2 tasks. In the first task, they were asked to pretend to use 8 common objects (e.g., "pretend to brush your teeth with a toothbrush"). There was an age-related progression in the symbolic quality of gestural representations. 3- and 4-year-olds used mostly body part gestures (e.g., using an extended finger as the toothbrush), whereas 5-year-olds used imaginary object gestures (e.g., pretending to hold an imaginary toothbrush). To determine if children's symbolic skill is sufficiently flexible to allow them to use gestures other than those spontaneously produced in the first task, in the second task children were asked to imitate, for each object, a gesture modeled by an experimenter. The modeled gesture was different from the one the child performed on the first task (e.g., if the child used a body part gesture to represent a particular object, the experimenter modeled an imaginary object gesture for that object). Ability to imitate modeled gestures was positively related to age but was also influenced by the symbolic mode of gesture. 3-year-olds could not imitate imaginary object gestures as well as body part gestures, suggesting that young preschoolers have difficulty performing symbolic acts that exceed their symbolic level even when the acts are modeled. Results from both tasks provide strong evidence for a developmental progression from concrete body part to more abstract imaginary object gestural representations during the preschool years.  相似文献   

18.
The purpose of this study was to explore the relationship between symbolic representation in dramatic play and art and the cognitive and reading readiness levels of kindergarten children. Specifically, the study attempted to determine if there is a significant difference in the performance of kindergarten children on the conservation of number tasks (reflective of the level of operational thought and cognitive development), the Metropolitan Reading Readiness Test, and their involvement and/or level of symbolic re resentation in dramatic play and/or art. Results indicated that children at diffrent cognitive levels (a) performed significantly differently on the Metropolitan Reading Readiness Test, (b) spent significantly different amounts of time involved in dramatic play, and (c) expressed significantly different levels of symbolic representations in dramatic play. No differences were found to exist, however, in their symbolic representation in art.  相似文献   

19.
To use a symbolic object such as a model, map, or picture, one must achieve dual representation; that is, one must mentally represent both the symbol itself and its relation to its referent. The studies reported here confirm predictions derived from this concept. As hypothesized, dual representation was as difficult for 2 1/2-year-olds to achieve with a set of individual objects as it was with an integrated model. Decreasing the physical salience of a scale model (by placing it behind a window) made it easier for 2 1/2-year-old children to treat it as a representation of something other than itself. Conversely, increasing the model's salience as an object (by allowing 3-year-old children to manipulate it) made it more difficult to appreciate its symbolic import. The results provide strong support for dual representation.  相似文献   

20.
A growing body of research indicates that children do not understand mental representation until around age 4. However, children engage in pretend play by age 2, and pretending seems to require understanding mental representation. This apparent contradiction has been reconciled by the claim that in pretense there is precocious understanding of mental representation. 4 studies tested this claim by presenting children with protagonists who were not mentally representing something (i.e., an animal), either because they did not know about the animal or simply because they were not thinking about being the animal. However, the protagonists were acting in ways that could be consistent with pretending to be that animal. Children were then asked whether the protagonists were pretending to be that animal, and children tended to answer in the affirmative. The results suggest that 4-year-olds do not understand that pretending requires mental representation. Children appear to misconstrue pretense as its common external manifestations, such as actions, until at least the sixth year.  相似文献   

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