The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.     

Getting one step closer to deduction: Introducing an alternative paradigm for transitive inference

Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT) were measured as is typically done. We also measured RT confined to correct responses (cRT). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was not at all evident for nRT; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B?D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held.     

3—7岁儿童不同类型的传递性推理的发展研究

本研究从发展的角度研究了3-7岁儿童在解决三类传递性推理问题时能力发展和策略发展状况,真传递性推理指推理的传递性是确定的,个体根据前提关系可以做出确定的传递性推理结论,不确定性传递性推理指该类推理的传递性是不确定的,关系是否传递需要根据实际的情况和社会经验来确定,否定性传递性推理指根据前提关系得出不能进行传递性的必然结论。结果表明：（1）三类传递性推理的解题能力随年龄的增长而不断增强,在7岁左右初步形成。（2）三类传递性推理,能力发展有不同的起始点、快速发展期以及初步形成期。真传递性推理发展最早最快,不确定传递性推理最晚最慢。（3）3-7岁儿童解决三类传递性推理问题时使用了猜测、视觉判断、定向反应、经验推测和逻辑推理等策略,然而随着年龄的增大,主导策略由准策略向真策略转换。     

小学儿童两维空间方位传递性推理能力的发展

研究了小学儿童两维空间方位传递性推理能力的发展水平及认知策略,同时,对心理模型理论进行了检验。被试为城市中等小学7岁、9岁、11岁儿童各24名,男女各半。单模型和双模型两种实验任务均为四前提。采用个别实验,儿童在前提呈现的情况下进行推理。主要研究结果：（1）7岁儿童开始萌发了两维空间方位传递性推理能力,9岁儿童和11岁儿童的推理能力处于发展和提高过程中;（2）随着年龄增长,使用模型建构策略解决问题的儿童人次越来越多,绝大部分11岁儿童都能使用这一策略进行推理。但即使儿童使用了模型建构策略,他们的推理成绩也没有反映出模型数量所造成的任务难度差异,即不符合心理模型理论关于模型数量的主要预期;（3）即使儿童能自发生成模型建构策略,儿童在两维空间方位传递性推理中使用这一策略的有效性程度并不高。     

5~6岁儿童传递推理能力的发展特点

通过有效的实验设计,在控制儿童记忆容量影响的前提下,考察了5~6岁儿童在长度传递推理和重量传递推理能力上的发展水平。结果表明:(1)5~6岁是儿童传递推理能力迅速发展的时期。在大概6岁左右,大多数儿童已经能够进行真正意义上的传递推理。(2)此年龄儿童在长度传递推理和重量传递推理能力上不具有显著差异。(3)条件排列的一致与不一致对于被试的推理成绩并不具有显著影响。     

Understanding inference as a source of knowledge: children's ability to evaluate the certainty of deduction, perception, and guessing

Three experiments investigated children's understanding of inference as a source of knowledge. Children observed a puppet make a statement about the color of one of two hidden toys after the puppet (a) looked directly at the toy (looking), (b) looked at the other toy (inference), or (c) looked at neither toy (guessing). Most 4-, 5-, and 6-year-olds did not rate the puppet as being more certain of the toy's color after the puppet looked directly at it or inferred its color than they did after the puppet guessed its color. Most 8 and 9-year-olds distinguished inference and looking from guessing. The tendency to explain the puppet's knowledge by referring to inference increased with age. Children who referred to inference in their explanations were more likely to judge deductive inference as more certain than guessing.     

Transitivity for height versus speed: To what extent do the under-7s really have a transitive capacity?

Transitive inference underpins many human reasoning competencies. The dominant task (the “extensive training paradigm”) employs many items and large amounts of training, instilling an ordered series in the reasoner's mind. But findings from an alternative “three-term paradigm” suggest transitivity is not present until 7 + years. Interestingly, a second alternative paradigm (the “spatial task”), using simultaneously displayed height relationships to form premise pairs, can uphold the 4-year estimate. However, this paradigm risks cueing children and hence is problematic. We investigated whether a height-task variant might correspond to a more ecologically valid three-term task. A total of 222 4–6-year-olds either completed a modified height task, including an increased familiarisation phase, or a computer-animated task about cartoon characters running a race in pairs. Findings confirmed that both tasks were functionally identical. Crucially, 4-year-olds were at chance on both, whereas 6-year-olds performed competently. These findings contrast with estimates from all three paradigms considered. A theoretical evaluation of our tasks and procedures against previous ones, leads us to two conclusions. First, our estimate slightly amends the 7-year estimate offered by the three-term paradigm, with the difference explained in terms of its greater relevance to child experiences. Second, our estimate can coexist alongside the 4-year estimate from the extensive training paradigm. This is because, applying a recently developed “dual-process” conception of reasoning, anticipates that extensive training benefits a species-general associative system, while the spatial paradigm and three-term paradigm can potentially index a genuinely deductive system, which has always been the target of transitive research.     

The link between deductive reasoning and mathematics

ABSTRACT

Recent studies have shown that deductive reasoning skills (including transitive and conditional inferences) are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions.     

3～5岁幼儿在视野阻隔任务中的长度传递性推理

设计视野阻隔任务,控制了短时记忆和直接比较的两难问题,考察3～5岁幼儿长度传递性推理能力的发展趋势和传递性推理这一认知过程的发展序列。以2(间隔长度)×2(摆放方式)×4(年龄)的三因素混合设计,研究了240名幼儿,结果表明:(1)3～4岁是长度传递性推理能力的快速发展期,4岁以后的幼儿大部分具备了这一能力,发展速度趋于平缓;(2)任务类型影响推理成绩;(3)基于传递关系的推理依据与推理总成绩显著正相关。研究认为:年仅4岁幼儿具备传递性推理能力蕴含教育价值;传递性推理的认知过程经历了四个可辨别的发展序列,依次主要发生在36～42个月、43～48个月、49～54个月和55～60个月的幼儿当中。     

小学儿童一维空间方位传递性推理能力的发展

研究了小学儿童一维空间方位传递性推理能力的发展水平及认知策略 ,同时 ,对心理模型理论进行了检验。被试为城市中等小学 7岁、9岁、11岁儿童各 2 4名 ,男女各半。 4种实验任务分别为三前提单模型、三前提双模型、四前提单模型和四前提双模型。采用个别实验 ,儿童在前提呈现的情况下进行推理。主要研究结果 :(1)从小学 7岁到 11岁 ,儿童的一维空间方位传递性推理能力明显提高 ,7岁儿童初步形成了一维空间方位推理能力 ,9岁和 11岁基本具有了这种能力 ;(2 )随着年龄增长 ,使用模型建构策略解决问题的儿童人次越来越多 ,绝大部分 11岁儿童都能使用这一策略进行推理。但即使儿童使用了模型建构策略 ,他们的推理成绩也没有反映出模型数量所造成的任务难度差异 ,即不符合心理模型理论关于模型数量的主要预期。     

Patterns of perceptual change in the ages 7 to 15 years: a cross-sectional study of the Rod-and-Frame Test and the spiral aftereffect technique

Abstract.— Studied cross-sectional changes in Rod-and-Frame Test (RFT) deviation scores and spiral aftereffect (SAE) duration scores in 124 boys and 124 girls aged 7, 9, 11, 13 and 15 years. The gradual decrease in magnitude of RFT deviation with age reached its minimum at the age of 13. A sex difference, disappearing with age, was adequately described by a measure of performance change, boys counteracting to a higher extent than girls the frame influence as the RFT trials proceeded. An increase in SAE duration, found previously with 5-year-olds, appeared here with 111-year-olds but later in a series of ten trials rather than initially as with the younger children. Relations between RFT and SAE scores were mainly found with 7-year-olds, i.e. at an age when per-ceptual-figural regulations may still dominate the cognitive organization of some children. The SAE results are viewed within a multi-line developmental model characterizing cognitive growth as a dialectic process of progressive shifts between objectivized and self-centered modes of representation.     

小学儿童在不同刺激材料中的左右空间方位传递性推理能力及策略分析

采用定性和定量相结合的研究方法,从图形刺激材料和文字刺激材料入手,探查了7岁、9岁、11岁儿童的一维空间方位传递性推理能力的发展水平及其认知策略。主要研究结果表明:(1)小学儿童的一维空间方位传递性推理能力从7岁到9岁,从9岁到11岁都有显著性提高。7岁儿童处于能力的初步形成期,9岁儿童是能力的提高和发展期,11岁儿童已基本具有了一维空间方位单模型条件下的传递性推理能力;(2)小学儿童在图形刺激材料条件下的推理成绩显著优于文字刺激材料条件下的推理成绩;(3)前提数量的增加没有对小学儿童的推理造成显著性影响;(4)随着儿童年龄的增长,模型建构策略的使用者越来越多,但在图形刺激材料和文字刺激材料下,儿童解决问题的策略有所不同。在图形刺激材料下,大部分7岁和9岁的儿童采用知觉策略,11岁儿童中只有少部分人使用这一策略。在文字刺激材料下,模型建构策略是儿童推理的主要策略。少部分7岁儿童使用模型建构策略,大部分9岁儿童和绝大部分11岁儿童使用模型建构策略来解决问题。     

Formal reasoning in Japanese older adults: The role of metacognitive strategy,task content,and social factors

This study investigated the availability of deductive reasoning competence in late adulthood. Forty-six Japanese older (mean age =71 years) and 58 Japanese young adults (mean age =19.6 years) were assessed for formal or deductive reasoning using Overton's (1990) revision of the four-card selection task. For older adults, metacognitive strategy—operating as a procedure designed to access reasoning competence—resulted in enhanced performance levels. When the semantic content of the reasoning task involved emotional issues, however, the metacognitive strategy failed to facilitate reasoning performance. This suggests that reasoning competence is available in late adulthood but that performance is susceptible to contextual variables. Social factors were not significantly related to older adults' reasoning performance. Thus, assessment of these factors may have been based on too broad a definition to describe adequately the status of the older adults. For the young, only semantic task content was related to reasoning performance.     

Improving time discrimination in children and adults in a temporal bisection task: The effects of feedback and no forced choice on decision and memory processes

In children aged 5 and 8 years old as well as in adults, Experiment 1 tested the effect of feedback on temporal performance using a bisection task. Experiment 2 added a no-forced-choice condition by giving the participants the possibility of responding “I don't know”. The results of Experiment 1 showed that providing feedback increased the bisection point value (point of subjective equality) in all age groups and increased sensitivity to time in the youngest children. The results of Experiment 2 showed that the proportion of “I don't know” responses peaked at the probe duration close to the arithmetic mean of the two anchor durations and decreased as the distance from this central value increased in both the adults and the 8-year-olds. In the 5-year-olds, the proportion of “I don't know” responses was lower and remained constant whatever the probe duration values. Unlike in the youngest children, giving the adults and the 8-year-olds the opportunity to respond “I don't know” increased their sensitivity to time. The modelling of our data suggests that providing feedback in a temporal bisection task affects both the memory and the decision processes. However, whereas the feedback-related effect had a similar effect on decision processes across the age groups, it had an opposite effect on memory processes in the 5-year-olds and the older participants, decreasing the variability of the memory representation of the anchor durations in the former while increasing it in the latter. Finally, in bisection, feedback only improved temporal performance when the memory for duration was imprecise as in the case of the children.     

The case for a dual-process theory of transitive reasoning

Ever since its popularisation by Piaget around 60 years ago, transitive reasoning (deductively-inferring A > C from premises A > B and B > C) has been of psychological interest both as a mental phenomenon and as a tool in areas of psychological discourse. However, the focus of interest in it has shifted periodically first from child development, to learning disability, to non-humans and currently to cognitive and clinical neuroscience. Crucially, such shifts have always been plagued by one core question – the question of which of two competing paradigms (extensive-training paradigm versus non-training paradigm) is valid for assessing transitive reasoning as originally conceived in Piagetian research. The continued avoidance of this question potentially undermines several important findings recently reported: Such as about exactly what is involved in deducing transitive inferences, which brain regions are critical for reaching transitive inference, and what links exist between weakened deductive transitivity and mental illnesses like schizophrenia. Here, we offer the view that both of the competing paradigms are indexing transitivity, but each one tends to tap a different aspect of it. Then, we summarise studies from child and adult cognitive psychology, disabilities research, and from cognitive neuroscience. These, together with studies of non-human reasoning, seem to afford a theory of transitive reasoning that has two major components; one deductive but the other associative. It is proposed that only a dual-process theory of transitivity (having analytic versus intuitive routes approximate to deductive versus associative processing respectively) can account both for the variety of findings and the apparently-disparate paradigms. However, fuzzy-trace theory (“Gist” processes and representations), if not already embodying such a dual-process theory, will need to be incorporated into any complete theory.     

"It's magic!" The effects of presentation modality on children's event memory, suggestibility, and confidence judgments

The current study investigated the influence of presentation modality (live, video, and slide show) on children's memory, suggestibility, recognition, and metamemorial monitoring processes. A total of 270 children in three age groups (5- and 6-year-olds, 7- and 8-year-olds, and 9- and 10-year-olds) watched a magic show and were questioned about it 1 week later. The live show yielded more correct answers to nonleading questions, higher resistance to misleading questions, and better recognition memory than did the video condition, which in turn resulted in better performance than did the slide show. Although presentation modality raised the general level of memory performance, the effects were equally strong in all age groups and did not affect memory phenomena such as the size of the misinformation effect and confidence judgments.     

Validating the Electric Maze Task as a Measure of Planning

The Electric Maze Task (EMT) is a novel planning task designed to allow flexible testing of planning abilities across a broad age range and to incorporate manipulations to test underlying planning abilities, such as working-memory and inhibitory control skills. The EMT was tested in a group of 63 typically developing 7- to 12-year-olds. Participants completed 4 mazes designed to alter working-memory demands (by increasing the number of steps required from 6 to 8) and inhibitory control demands (by using a modified Dimensional Change Card Sort task) and 3 standardized measures using the Cambridge Neuropsychological Test Automated Battery. The EMT was found to correlate with measures of visual memory, working memory, and planning. The 6-step mazes were simpler for participants to solve and mapped on to performance on the visual memory task. The 8-step mazes were more difficult and mapped on to performance on the spatial working-memory and planning tasks. Children who were 10 to 12 years old were also better than 7- to 9-year-olds at solving all mazes, as evidenced by fewer errors and fewer errors later in solving the mazes. Younger children also struggled more than older children after a rule switch. Performance on the maze task differentiated 7- to 12-year-old children with better planning skills, and manipulations of the maze task were successful in altering the working-memory and inhibitory control demands.     

The effects of task instructor status on prospective memory performance in preschoolers

The present study applied a 2 × 2 experimental design to assess prospective memory (PM) development across preschool age and to examine the effect of task instructor status (researcher vs. significant other) on PM performance in 80 preschool children. Participants were required to name pictures (ongoing task [OT]), and to remember to refrain from naming but instead give a different response to certain target cues (PM task). Although the OT was of comparable difficulty for both age groups (as indicated by no performance differences), results still indicated significantly higher PM performance in 5-year-olds than in 3-year-olds, confirming the age-related increase of PM capacities between 3 and 5 years. Furthermore, results showed a performance-enhancing effect of significant others as task instructors on both age-groups. Post-hoc analysis revealed that 3-year-olds instructed by a significant other still performed marginally worse than 5-year-olds instructed by a researcher, underlining the finding that substantial changes of PM capacities take place during early childhood.     

Developmental change on a five-term transitive inference

Three experiments are reported which utilize the five-term transitive inference task developed by P. E. Bryant and T. Trabasso (Nature (London) 1971, 232, 456–458). In Experiment I, preschool children (mean age = 4 years 8 months) required fewer trials to learn the premises and showed a higher proportion of correct responses on the inferences when the presentation order was serial (i.e., AB, BC, CD, DE) throughout training as compared to when a nonserial presentation order (i.e., BC, DE, AB, CD) was used. In Experiments II and III, preschool (mean age = 4 years 7 months), second grade (mean age = 7 years 8 months), fourth grade (mean age = 9 years 9 months), and college students (mean age = 18 years 11 months) were administered the nonserial presentation version of the five-term transitive inference. An ontogenetic decrease in trials to learn the premises and corresponding increase in proportion correct on both premises and inferences was observed. A developmental model specifying changes at two stages of constructing an internal linear order is proposed to explain the results.     

THOG问题的演译结构及其非Wason-Brooks判定方法

本文探讨THOG问题的演绎结构及其非Wason-Brooks判断方法,据于Wason-Brooks判断程序和THOG问题逻辑结构的分析导致如下结论：1．Wason-BrooksTHOG判定方法并非判定THOG的唯一方法;2、被试选择那一种演绎判定模式取决于被试如何对原问题进行等效表征转换;3．判断失败可能意味着被试存在短时记忆容量障碍或者等效表征转换障碍。