On the emergence of the discriminative mode for transitive-inference

Transitive-inference tasks play increasing roles in many areas of cognitive science. However, discrepancies between the two competing paradigms (classical-Piagetian and IP-paradigm) imply that one paradigm fails to index its target (deductive) competence. Here, potential flaws of one were addressed using considerations from the other. Children of 5–7 years (N=216) solved 3-term transitive problems, some implying a single largest item, and some not. Findings indicate a discriminative competence (a Transitive-Switch) at least 2 years before competence in actually deducing correct solutions. Interestingly, although the transitive-switch was constant across age with both memory and inference increasing with age, it was nevertheless a much stronger predictor of transitive performance than either memory or age. A predictive relationship between memory and inference held for the 5- and 6-year-olds but not the 7-year-olds; suggesting as it approaches maturity, transitive-inference becomes independent of memory. Coincidental with this latter finding, only the 7-year-olds’ transitive performance approximated a deductive competence. As the initial validation of the IP-paradigm rested on acceptance of its age estimate of 4 years, its claim to index deduction must now be revisited.     

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.     

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。     

Understanding children's activity memory: the role of outcomes

In three experiments the effectiveness of activity outcomes as memory cues was investigated. In the first experiment, 5-year-olds participated in four activities. In two of these activities, action results were maintained during the unfolding of the activity and perceptually preserved in the activity's end product. In the other two activities, action results "disappeared" from view during the activity and were transformed within the end product. Each activity was recalled under one of four cue conditions: verbal, object, action, and reenactment. For half of the children, the end product was also present during retrieval. Memory for the two types of activities varied with cue condition and with the presence of the end product. In a second experiment, children attempted to describe how the end products could be recreated from the materials used in the activities without participating in them. Patterns of performance confirmed that memory and not inference was responsible for the effects observed in the first experiment. In a third experiment, 5- and 7-year-olds participated in activities of the two types. Within each, picture supports were provided to investigate whether the perceptual availability of action results during encoding influences memory. Results are discussed with respect to an activity memory framework and implications for science education.     

儿童的直接推理能力及策略的发展

采用文字形式陈述前提,让儿童根据前提内容回答问题,以了解儿童在语言条件下的直接推理能力。并通过事后追问儿童作答的原因,对儿童推理的策略进行分析。结果表明：（1）6岁和7岁儿童初步发展了语言条件下的直接推理能力,8岁儿童形成了这种能力。从6岁到8岁,儿童的这种推理能力随年龄增长而迅速提高。（2）否定前提和肯定前提没有给儿童的直接推理造成影响。而且,反义词的转换,也没有增加任务的推理难度。（3）从6岁到8岁儿童的有效生成能力和使用能力都在明显提高。6岁、7岁儿童在直接推理时有效策略和无效策略并存,但几乎所有的8岁儿童都使用了“重复或解释前提”这一有效策略。     

Reconceptualizing the Transitive Inference Ability: A Framework for Existing and Future Research

It has often been claimed that to demonstrate transitive inference is to demonstrate a logical ability, and by implication that transitivity as a property is generally a logical entity. Both claims are considered using a theoretically driven analysis together with consideration of relevant existing experimental research and some newly reported findings. This approach suggests an account of transitivity and transitive inferential reasoning that differs not only from the classic Piagetian account, but also from the information processing account so dominant today. We begin by considering one important issue, that the “logical” definitional criterion can only be approached if individuals are required to demonstrate a capacity for transitive inference that is discriminative in nature. This, together with interpretation of findings from existing transitive tasks, leads to the postulate of a three-component psychological system, with the components relying on perceptual, linguistic, and conceptual subprocesses and sensitivity to simple cues. The framework is testable and accommodates important aspects of classic and modern accounts of “transitive development” that until now have been taken to be mutually exclusive. It also readily accommodates both human and nonhuman research, yet neither a formal logical structure nor memory in any general sense need be assigned the primary role.     

The development of automatic numerosity processing in preschoolers: evidence for numerosity-perceptual interference

Three experiments examined developmental changes in the automatic processing of numerosity and perceptual information using a nonsymbolic numerical Stroop paradigm. In Experiments 1 and 2 (E1 and E2), 4-, 5-, and 6-year-olds had to compare the numerosities or the total filled areas of collections of dots (E1) or bars (E2) varying along both dimensions. Experiment 3 replicated E2's results in 3-, 4-, and 5-year-olds. Results demonstrated the existence of reciprocal influences between numerical and perceptual information beginning at age 3. Moreover, the irrelevant perceptual influences remained stable throughout development, whereas the sensitivity to irrelevant numerical cues tended to increase with age despite children's growing inhibition capacities. No significant correlation could be found between these developmental changes and the acquisition of counting knowledge.     

Belief-based and analytic processing in transitive inference depends on premise integration difficulty

Three experiments investigated belief-based versus analytic processing in transitive inference. Belief-based and analytic processing were inferred from conclusion acceptance rates for problems with conclusions that were either valid or invalid and believable or unbelievable. Premise integration difficulty was manipulated by varying premise integration time (Experiment 1), premise presentation order (Experiment 2), and the markedness of the relational terms in the premises (Experiment 3). In all the conditions, reasoning accuracy and rated confidence were lower on conflict problems, where belief-based and analytic processes yielded different responses. Participants relied more on analytic processing and less on belief-based processing in conditions in which premise integration was easier. Fluid intelligence and premise integration ability predicted analytical reasoning on conflict problems after reasoning on the no-conflict problems was controlled for. The findings were related to three dual-process models of belief bias. They provide the first evidence of belief bias in transitive inference.     

The role of local and distal landmarks in the development of object location memory

To locate objects in the environment, animals and humans use visual and nonvisual information. We were interested in children's ability to relocate an object on the basis of self-motion and local and distal color cues for orientation. Five- to 9-year-old children were tested on an object location memory task in which, between presentation and test, the availability of local and distal cues was manipulated. Additionally, participants' viewpoint could be changed. We used a Bayesian model selection approach to compare our hypotheses. We found that, to remain oriented in space, 5-year-olds benefit from visual information in general, 7-year-olds benefit from visual cues when a viewpoint change takes place, and 9-year-olds do not benefit from the availability of visual cues for orientation but rely on self-movement cues instead. Results are discussed in terms of the adaptive combination model (Newcombe & Huttenlocher, 2006).     

Children''s ability to make transitive inferences: The importance of premise integration and structural complexity

Four experiments investigated 4- to 6-year-olds' transitive inferences. In Experiments 1–3, there was a nonmapping condition in which inferences were made either about stacked blocks, or about sticks ordered left to right. In the mapping condition, inferences were made by mapping either from blocks to sticks, or the reverse. In Experiments 2–4, relational complexity was manipulated by requiring either 1 or 2 premise relations to be processed in a single decision. Mapping was harder than nonmapping, but relational complexity was the main source of variance, with 2 relations being harder in both mapping and nonmapping conditions. The percentage of participants integrating 2 relations in a single decision was estimated at 20% at age 4, 53% at age 5 and 57% at age 6, suggesting gradual development of transitive inference ability. Results suggest that relational complexity has a strong effect on transitive inference in 4- to 6-year-old children.     

Verbs and Syntactic Frames in Children’s Elicited Actions: A Comparison of Tamil- and English-Speaking Children

We directly compare children learning argument expressing and argument dropping languages on the use of verb meaning and syntactic cues, by examining enactments of transitive and intransitive verbs given in transitive and intransitive syntactic frames. Our results show similarities in the children’s knowledge: (1) Children were somewhat less likely to perform an action when the core meaning of a verb was in conflict with the frame in which it was presented; (2) Children enacted the core meaning of the verb with considerable accuracy in all conditions; and (3) Children altered their actions to include or not include explicit objects appropriately to the frame. The results suggest that 3-year-olds learning languages that present them with very different structural cues still show similar knowledge about and sensitivity to the core meanings of transitive and intransitive verbs as well as the implications of the frames in which they appear.     

Adjective Semantics, World Knowledge and Visual Context: Comprehension of Size Terms by 2- to 7-Year-Old Dutch-Speaking Children

The interpretation of size terms involves constructing contextually-relevant reference points by combining visual cues with knowledge of typical object sizes. This study aims to establish at what age children learn to integrate these two sources of information in the interpretation process and tests comprehension of the Dutch adjectives groot ‘big’ and klein ‘small’ by 2- to 7-year-old children. The results demonstrate that there is a gradual increase in the ability to inhibit visual cues and to use world knowledge for interpreting size terms. 2- and 3-year-old children only used the extremes of the perceptual range as reference points. From age four onwards children, like adults, used a cut-off point in the mid-zone of a series. From age five on, children were able to integrate world knowledge and perceptual context. Although 7-year-olds could make subtle distinctions between sizes of various object classes, their performance on incongruent items was not yet adult-like.     

Do preschoolers remember what to do? Incentive and external cues in prospective memory

Prospective memory, which involves remembering to perform an action at a future time, is used frequently in daily life. Few researchers, however, have studied this type of memory with children. The present study examined and compared 3- and 5-year-olds' performance on naturalistic and computer-based prospective memory tasks. The effects of incentive and external cues on memory performance were examined along with the relationship between prospective and retrospective memory. The results indicated that 5-year-olds demonstrated greater prospective memory performance than did 3-year-olds and neither incentive nor external cues consistently improved performance. Relationships between performance on the naturalistic and computer tasks varied with age. In contrast to the adult literature, younger children's prospective and retrospective memory performances were related. Implications of these findings are discussed.     

Retrieval of Episodic Information From Memory: Comparisons Among 3- and 4-Year-Olds, 7- and 8-Year-Olds,and Adults

Young children's and adults' recall of episodic information was explored in 4 experiments. The task required participants to recall a target noun presented as the last item of a 4-noun string of related (either categorically or thematically) or unrelated words. Providing all 3 preceding nouns or a subset of them cued recall. Experiment 1 found that 7- and 8-year-old children's recall was better with pictures as opposed to text, and children showed performance equal to adults with thematically related pictorial stimuli. Using pictorial stimuli, Experiment 2 showed that the number of cues present at retrieval affected 7- and 8-year-olds' recall. Experiments 3 and 4 tested recall of episodic information in 3- and 4-year-olds using pictorial stimuli. The results suggested that young children also have access to episodic information in memory and the number of cues present at retrieval influenced recall. The findings are discussed in the context of children's memory for events.     

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。     

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。     

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。     

Gender differences in remembering and inferring spatial distances

The abilities of males and females to make spatial inferences were compared. Spatial inference is concerned with the ability to work out new spatial information from memory. In two experiments, participants had to study line drawings depicting shapes linked either by straight or meandering lines. Afterwards, they had to remember the straight-line distances or to infer the straight-line distances. Several spatial abilities were also assessed: perceptual discrimination, mental rotation, and visuo-spatial working memory span. The results showed that males outperformed females in spatial inference and mental rotation. Experiment 2 extended the study to old people. The results replicated and clarified those obtained in Experiment 1. Spatial inference and mental rotation showed age-related and gender-related differences; in addition, age reduced the visuo-spatial memory span. Overall, the findings suggest that gender differences favouring males are maximised with tasks requiring active processing and strategic control of metric information.     

Gender differences in remembering and inferring spatial distances

The abilities of males and females to make spatial inferences were compared. Spatial inference is concerned with the ability to work out new spatial information from memory. In two experiments, participants had to study line drawings depicting shapes linked either by straight or meandering lines. Afterwards, they had to remember the straight-line distances or to infer the straight-line distances. Several spatial abilities were also assessed: perceptual discrimination, mental rotation, and visuo-spatial working memory span. The results showed that males outperformed females in spatial inference and mental rotation. Experiment 2 extended the study to old people. The results replicated and clarified those obtained in Experiment 1. Spatial inference and mental rotation showed age-related and gender-related differences; in addition, age reduced the visuo-spatial memory span. Overall, the findings suggest that gender differences favouring males are maximised with tasks requiring active processing and strategic control of metric information.     

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。