Child proportional scaling: Is 1/3 = 2/6 = 3/9 = 4/12?

The current experiments examined the role of scale factor in children's proportional reasoning. Experiment 1 used a choice task and Experiment 2 used a production task to examine the abilities of kindergartners through fourth-graders to match equivalent, visually depicted proportional relations. The findings of both experiments show that accuracy decreased as the scaling magnitude between the equivalent proportions increased. In addition, children's errors showed that the cost of scaling proportional relations is symmetrical for problems that involve scaling up and scaling down. These findings indicate that scaling has a cognitive cost that results in decreasing performance with increasing scaling magnitude. These scale factor effects are consistent with children's use of intuitive strategies to solve proportional reasoning problems that may be important in scaffolding more formal mathematical understanding of proportional relations.     

Age and probabilistic reasoning: Biases in conjunctive,disjunctive and Bayesian judgements in early and late adulthood

Probabilistic reasoning plays an essential part in many aspects of our daily routine and it has been argued that as we grow older, the need to make judgements under uncertainty becomes increasingly important. Two studies were conducted to establish whether the propensity to commit probabilistic reasoning errors increased with age. Young (aged 16–24), middle aged (25–54), and older persons (55 years and above) were included. Study 1 revealed systematic biases and errors across a range of judgement tasks. However, no evidence of any age effect in Bayesian inference, the incidence of the conjunction fallacy, or in the number of disjunction errors was found. The results obtained in Study 1 were replicated in Study 2, where the potential mediating role of working memory processes and intellectual capacity were explicitly assessed. While some aspects of probabilistic reasoning performance were correlated with measures of intelligence and working memory functioning among young adults, this was much less evident in older persons. The present findings are discussed in relation to the evolution of the dualistic heuristic–analytical system over the adult lifespan. Copyright © 2005 John Wiley & Sons, Ltd.     

Information processing and reasoning with premises that are empirically false: Interference,working memory,and processing speed

In this study, we looked at the contributions of individual differences in susceptibility to interference and working memory to logical reasoning with premises that were empirically false (i.e., not necessarily true). A total of 97 university students were given a sentence completion task for which a subset of stimuli was designed to generate inappropriate semantic activation that interfered with the correct response, a measure of working memory capacity, and a series of logical reasoning tasks with premises that were not always true. The results indicate that susceptibility to interference, as measured by the error rate on the relevant subset of the sentence completion task, and working memory independently account for variation in reasoning performance. The participants who made more errors in the relevant portion of the sentence completion task also showed more empirical intrusions in the deductive reasoning task, even when the effects of working memory were partialed out. Working memory capacity was more clearly related to processes involved in generating uncertainty responses to inferences for which there was no certain conclusion. A comparison of the results of this study with studies of children's reasoning suggests that adults are capable of more selective executive processes than are children. An analysis of latency measures on the sentence completion task indicated that high working memory participants who made no errors on the sentence completion task used a strategy that involved slower processing speed, as compared with participants with similar levels of working memory who did make errors. In contrast, low working memory participants who made no errors on the sentence completion task had relatively shorter reaction times than did comparable participants who did make errors.     

Everyday scale errors

Young children occasionally make scale errors – they attempt to fit their bodies into extremely small objects or attempt to fit a larger object into another, tiny, object. For example, a child might try to sit in a dollhouse-sized chair or try to stuff a large doll into it. Scale error research was originally motivated by parents' and researchers' informal accounts of these behaviors. However, scale errors have only been documented using laboratory procedures designed to promote their occurrence. To formally document the occurrence of scale errors in everyday settings, we posted a survey on the internet. Across two studies, participants reported many examples of everyday scale errors that are similar to those observed in our labs and were committed by children of the same age. These findings establish that scale errors occur in the course of children's daily lives, lending further support to the account that these behaviors stem from general aspects of visual processing.     

Evidence for an explanation advantage in naïve biological reasoning

The present studies compare young children's explanations and predictions for the biological phenomenon of contamination. In Study 1, 36 preschoolers and 24 adults heard vignettes concerning contamination, and were asked either to make a prediction or to provide an explanation. Even 3-year-olds readily supplied contamination-based explanations, and most children mentioned an unseen mechanism (germs, contact through bodily fluids). Moreover, unlike adults who performed at ceiling across both explanation and prediction tasks, children were significantly more accurate with their explanations than their predictions. In Study 2, we varied the strength of cues regarding the desirability of the contaminated substance (N=24 preschoolers). Although desirability affected responses, for both levels of desirability participants were significantly more accurate on explanation than prediction questions. Altogether, these studies demonstrate a significant "explanation advantage" for children's reasoning in the domain of everyday biology.     

Children's development of analogical reasoning: insights from scene analogy problems

We explored how relational complexity and featural distraction, as varied in scene analogy problems, affect children's analogical reasoning performance. Results with 3- and 4-year-olds, 6- and 7-year-olds, 9- to 11-year-olds, and 13- and 14-year-olds indicate that when children can identify the critical structural relations in a scene analogy problem, development of their ability to reason analogically interacts with both relational complexity and featural distraction. Error patterns suggest that children are more likely to select a distracting object than to make a relational error for problems that present both possibilities. This tendency decreases with age, and older children make fewer errors overall. The results suggest that changes in analogical reasoning with age depend on the interplay among increases in relational knowledge, the capacity to integrate multiple relations, and inhibitory control over featural distraction.     

不同任务类型条件下4～6年级儿童比例推理策略的表现

随机选取小学4~6年级被试86名,从辅助策略、比例推理策略的策略选择和策略效用三方面,通过五种类型的天平任务考察儿童比例推理策略的表现。结果表明:(1)儿童最常使用手指动作辅助加工基本数量信息。辅助策略的使用率随年龄增长而减少,五年级开始使用出声思维,反映出元认知能力的发展。(2)在正式学习比例知识之前,各年级儿童都能使用两种以上策略,也能根据任务难度自发产生新策略,具备策略选择的多样性和适应性。其中,三个年级均能使用定性比例推理策略(双维策略,IIIA策略,补偿策略),表明儿童初步认识了距离和重量两个维度的共变关系。此外,六年级儿童能使用"运货车策略"将冲突问题灵活地化解为简单问题。(3)儿童的错误策略表现为:在冲突任务中盲目使用补偿策略、简单策略或加法策略。(4)分层回归分析表明,在控制年龄后,儿童的一般推理能力越高,其对重量策略的依赖性越低,且可能更容易发掘距离维度的意义,其使用运货车策略的频次更多。此外,一般推理能力对解决冲突类天平任务的正确次数有正向预测作用。     

True or false: do 5-year-olds understand belief?

In 3 studies (N = 188) we tested the hypothesis that children use a perceptual access approach to reason about mental states before they understand beliefs. The perceptual access hypothesis predicts a U-shaped developmental pattern of performance in true belief tasks, in which 3-year-olds who reason about reality should succeed, 4- to 5-year-olds who use perceptual access reasoning should fail, and older children who use belief reasoning should succeed. The results of Study 1 revealed the predicted pattern in 2 different true belief tasks. The results of Study 2 disconfirmed several alternate explanations based on possible pragmatic and inhibitory demands of the true belief tasks. In Study 3, we compared 2 methods of classifying individuals according to which 1 of the 3 reasoning strategies (reality reasoning, perceptual access reasoning, belief reasoning) they used. The 2 methods gave converging results. Both methods indicated that the majority of children used the same approach across tasks and that it was not until after 6 years of age that most children reasoned about beliefs. We conclude that because most prior studies have failed to detect young children's use of perceptual access reasoning, they have overestimated their understanding of false beliefs. We outline several theoretical implications that follow from the perceptual access hypothesis.     

Children's understanding of posterior probability

Do young children have a basic intuition of posterior probability? Do they update their decisions and judgments in the light of new evidence? We hypothesized that they can do so extensionally, by considering and counting the various ways in which an event may or may not occur. The results reported in this paper showed that from the age of five, children's decisions under uncertainty (Study 1) and judgments about random outcomes (Study 2) are correctly affected by posterior information. From the same age, children correctly revise their decisions in situations in which they face a single, uncertain event, produced by an intentional agent (Study 3). The finding that young children have some understanding of posterior probability supports the theory of naive extensional reasoning, and contravenes some pessimistic views of probabilistic reasoning, in particular the evolutionary claim that the human mind cannot deal with single-case probability.     

Reasoning with premises that are not empirically true: evidence for the role of inhibition and retrieval

Two studies examined conditional reasoning with false premises. In Study 1, 12- and 16-year-old adolescents made "if-then" inferences after producing an alternative antecedent for the major premise. Older participants made more errors on the simple modus ponens inference than did younger ones. Reasoning with a false premise reduced this effect. Study 2 examined the relation between performance on a negative priming task (S. P. Tipper, 1985) and reasoning with contrary-to-fact premises in 9- and 11-year-olds. Overall, there was a correlation between the relative effect of negative priming on reaction times and the number of knowledge-based responses to the reasoning problems. The results of these studies are consistent with the idea that reasoning with premises that are not true requires an interaction between information retrieval and inhibition.     

小学儿童对日常生活事件时间关系推理能力的初探

探查小学儿童对含有“在什么之前”“同时”日常生活事件时间关系的推理发展过程及其影响因素。被试为7岁、9岁、11岁3个年龄组共54名小学儿童,每个年龄组18人。4种问题模式分别为带有传递关系的单模型问题、带有无关前提的单模型问题、含两个前提的单模型问题、有肯定答案的多模型问题。每种问题模式含3种具体探察任务。主要研究结果表明：在本实验条件下,（1）儿童对事件时间顺序关系的推理从7岁到9岁有快速发展的趋势;（2）单模型和多模型任务无显著差异,模型数量似乎不是影响儿童推理成绩的关键因素;（3）儿童能够主动采用5种策略解决问题。逆向关系传递策略是问题解决的有效策略。     

Concept Discovery in a Scientific Domain

The scientific reasoning strategies used to discover a new concept in a scientific domain were investigated in two studies. An innovative task in which subjects discover new concepts in molecular biology was used. This task was based upon one set of experiments that Jacob and Monod used to discover how genes are controlled, and for which they were awarded the Nobel prize. In the two studies reported in this article, subjects were taught some basic facts and experimental techniques in molecular biology, using a simulated molecular genetics laboratory on a computer. Following their initial training, they were then asked to discover how genes are controlled by other genes. In Study 1, subjects found no evidence that was consistent with their initial hypothesis. Subjects then set one of two goals for conducting experiments and evaluating data. One goal was to search for evidence consistent with the current hypothesis (and they did not attend to the features of discrepant findings); none of the subjects who only had this goal succeeded at discovering how the genes were controlled. Other subjects in Study 1 used a different goal: Upon noticing evidence inconsistent with their current hypothesis, these subjects set a new goal of attempting to explain the cause of the discrepant findings. Using this goal, a subset of these subjects discovered the correct solution to the problem. Study 2 was conducted to test the hypothesis that subjects' goals of finding evidence consistent with their current hypothesis blocks consideration of alternate hypotheses and generation of new goals, it was predicted that if subjects could achieve their initial goal of discovering evidence consistent with their current hypothesis, they would then attend to particular features of discrepant evidence and solve the problem. To test this prediction, an additional mechanism of genetic control that was consistent with subjects' initial goal was added to the genes. Here, subjects had to discover two mechanisms of control: one mechanism consistent with their current hypothesis, and one inconsistent with their hypothesis. Twice as many subjects reached the correct solution in Study 2 than in Study 1. The findings of the two studies indicate that goals provide a powerful constraint on the cognitive processes underlying scientific reasoning and that the types of goals that are represented determine many of the reasoning errors that subjects make.     

Do reasoning limitations undermine discourse?

Why does discourse so often seem shallow, with people arguing past one another more than with one another? Might contributing causes be individual and logical rather than only dialogical? We consider here whether there exist errors in reasoning that could be particularly damaging in their effects on argumentive discourse. In particular, we examine implications for discourse of two such errors – explanation as a replacement for evidence and neglecting the likelihood of multiple causes contributing to an outcome. In Studies 1 and 2, we show these errors to be prevalent in a cross section of adults, as well as samples of community college students and young adolescents, with minimal age-related improvement. They also occur, although less frequently, among a sample of highly educated adults, and in Study 3, we examine their role in the discourse of college-educated adults. We point finally to evidence that these individual reasoning errors are potentially addressable through education.     

因果条件中儿童社会信息推理的发展

采用因果条件性逻辑推理研究的一般模式,研究了儿童社会信息因果推理发展状况。实验结果表明：(1)儿童社会信息推理能力呈年级性递增。(2)社会信息的内容会影响儿童社会信息推理的能力。(3)儿童四种逻辑形式推理能力之间的差异显著．AC、DA在年级水平上差异都十分显著,但MP和MT在年级水平上差异不显著,儿童在各个年级四种推理能力之间的差异都显著,确定型和非确定型逻辑推理能力之间的差异显著。(4)逻辑形式的难度、儿童的年龄影响儿童合理化解释的类型。     

Classifying color materials: children are less holistic than adults

Much recent research indicates that children respond to materials which are separable for adults as though those materials were integral. The present studies examined differences between 5-year-olds and adults in the processing of integral materials. In Study 1, both children and adults made a majority of similarity classifications for those materials. However, the children were found to make fewer of those integral similarity classifications and more dimensional classifications than adults for materials varying in the integral dimensions of chroma and value. In Study 2, children's similarity judgments were also indicative of greater separability of those dimensions. For both children and adults, similarity ratings given in Study 2 were predictive of classification behavior in Study 1. Age differences in similarity ratings were also predictive of age differences in classification. The overall pattern of results is consistent with the idea that children's perception is neither more nor less holistic than that of adults. Whether children or adults are found to be more holistic depends on the nature of the material presented. With integral materials, young children respond in a manner which appears less holistic than that of adults.     

The Fallacy Fallacy: From the Owl of Minerva to the Lark of Arete

The fallacy fallacy is either the misdiagnosis of fallacy or the supposition that the conclusion of a fallacy must be a falsehood. This paper explores the relevance of these and related errors of reasoning for the appraisal of arguments, especially within virtue theories of argumentation. In particular, the fallacy fallacy exemplifies the Owl of Minerva problem, whereby tools devised to understand a norm make possible new ways of violating the norm. Fallacies are such tools and so are vices. Hence a similar problem arises with argumentative vices. Fortunately, both instances of the problem have a common remedy.

     

Perception Versus Knowledge of Cause and Effect in Children: When Seeing Is Believing

Recent research has shown that even infants have perceptual sensitivity to the causal structure of the world, and it is often claimed that causal knowledge supports many of preschoolers' impressive cognitive achievements. That older children nevertheless can encounter difficulties in causal-reasoning tasks is typically attributed to lack of domain knowledge. A different explanation, however, is that causal structure may appear at more than one level, in perception, as well as in underlying knowledge. Children may make some reasoning errors because they have difficulty coordinating these levels. This article reviews relevant evidence on physical causality: Even infants in their first year perceive the causal structure of simple collision events. This perceptual skill could support rapid causal learning without prior knowledge and thus helps us understand children's precocity preschoolers already reason with the assumption that causes and effects are linked by underlying physical mechanisms. However, what may promote early development may later become a hindrance: When perception and mechanism point to different causes, children may not realize that mechanism is superordinate. Although the components of competent causal reasoning are available early in development, much experience may be required before children learn how to integrate them.     

What the stories children tell can tell about their memory: narrative skill and young children's suggestibility

The authors examined the relation between children's narrative ability, which has been identified as an important contributor to memory development, and suggestibility. Across 2 studies, a total of 112 preschool-aged children witnessed a staged event and were subsequently questioned suggestively. Results from Study 1 indicated that children's ability to provide a high-quality narrative of the event was related to resistance to suggestive questions, and narrative ability appeared to supersede age as a predictor of such resistance. In Study 2, children's general language and narrative abilities were measured in addition to their ability to produce a high-quality narrative about the target event. These results replicated Study 1's findings that children's ability to produce a high-quality narrative of a previously experienced event predicted resistance to suggestion. However, the quality of children's autobiographical memory narratives predicted shifting from denial to assent. Findings are considered in light of narrative's role in memory development and underlying mechanisms that may explain children's suggestibility.     

The relative importance of two different mathematical abilities to mathematical achievement

Background. Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. Aims. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Sample. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Method. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Results. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non‐specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. Conclusions. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills.     

提示对3～11岁儿童解决类比推理问题的影响

随机抽取360名3~11岁儿童,采用几何图形、关系图形、词语、数字、故事五种材料,考察提示对儿童类比推理的影响。结果发现:(1)提示对3~4岁和8~9岁儿童几何图形类比推理成绩有影响;提示对3~4岁和9~11岁儿童词语类比推理成绩有影响;提示对3~11岁儿童数字类比推理成绩均有影响;提示对3岁和8~11岁儿童关系图形类比推理成绩有影响;提示对3~4岁和8~11岁儿童故事类比推理成绩有影响;(2)提示使原本不会类比推理的3岁儿童能够初步进行类比推理。