“合情推理”辨析

波利亚的"合情推理"模式引进我国数学课程标准后,就成了我国数学教育研究的关键词。然而,"合情推理"的科学性尚需考证:(1)它的中文意义不明确;(2)它不满足推理模式的客观性要求,存在明显的缺陷;(3)过分强调"合情推理模式"则是过分强调归纳推理和演绎推理的区别,容易割裂它们之间的关系。     

地方师范院校数学“准教师”合情推理状况的初步调查

教师的合情推理状况直接影响学生的合情推理能力和创新能力的发展.调查发现数学"准教师"在掌握合情推理基本知识和科学灵活运用推理模式方面都有明显不足,且与大一学生的合情推理状况无显著差异.     

论中学数学合情推理的教学

合情推理又称之为似真推理。中学数学合情推理的教学有利于培养学生的创造能力和创新精神，符合素质教育的要求。归纳与类比，一般化与特殊化是合情推理的基本方法，是中学教学合情推理教学的主要内容。中学数学的合情推理教学要在相关数学知识的教学过程中随机进行。     

合情推理在高等数学学习中的作用

结合教学实践,从概念形成、定理掌握、问题解决等几个方面分析了合情推理在数学知识学习中．以及在分析问题和解决问题中的作用。认为在高等数学教学中充分利用合情推理的各种模式培养学生创新能力是非常必要的。     

Natural-Born Arguers: Teaching How to Make the Best of Our Reasoning Abilities

We summarize the argumentative theory of reasoning, which claims that the main function of reasoning is to argue. In this theory, argumentation is seen as being essentially cooperative (people have to listen to others' arguments and be ready to change their mind) but with an adversarial dimension (their goal as argument producers is to convince). Consistent with this theory, the experimental literature shows that solitary reasoning is biased and lazy, whereas reasoning in group discussion produces good results, provided some conditions are met. We formulate recommendations for improving reasoning performance, mainly, to make people argue more and better by creating felicitous conditions for group discussion. We also make some suggestions for improving solitary reasoning, in particular to maximize students' exposure to arguments challenging their positions. Teaching people about the value of argumentation is likely to improve not only immediate reasoning performance but also long-term solitary reasoning skills.     

How logical reasoning mediates the relation between lexical quality and reading comprehension

The present study aimed to examine the role of logical reasoning in the relation between lexical quality and reading comprehension in 146 fourth grade Dutch children. We assessed their standardized reading comprehension measure, along with their decoding efficiency and vocabulary as measures of lexical quality, syllogistic reasoning as measure of (verbal) logical reasoning, and nonverbal reasoning as a control measure. Syllogistic reasoning was divided into a measure tapping basic, coherence inferencing skill using logical syllogisms, and a measure tapping elaborative inferencing skill using indeterminate syllogisms. Results showed that both types of syllogisms partly mediated the relation between lexical quality and reading comprehension, but also had a unique additional effect on reading comprehension. The indirect effect of lexical quality on reading comprehension via syllogisms was driven by vocabulary knowledge. It is concluded that measures of syllogistic reasoning account for higher-order thinking processes that are needed to make inferences in reading comprehension. The role of lexical quality appears to be pivotal in explaining the variation in reading comprehension both directly and indirectly via syllogistic reasoning.     

Where the wild things are: informal experience and ecological reasoning

Category-based induction requires selective use of different relations to guide inferences; this article examines the development of inferences based on ecological relations among living things. Three hundred and forty-six 6-, 8-, and 10-year-old children from rural, suburban, and urban communities projected novel diseases or insides from one species to an ecologically or taxonomically related species; they were also surveyed about hobbies and activities. Frequency of ecological inferences increased with age and with reports of informal exploration of nature, and decreased with population density. By age 10, children preferred taxonomic inferences for insides and ecological inferences for disease, but this pattern emerged earlier among rural children. These results underscore the importance of context by demonstrating effects of both domain-relevant experience and environment on biological reasoning.     

支持语义web模糊本体的描述逻辑

为实现语义web上包含复杂模糊知识的模糊本体的表示和推理,提出了一种描述逻辑的模糊扩展———支持比较表达式的模糊描述逻辑(FCDLs).给出FCDLs语法和语义的形式化定义,并规定FCDLs知识库中的公理和断言形式.FCDLs将模糊描述逻辑(FDLs)中的模糊概念和扩展模糊描述逻辑(EFDLs)中的截概念结合在同一理论中,并将截概念扩展为比较截概念,从而支持对实际中经常用到的模糊隶属度之间比较表达式的描述,而其他的描述逻辑模糊扩展均不支持比较表达式.FCDLs具有比FDLs和EFDLs更强的表达能力,能够表示复杂的模糊知识并基于它们完成推理任务.因此FCDLs可实现语义web上包含复杂模糊知识的模糊本体的表示和推理.     

Embodied Cognition: Somatic Markers, Purposes and Emotional Orientations

We describe the “somatic marker hypothesis” proposed by Damasio (1996) to account for the ability of most people to make decisions quickly and continually in the course of their lives. We relate this hypothesis to two other theoretical constructs, emotional orientations and purposes, which we have used in our research on students' reasoning and teachers' decision making. Given that somatic markers are a part of unconscious mental activity, they cannot be observed by introspective reflection. How then can we research something we cannot see? Beginning with the hypothesis that somatic markers influence actions, we observe, particularly, the actions of student teachers, teachers and children in mathematics classrooms at points where they make decisions. This process is illustrated through examples both of teaching and learning in mathematics, and through the account (see Op't Eynde and Hannula, this issue) of ‘Frank’ reflecting on his decision-making in mathematical activity. We use the case of Frank to illustrate some differences between viewing mathematical activity from our perspective and from those of some other contributors to this special issue. The connections between emotional orientations, somatic markers and purposes are further illustrated by two examples drawn from our research into teacher development and students' reasoning processes.     

A schematic–Theoretic view of problem solving and development of algebraic thinking

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and types of schemas that students developed through examples of problems used to develop schemas, examples of students' reasoning and writing, and excerpts from student interviews. Findings from the study indicated that there is a link between the type of generalizations students construct and the schemas they are forming. By using these schemas students recognize, extend, and generalize patterns and quantitative relationships both verbally and symbolically. This revised version was published online in July 2006 with corrections to the Cover Date.     

Discourse Generation for Instructional Applications: Identifying and Exploiting Relevant Prior Explanations

To reap the benefits of natural language interaction, tutorial systems must be endowed with the properties that make human natural-language interaction so effective. One striking feature of naturally occurring interactions is that human tutors and students freely refer to the context created by prior explanations. In contrast, computer-generated utterances that do not draw on the previous discourse often seem awkward and unnatural and may even be incoherent. The explanations produced by such systems are frustrating to students because they repeat the same information over and over again. Perhaps more critical is that, by not referring to prior explanations, computer-based tutors are not pointing out similarities between problem-solving situations and therefore may be missing out on opportunities to help students form generalizations. In this article, we discuss several observations from an analysis of human-human tutorial interactions and provide examples of the ways in which tutors and students refer to previous explanations. We describe how we have used a case-based reasoning algorithm to enable a computational system to identify prior explanations that may be relevant to the explanation currently being generated. We then describe two computational systems that can exploit this knowledge about relevant prior explanations in constructing their subsequent explanations.     

Inferential reasoning and the influence of cognitive conflict

This study follows two earlier studies of school students' abilities to draw inferences when comparing two datasets presented in graphical form (Watson and Moritz, 1999; Watson, 2001). Using the same interview protocol with a new sample of 60 students, 20 from each of grades 3,6 and 9, cognitive conflict was introduced in the form of video clips of reasoning expressed by students in the earlier studies. This methodology was intended to mimic the type of argumentation that might take place in the classroom but in a controlled setting where identical arguments could be presented to different students. Interviews were videotaped and analysed in a similar fashion to the earlier studies in order to document change associated with the presentation of cognitive conflict. Change was documented with respect to the levels of observed response for two parts of the protocol and for the use of displayed variation in the graphs. Implications of the methodology for future research and teaching are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Making More Plausible What is Hard to Believe: Historical Justifications and Illustrations of Newton's Third Law

It has been claimed that conceptual change in students is more likely to occur if the alternative to present conceptions is a plausible one for the students. Many studies have shown that students today do not believe Newton's law of action and reaction and in this paper ways in which its plausibility might be enhanced are explored. In it the various justifications of the law by means of which Newton and those who came after him attempted to make it more plausible for their contemporaries are discussed.     

Inference making ability and its relation to comprehension failure in young children

Young children's reading comprehension skill is associated with their ability to draw inferences (Oakhill 1982, 1984). An experiment was conducted to investigate the direction of this relation and to explore possible sources of inferential failure. Three groups of children participated: Same-age skilled and less skilled comprehenders, and a comprehension-age match group. The pattern of performance indicated that the ability to make inferences was not a by-product of good reading comprehension, rather that good inference skills are a plausible cause of good reading comprehension ability. Failure to make inferences could not be attributed to lack of relevant general knowledge. Instead, the pattern of errors indicated that differences in reading strategy were the most likely source of these group differences.     

All Other Things Being Equal: Acquisition and Transfer of the Control of Variables Strategy

The ability to design unconfounded experiments and make valid inferences from their outcomes is an essential skill in scientific reasoning. The present study addressed an important issue in scientific reasoning and cognitive development: how children acquire a domain-general processing strategy (Control of Variables Strategy or CVS) and generalize it across various contexts. Seven- to 10-year-olds (N = 87) designed and evaluated experiments and made inferences from the experimental outcomes. When provided with explicit training within domains, combined with probe questions, children were able to learn and transfer the basic strategy for designing unconfounded experiments. Providing probes without direct instruction, however, did not improve children's ability to design unconfounded experiments and make valid inferences. Direct instruction on CVS not only improved the use of CVS, but also facilitated conceptual change in the domain because the application of CVS led to unconfounded, informative tests of domain-specific concepts. With age, children increasingly improved their ability to transfer learned strategies to remote situations. A trial-by-trial assessment of children's strategy use also allowed the examination of the source, rate, path, and breadth of strategy change.     

Epistemological resources for thought experimentation in science learning

Thought Experiments (TEs) are reasoning processes that are based on 'results' of an experiment carried out in thought. What is the validity of an experiment- that has not been actually executed- for knowledge about the physical world? What are the features that make it distinctive and how do we integrate it into learning environments to support such thought processes? This study suggests that a thought experiment draws on three epistemological resources: conceptual-logical inferences, visual imagery and bodily-motor experience. We start by stating how students' TEs are related to recent research on learning science and then proceed to describe the nature of TEs. The central part of the paper deals with cognitive theories and empirical examples of visual imagery and bodily imagery. It also deals with how these enable implicit knowledge about the world to be retrieved. Students may have, but are not aware of, such knowledge for it is hidden when learning is only based on formal representations. We show that imagination is structured, goal-oriented, based on prior experiential imagery and internally coherent. Students can, for example, mentally rotate objects at constant velocity. Students can 'zoom in and out' to inspect imaginary situations, transfer objects, predict paths of imaginary moving objects and imagine the impact of forces on mechanical systems. We show that the TEs are powerful because of these capabilities. We further claim that these are not exploited by school learning environments and offer a first step towards understanding imagery in science learning.     

Common errors of reasoning in child protection work.

OBJECTIVE: Repeated public inquiries into child abuse tragedies in Britain demonstrate the level of public concern about the services designed to protect children. These inquiries identify faults in professionals' practice but the similarities in their findings indicate that they are having insufficient impact on improving practice. This study is based on the hypothesis that the recurrent errors may be explicable as examples of the typical errors of human reasoning identified by psychological research. METHODS: The sample comprised all child abuse inquiry reports published in Britain between 1973 and 1994 (45 in total). Using a content analysis and a framework derived from psychological research on reasoning, a study was made of the reasoning of the professionals involved and the findings of the inquiries. RESULTS: It was found that professionals based assessments of risk on a narrow range of evidence. It was biased towards the information readily available to them, overlooking significant data known to other professionals. The range was also biased towards the more memorable data, that is, towards evidence that was vivid, concrete, arousing emotion and either the first or last information received. The evidence was also often faulty, due, in the main, to biased or dishonest reporting or errors in communication. A critical attitude to evidence was found to correlate with whether or not the new information supported the existing view of the family. A major problem was that professionals were slow to revise their judgements despite a mounting body of evidence against them. CONCLUSIONS: Errors in professional reasoning in child protection work are not random but predictable on the basis of research on how people intuitively simplify reasoning processes in making complex judgements. These errors can be reduced if people are aware of them and strive consciously to avoid them. Aids to reasoning need to be developed that recognize the central role of intuitive reasoning but offer methods for checking intuitive judgements more rigorously and systematically.     

《淮南子》的推类理论解析

《淮南子》所包含的逻辑思想承先启后,在推类理论上,发挥了公孙龙注重类的内涵的研究,把墨辩提出的推类之难进行了深入探索;同时把《吕氏春秋》所提的类不可必推问题作了阐发,丰富了我国古代的推类理论,推动了中国逻辑学的发展.     

法律适用中的类比推理

类比推理是法律推理的重要形式,它不仅涉及到逻辑问题,而且涉及到心理学问题。类比推理具有超越法系的穿透力,在大陆法系、英美法系以及中华法系的法律适用中都非常重要。一方面,类比推理满足了人们追求“相同案件相同处理”的法治原则的需要,是实现“实质法治”的“第二好的方法”;另一方面,由于类比推理缺乏一个足够科学的、客观的理论基础,过度地依赖于直觉,因此,也存在一定的缺陷。法律中适用类比推理的关键是寻找到相类比事物之间的相似性,相似性的问题不是一个简单的逻辑问题,而是一个“合目的性”的问题。     

无教学不足以成课程：美感认知理论的观点

美感认识理论的基本论点是：人的认知活动除了逻辑思考,还包含感官知觉和情感的作用。不同的感官知觉让人藉着不同的途径由外界获得信息,细致分辨其中的特质,让人有真切的认识。基于感官知觉所发展出来的表征形式,更让人藉以将自己的知识公开化,参与社会与文化的建构。当知觉与知识相互结合,人还能发展出直觉的能力,让我们藉着“有信息基础的猜测”,迅速掌握整体情境特质。学校课程若要改变孩子的心智能力,则应提供孩子通过多重表征形式去理解与建构意义的经验。如此具有美感体验的课程无法事先完全规划,而必须由教与学的历程经验来完成,所以,由美感认识理论来看,课程根本是在教学中形成的,无教学不足以成课程。