关于推理能力问题的几点思考

推理能力的培养是义务教育教学课程的核心目标之一，推理能力主要包括合情推理与逻辑推理2种，而推理能力的培养途径是多方面的，它不仅可以通过几何的教学来实现，在代数、统计等领域中也可以进行推理的训练。在培养学生推理能力的过程中，要注重培养学生通过观察、实验、归纳、类比等获得数学猜想的能力；寻求证据，给出证明或举出反例的能力；以及有条理地表达自己思考过程的能力和用数学语言合乎逻辑地进行讨论与质疑的能力。     

略论法律推理与逻辑推理

逻辑推理和法律推理的关系十分密切,法律推理是逻辑推理的一般方法在法律领域中广泛、综合的运用,逻辑推理是法律推理重要的理性工具之一。法律推理中的逻辑推理形式必须是有效的,有效的逻辑推理可以消解裁判中的任意性,避免谬误,帮助获得正当的裁判结论。     

Genetics Reasoning with Multiple External Representations

This paper explores a case study of a class of Year 10 students (n=24) whose learning of genetics involved activities of BioLogica, a computer program that features multiple external representations (MERs). MERs can be verbal/textual, visual-graphical, or in other formats. Researchers claim that the functions of MERs in supporting student learning are to complement information or processes, to constrain the interpretation of abstract concepts, and to construct new viable conceptions. Over decades, research has shown that genetics remains linguistically and conceptually difficult for high school students. This case study using data from multiple sources enabled students' development of genetics reasoning to be interpreted from an epistemological perspective. Pretest-posttest comparison after six weeks showed that most of the students (n=20) had improved their genetics reasoning but only for easier reasoning types. Findings indicated that the MERs in BioLogica contributed to students' development of genetics reasoning by engendering their motivation and interest but only when students were mindful in their learning. Based on triangulation of data from multiple sources, MERs in BioLogica appeared to support learning largely by constraining students' interpretation of phenomena of genetics.     

Reasoning about Representations: Effects of an Early Math Intervention

ABSTRACT

The outcomes of a longitudinal randomized number sense intervention including pre-, post- and follow-up tests are reported. The intervention was conducted in Grade 0 when children were six years old. Using Concrete-Representational-Abstract principles, a structured explicit 10-week program focusing on numbers and collective reasoning about representations was conducted by the classroom teachers. In addition to their regular mathematics teaching, a trained control group received an equally structured and explicit intervention program but without the critical mathematics component. The children in the experimental group outperformed the children in the control group on number sense growth between the pre- and the post-test. There was also a sustained effect of the intervention nine months later when children were assessed in Grade 1.     

数学的原创性推理和模仿性推理之差异比较

数学推理有两种截然不同的推理方式:原创性推理和模仿性推理.数学推理的认知成分和结构包括:阅读、分析、探索、计划、实施、验证等6个环节.原创性推理和模仿性推理的差异主要体现在阅读、分析、探索、计划这4个认知成分上,前者更注重深层理解、内在比较、再结构化、适时调整目标,后者更多采用记忆、类比、联结方式作推理动力.换句话说,原创性推理更强调思维的自主性、发散性.教师在教学中应注重学生的原创性自主思维.     

Consistent and Inconsistent Pupils' Reasoning about Intensive Quantities: The Case of Density and Pressure

In this research we investigate whether the categorisation of physical quantities into intensive and extensive, according to scientific knowledge, is perceivable and understood by pupils aged 12–15 years. For this purpose we administered written questionnaires to 300 pupils, comprising four tasks for each intensive quantity: density and pressure. The tasks investigate whether pupils realise that intensive quantities do not depend on the amount of the system they refer to and the factors affecting pupils' reasoning and their consistency when studying phenomena involving fluids at rest or in transition. The analysis of responses led us to identify three models of consistent pupils' reasoning. It was also observed that a significant percentage of the pupils provide inconsistent answers, that is, they change their reasoning across tasks and use alternatives to scientific reasoning, influenced by phenomenological features of the tasks. According to our results we propose a number of recommendations, such as the introduction of intermediate teaching/learning steps to be followed as well as suitable experiments to be used towards the acquisition of the scientific model for density and pressure.     

Reasoning across ontologically distinct levels: Students' understandings of molecular genetics

In this article we apply a novel analytical framework to explore students' difficulties in understanding molecular genetics—a domain that is particularly challenging to learn. Our analytical framework posits that reasoning in molecular genetics entails mapping across ontologically distinct levels—an information level containing the genetic information, and a physical level containing hierarchically organized biophysical entities such as proteins, cells, tissues, etc. This mapping requires an understanding of what the genetic information specifies, and how the physical entities in the system mediate the effects of this information. We therefore examined, through interview and written assessments, 10th grade students' understandings of molecular genetics phenomena to uncover the conceptual obstacles involved in reasoning across these ontologically distinct levels. We found that students' described the genetic instructions as containing information about both the structure and function of biological entities across multiple organization levels; a view that is far less constrained than the scientific understandings of the genetic information. In addition, students were often unaware of the different functions of proteins, their relationship to genes, and the role proteins have in mediating the effects of the genetic information. Students' ideas about genes and proteins hindered their ability to reason across the ontologically distinct levels of genetic phenomena, and to provide causal mechanistic explanations of how the genetic information brings about effects of a physical nature. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 44: 938–959, 2007     

不同类型推理偏差和困难研究综述

心理学对推理困难的研究主要体现在演绎推理、归纳推理和类比推理等方面。不同类型的推理困难研究有自己的特点,但都有深厚的逻辑学渊源。国内学者对推理困难的研究比较零散,主要针对引起困难的原因进行探讨。文章从研究内容和研究方法等方面分析了推理困难研究的不足,对研究的发展趋势进行了预测。     

缺省模态逻辑

本文在Reiter 1980年提出的缺省逻辑的基础上,将缺省条件视为获取知识的背景知识与所得到的知识同等地加以考虑,提出了一种缺省模态逻辑。它是一种非单调逻辑,并且具有在Reiter的系统中所不能保证的两个重要性质:扩充的存在性和非单调性,然后通过知识从其背景中分离出来的方法,给出了一个缺省理论扩充的概念,它是Reiter的扩充概念的一种推广。     

浅谈数学概念教学中学生创新思维的培养

数学概念是数学教学中培养学生创新思维的重要环节 ,文章从概念的引入、形成、表达、巩固和实际运用等五方面浅谈在概念教学中优化学生的创新心理 ,培养学生创新思维和能力的具体运作。     

儿童对人的行为进行归纳推理的多样性效应

儿童在对人的行为进行归纳推理时是否遵循多样性原则,是否受到了其他认知因素的影响？本研究采用归纳推理多样性效应的范式,分析了4-5岁、6-7岁、8岁、9岁儿童和成人在对人的行为进行推理时表现出多样性效应的发展趋势。结果表明,6-7岁、8岁、9岁和成人表现出了多样性效应,并且9岁儿童运用多样性信息的能力已达到成人水平。但6-7岁和8岁儿童的多样性表现与成人仍有显著差别。从发展趋势上,对年龄、属性特征外显性和人格特质理解等因素的影响进行了初步探讨。     

儿童归纳推理的多样性效应及其争论

儿童在归纳推理中是否遵循多样性原则,表现出多样性效应,这个问题一直存在争论。在Lopez等、Gutheil等和李富洪等的研究中,小于9岁儿童的归纳推理不遵循多样性原则。Heit等的研究中,5岁儿童却表现出了一定的多样性效应。而Lo等更是基于贝叶斯模型,提出了用前提概率与论断力度的关系(即ppp)来衡量儿童运用多样性信息的能力。事实上,儿童归纳推理多样性效应的争论是由推理范畴的不同所引起,一种是涉及生物概念范畴,另一种是涉及人格特质概念范畴。在人格特质概念范畴中,可以运用心理理论、人格特质与行为之间稳定的关系,以及共变原则的归因促进儿童对前提多样性信息的运用。     

直觉理性:创新决策的思维路径

本文主要探讨西方著名管理学家、诺贝尔奖获得者赫伯特.A.西蒙所提出的“直觉理性”作为创新决策的思维路径及其在创新决策的问题发现、目标确立、方案抉择、实施反馈等环节中的具体作用,分析了其形成过程、性质特点。明确指出:西蒙所提出的直觉理性作为一种非理性的直觉思维模式,是以认知、经验为基础,通过洞察、顿悟、创造性思考来刻画认知世界,从而为人们创造决策的形成和实施提供重要的工具。     

Affordances of ICT in science learning: implications for an integrated pedagogy

This paper presents an analysis of how affordances of ICT‐rich environments identified from a recent review of the research literature can support students in learning science in schools within a proposed framework for pedagogical practice in science education. Furthermore other pedagogical and curriculum innovations in science education (promoting cognitive change, formative assessment and lifelong learning) are examined to see how they may be supported and enhanced by affordances of ICT‐rich environments. The affordances that I have identified support learning through four main effects: promoting cognitive acceleration; enabling a wider range of experience so that students can relate science to their own and other real‐world experiences; increasing students' self‐management; and facilitating data collection and presentation. ICT‐rich environments already provide a range of affordances that have been shown to enable learning of science but integrating these affordances with other pedagogical innovations provides even greater potential for enhancement of students' learning.     

培养学生推理能力的意义与途径

推理能力是现代公民必须具备的基本素质之一.培养学生推理能力,有助于实施创新教育和培养创新人才.教师应把推理能力的培养有机地融合到数学教学的过程中,在解题教学中把培养学生的推理能力落到实处.培养学生的推理能力必须充分考虑学生的身心特点和认知水平,并注意层次性.     

中国青少年在与权威、群体关系中权利之推理

中国青少年对自身权利和自由具有明确认识，相信在事关自己生活的重要领域具有自主性和决定权，这与对西方文化中青少年所做的研究结果是近似的。同西方青少年一样，中国青少年也存在类似的发展模式，即随着年龄的增长，儿童的自主性变得越来越重要。据此，应超越普遍的文化倾向，更细致地考察不同文化中青少年权利推理所存在的复杂而细微的区别。     

Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and communicating in mathematics classrooms.     

数学理智与培养策略

数学理智水平是影响初中学生数学学习成绩的一个重要因素。指出了数学理智的基本内涵、心理表征和教学价值,创设探究情境、重视反思教学、正确归因是培养初中学生数学理智的有效策略。