剖析初中数学解(证)题中的几类逻辑错误

数学思维能力的核心是逻辑思维能力,学生在解题中存在的概念不明确、判断不恰当,推理不严谨等问题,主要原因是不能正确运用逻辑规律。因此,本文针对初中数学解题中较常见的、典型的逻辑错误进行剖析,以期引起教学中的注意。     

数学常见逻辑错误剖析

对于学生数学学习和解题中常见的一些逻辑错误，诸如概念不清，命题变换错误，违反证明规则，推理方法错误等，列举实例进行剖析，揭示了错误的实质和原因，以帮助学生避免和纠正这类逻辑错误的发生，不断提高逻辑思维能力。     

充要条件与思维严谨性的养成

充分条件、必要条件与充要条件是重要的逻辑概念,反映的是命题中条件与结论之间的逻辑关系,其思想贯穿于整个数学内容之中.准确地把握这几个概念并在解题时正确地运用,对于培养学生的逻辑思维能力、养成严谨的思维品质有着不可替代的作用.然而许多学生由于没能很好地理解、准确地把握这几个概念,以至于在解题时屡屡出现错误而全然不知.本文撷取几例作一剖析.一、常见的错误1.解题变形时用必要不充分条件代替充要     

高中物理解题中常见的逻辑谬误剖析

逻辑谬误是指削弱论证的缺陷,即破坏论证的错误.高中物理解题中可能出现的逻辑谬误大致有:轻率归纳、歪曲原意、偷换概念、推不出、假设非事实、不合理预设、类比不当等.本文对高中解题中几种常见的逻辑谬误的现象、成因和对策进行分析.一、物理解题中常见的逻辑谬误1.歪曲原意歪曲题意在物理解题中极为常见,存在此类谬误的解题过程往往看似推理严密,因而使得解题者本人亦难以觉察,有时甚至可以迷惑他人.     

浅析“论据不确切”的各类“误解”

在数学学习中,学生解题或证题易犯这样那样的错误,其中“论据不确切”也是常见的错误之一。它包括忽略已知条件、逻辑混乱、概念不清、变形不合理等错误。下面通过举例对各种错误类型进行分析:     

高考数学解题错误的成因分析与应对策略

在数学高考中，绝大多数考生都存在着不同程度的解题错误（或失误）．这些错误除考生的心理因素外，常见的主要错误及原因还有以下5种：（1）审题不严谨导致解题错误；（2）运算能力欠缺或变形方法不当导致解题错误；（3）数学基础知识掌握的缺漏导致解题错误；（4）数学方法使用不当导致解题错误；（5）思维过程不严谨导致解题错误．     

数学证题中易犯的逻辑错误与剖析

在数学课堂教学过程中,培养学生遵守正确的思维规律,掌握好推理和证明方法,是使学生学好数学基础知识、提高基本能力的有效途径.而数学的推理、证明必须遵循形式逻辑的基本规律,形式逻辑的基本规律有同一律、矛盾律、排中律,充足理由律.如果学生在解题过程中违背了这些基本规律,就会产生不同的逻辑错误.下面,我们针对学生在解题中常犯的逻辑错误进行分析,引起大家在教学中的重视.这些逻辑错误主要表现在:     

高中数学解题逻辑性错误分析

解题是实现数学教学目的的一种手段，也是数学教学活动的重要形式．学生的认知结构包括知识结构和认识结构，当学生的认知结构不能同化他所接触的题目时，就发生解题错误，数学解题的错误其终极表现必然在数学知识上．学生知识结构和认识结构不完善是数学解题错误的两个主要原因．数学逻辑性错误是认知结构不完善的常见错误之一．     

一道2011年高考立体几何题的错解分析

高考中,大多数考生都存在着不同程度的解题错误（或失误）,常见的主要错误原因除考生的心理因素外,还有以下几种：受到思维定势的影响;认知发生负迁移;数学概念模糊;解题策略使用不当.以一道立体几何题为例,重点分析产生错误的原因,认识错误的成因有助于在高考中减少错误的产生.     

初中数学解题中常见错误成因及应对策略

在初中数学学习中，知识点越来越复杂，学生解题也经常出错.文章主要对初中学生数学解题中常见错误成因进行深度分析，并提出对应的教学策略，旨在帮助初中学生提高数学解题效率，提升数学学习综合水平.     

A coding scheme for analysing problem-solving processes of first-year engineering students

This study describes the development and structure of a coding scheme for analysing solutions to well-structured problems in terms of cognitive processes and problem-solving deficiencies for first-year engineering students. A task analysis approach was used to assess students’ problem solutions using the hierarchical structure from a theoretical framework from mathematics research. The coding scheme comprises 54 codes within the categories of knowledge access, knowledge generation, self-management, conceptual errors, mechanical errors, management errors, approach strategies and solution accuracy, and was demonstrated to be both dependable and credible for analysing problems typical of topics in first-year engineering courses. The problem-solving processes were evaluated in terms of time, process elements, errors committed and self-corrected errors. Therefore, problem-solving performance can be analysed in terms of both accuracy and efficiency of processing, pinpointing areas meriting further study from a cognitive perspective, and for documenting processes for research purposes.     

一道中考题的探究与思考

通过对2009年福州市中考一道数学试题的探析,分析学生答卷以及学习中存在的问题,探讨培养学生解题能力与总复习备考的建议.     

A Meta-Analysis of Single-Case Research on Mathematics Word Problem-Solving Interventions for English Learners with Learning Disabilities and Mathematics Difficulties

This single-case meta-analysis is the first to provide a quantitative synthesis of the published literature on mathematics word problem-solving intervention studies for English learners with learning disabilities and mathematics difficulties. A total of ten single-subject studies were included for analysis. The current study investigated the magnitude of the effect of mathematics interventions targeting the improvement of students’ mathematics word problem-solving performance, and analyzed variables that moderated this effect. Results indicate a moderate overall effect size of 0.81 (95% CI [0.71, 0.90]) on word problem-solving performance for English learners with learning disabilities and mathematics difficulties. Moderator variables such as the implementer of the interventions, instructional focus, and word problem-solving content significantly moderated the mathematics intervention effects.     

小学数学教学中培养学生应用能力探析

小学数学教学在小学课程的编排体系当中占据了文化课的半壁江山,是教学中的重中之重,因此上小学数学教学当中,培养学生的数学应用能力是一大教学难点。众所周知,小学生因为年龄小,数学思维能力有限,这就需要教师全力以赴培养学生的数学应用能力,全面提高学生的数学素养。首先要增强学生丰富的基础知识,有了丰富的数学知识,才能在生活当中加以应用,提高自身的数学思维逻辑能力,掌握最基本的解决问题的方法技巧,为今后的学习打下扎实的基础。     

论中小学数学课程中的情境及其作用

作为一种数学学习资源,情境在数学教学中发挥着多种作用:激发兴趣,促进学生参与数学学习;揭示知识的产生背景,促进学生对数学的理解;启迪思维,引导学生探寻解决问题的策略;提供运用数学的机会,培养学生解决问题的能力;等等。深刻理解情境多方面的作用,有助于促进学生有意义的数学学习。     

Meeting the mathematical demands of the safety-critical workplace: medication dosage calculation problem-solving for nursing

This article addresses a key issue for mathematics educators preparing students for work: How should teaching, learning and assessment be designed to meet the mathematical demands of the workplace, especially when those demands are safety-critical? We explore this question through a discussion of our interdisciplinary research on numeracy for nursing, focusing in particular on the characterization and authentic assessment of competence in medication dosage calculation problem-solving, where errors can and do cause patient morbidity and mortality.     

数学解题中隐含条件的挖掘与转化

在数学解题过程中,很多同学思维方式呆板直接,考虑问题公式化、模式化,不能抓住题目条件中的隐含条件,从而使解法得以简化。从五个方面,以例题形式给出不同的解题方法,意在拓宽解题思路,挖掘题目中的内涵,将复杂问题转化为简单问题,使大家在数学学习中多角度、深层次地分析题目的要求,领会题目考察的目的,从而得到意想不到的收获。     

Using video-based anchored instruction to enhance learning: Taiwan's experience

The purpose of this study is to investigate the effects of computer-assisted videodisc-based anchored instruction on attitudes toward mathematics and instruction as well as problem-solving skills among Taiwanese elementary students. Results from a t-test indicate a significant main effect on student attitudes toward mathematics. Results from a two-way Repeated Measures ANOVA show that students' problem-solving skills improve significantly with anchored instruction. Results also indicate that all the students benefit from the effects of anchored instruction on their problem-solving performance regardless of their mathematics and science abilities. The findings suggest that video-based anchored instruction provide a more motivating environment that enhanced students' problem-solving skills. This study is significant because it establishes an example of video-based anchored instruction for Taiwanese students and also provides empirical evidence of its effects on affective and cognitive responses among fifth graders in learning mathematics. This study is helpful to educators who want to help students learn to think and learn throughout technology.     

What factors support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience?

There is an acknowledged gap between the theory presented in university preparation programmes and the reality of classroom practice that has resulted in many secondary mathematics pre-service teachers failing to implement university-endorsed teaching strategies. Using responses to a questionnaire and interviews, this qualitative study examined the factors that support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience. The results showed that even though the majority of pre-service teachers reported having beliefs compatible with using problem-solving tasks, the secondary students’ ability, preparation time, and the cooperating teacher were key factors that inhibited pre-service teachers’ implementation of problem-solving tasks. It is recommended that pre-service teachers regularly visit classrooms to observe the evolving implementation of problem-solving approaches. Furthermore, cooperating teachers should be required to attend professional development before the professional experience so they understand the goals of the university preparation programme and have the requisite skills and knowledge to support the implementation of problem-solving tasks in learning mathematics.     

浅谈初中数学解题教学中学生思维品质的培养

在初中数学解题教学中,怎样培养学生的思维品质直接影响着教学的成败。笔者认为,在初中数学解题教学中,除了让学生熟练解题的一般步骤,学会解题的一些通法与利用认知理论做解题后反思外,还应让学生不断感受数学的思维过程,学到思维方法,培养思维品质,从而学会独立探索,有所发现,有所创新,以便更好地掌握和应用知识。思维品质是衡量数学思维质量的指标,它包括思维的广阔性、敏捷性、深刻性、批判性等。