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数学问题解决中的模式识别的研究视角,可以分为基于数学解题认知过程与解题策略角度、基于"归类"的视角、基于数学问题解决中模式识别与其他因素的关系的视角等,具体研究领域涉及几何解题中的视觉模式识别、几何问题解决中的模式识别、解代数应用题的认知模式、数学建模中的模式识别等.由于在知觉领域与问题解决领域"模式识别"的表述存在一定的混乱性,将基于数学问题解决的模式识别界定为:当主体接触到数学问题后,与自己认知结构中的某数学问题图式相匹配的思维与认知过程.并进一步通过其与"归类"的区别与联系、与"化归"的区别与联系使"基于数学问题解决的模式识别"的概念得以澄清.在范围上,把问题解决中的模式识别界定为一种思维过程的阶段或者思维策略,认为它是解题的重要组成部分,但并不是解题的全部.对于未来的展望,期望系统的理论研究、期望对学生问题解决中模式识别的认知过程与机理的实质性的研究以及对学生问题解决中模式识别的教学实验研究. 相似文献
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数学问题解决是儿童早期数学教育的基本目标。从数学问题解决的生态观来看,儿童早期数学问题解决具有显著的文化特征,其数学问题解决的过程是认知加工与情感态度交互作用的过程,也是一个知识提取与知识建构的共生过程,同时还是一个开放式的循环渐进过程。 相似文献
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Two important aspects of transfer in mathematics learning are the application of mathematical knowledge to problem solving and the acquisition of more advanced concepts, both in mathematics and in other domains. This paper discusses general assumptions and themes of current cognitive research on mathematics learning, focusing on issues of the understanding thought to facilitate transfer of mathematical knowledge. Two studies illustrating these themes are presented, one concerning students' understanding of numerical relationships involved in basic addition and subtraction combinations, the other dealing with students' understanding of algebraic expressions and transformations. Implications of these cognitive perspectives for instruction are discussed. 相似文献
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A Comparison of Verbal and Written Descriptions of Students' Problem Solving Processes 总被引：1，自引：0，他引：1
David K. Pugalee 《Educational Studies in Mathematics》2004,55(1-3):27-47
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Karen L. Anderson M. Beth Casey William L. Thompson Marie S. Burrage Elizabeth Pezaris Stephen M. Kosslyn 《Mind, Brain, and Education》2008,2(4):188-197
ABSTRACT— This study investigated the relationship between 3 ability‐based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems provided clues compatible with their cognitive style. Students were identified as having a particular cognitive style when they scored equal to or above the median on the measure assessing this ability. A geometry test was developed in which each problem could be solved on the basis of verbal reasoning clues (matching verbal deductive cognitive style), mental rotation clues (matching spatial imagery cognitive style), or shape memory clues (matching object imagery cognitive style). Straightforward cognitive style–clue‐compatibility relationships were not supported. Instead, for the geometry problems with either mental rotation or shape memory clues, students with a combination of both verbal and spatial cognitive styles tended to do the best. For the problems with verbal reasoning clues, students with either a verbal or a spatial cognitive style did well, with each cognitive style contributing separately to success. Thus, both spatial imagery and verbal deductive cognitive styles were important for solving geometry problems, whereas object imagery was not. For girls, a spatial imagery cognitive style was advantageous for geometry problem solving, regardless of type of clues provided. 相似文献
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It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats, the cognitive demand of a problem changes. The main objective of this study is to investigate the degree to which cognitive variables, such as developmental level, mental capacity, and disembedding ability explain student performance on problems which: (1) could be addressed by algorithms or (2) require conceptual understanding. All conceptual problems used in this study were based on a figurative format. The results obtained show that in all four problems requiring algorithmic strategies, developmental level of the students is the best predictor of success. This could be attributed to the fact that these are basically computational problems, requiring mathematical transformations. Although all three problems requiring conceptual understanding had an important aspect in common (the figurative format), in all three the best predictor of success is a different cognitive variable. It was concluded that: (1) the ability to solve computational problems (based on algorithms) is not the major factor in predicting success in solving problems that require conceptual understanding; (2) solving problems based on algorithmic strategies requires formal operational reasoning to a certain degree; and (3) student difficulty in solving problems that require conceptual understanding could be attributed to different cognitive variables. 相似文献
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Cognitive correlates of math skills in third-grade students 总被引：1，自引：1，他引：0
Math achievement is not a unidimensional construct but includes different skills that require different cognitive abilities. The focus of this study was to examine associations between a number of cognitive abilities and three domains of math skills (knowing, applying and problem solving) simultaneously in a multivariate framework. Participants were 723 third-grade children (mean age?=?9.07) from 28 elementary schools. Confirmatory factor analyses with binary indicators showed that a four-factor model of math skills (Knowing-Recalling, Knowing-Computing, Applying and Problem Solving) and a nine-factor model of cognitive abilities (Nonverbal and Verbal Reasoning, Verbal Concepts, Planning, Visuo-Spatial Working Memory (WM), two types of Verbal WM, Phonological Awareness and Phonological WM) fit the data well. Results from structural equation modelling showed that verbal reasoning and verbal concepts were most consistently associated with math knowing and problem solving domains. Verbal concepts contributed also to the math applying domain. In addition, simultaneous processing of verbal WM predicted problem solving skills in math. The results can be used in supporting the learning process of students with difficulties in math. 相似文献
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A review of cognitive teaching models 总被引：3，自引：0，他引：3
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马晓丹 《天津市教科院学报》2021,(1):75-82
在过去的70年里,问题解决一直是我国数学教育领域的研究热点,其成果不仅影响着学生高层次思维的发展,还促进了积极的学习态度。基于问题解决的数学教育研究历程可分为三个阶段:初兴阶段、发展阶段和深化阶段。问题解决在不同阶段的名称反映了不同时期的价值追求。认知结构研究的抽象化、过程模型研究的多元化、策略研究的高度概括以及元认知研究的外显是数学问题解决研究的趋势。展望未来,关注同一情境中的不同结构、同一结构在不同情境间的迁移,为知识、技能向问题解决能力的转化匹配学习条件,加强数学问题解决的表现性评价研究是今后的研究方向。 相似文献
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儿童数学认知策略研究新进展 总被引：10，自引：0，他引：10
认知策略是指向认知目标的一种心理操作,主体通过使用策略,可以达到解决问题的目的,关于儿童数学认知策略的研究是探讨个体整个认知策略发展的重要途径之一。儿童数学认知策略的特性主要表现为多样性和差异性、竞争性和适应性、突变性和渐进性。儿童数学认知策略的发展主要受教育环境、工作记忆、数学焦虑的影响。微观发生学的研究方法为儿童数学认知策略的研究提供了一个新的视角。目前儿童数学认知策略研究的新趋势主要集中在有意识和无意识之间的关系、影响儿童数学认知策略发展的内在因素和外在因素之间的关系、进一步扩大儿童数学认知策略的研究范围等方面。 相似文献
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学习者的认知结构对数学解题起着及其重要的作用,合理、完善、优良的认知结构能促进更有效地数学解题。主要探讨在数学解题的认知活动中,认知结构如何影响数学解题以及认知结构的一些特点,并针对如何培养良好的认知结构提出相应的对策。 相似文献
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Foong Pui Yee 《Asia Pacific Journal of Education》1993,13(1):61-69
The taxonomy described in this paper was developed to investigate the process of mathematical problem solving in terms of definable behaviours. It was also used as an instrument to classify and encode behaviours in their sequence of observed occurrence during the process of mathematical problem solving. It is a behavioural analysis framework formulated to examine the “thinking-aloud” protocols of individuals for comprehensive information about the problem solving process itself, the individual differences in the behaviours of subjects and the strategies applied by each in dealing with non-routine mathematical problems. 相似文献
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Greater understanding of the clinical judgment and problem-solving processes used by counselors and psychologists could add significantly to a working knowledge of how competent practitioners function. This investigation used a standardized treatment planning simulation and a process tracing strategy to qualitatively examine how 15 mental health clinicians solved a typical client management problem. Purposes of the study included (a) demonstration of an empirical methodology for conducting research into clinical problem solving; (b) preliminary observation about the relationship between cognitive processes of inquiry and subsequent treatment planning; and (c) identification of hypotheses about critical factors involved in mental health problem solving that warrant further research. This report describes how those objectives were met and reviews their implications for training and assessment of mental health professionals. 相似文献
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《学习科学杂志》2013,22(2):215-234
In this article, I present a framework for the study of children's learning in cultural practices and educational activities. The framework consists of three analytic components, each of which is grounded in a constructivist treatment of cognitive development: (a) a model for the analysis of emergent cognitive goals in practices, (b) a model for the analysis of cognitive developments linked to emergent goals, and (c) a model for the analysis of the interplay between cognitive developments linked to one practice or activity to accomplish emergent goals in another. The article describes the early history of the framework and its current application to the design and analysis of a classroom practice in the United States involving arithmetical problem solving in third and fourth grade inner-city classrooms. I close with a discussion of the framework with reference to Schoenfeld's (1992) standards for methodological innovations. 相似文献
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Hélia Jacinto Susana Carreira 《International Journal of Science and Mathematics Education》2017,15(6):1115-1136
This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency. 相似文献
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本文通过分析英国剑桥评价提出的问题解答过程模型,探讨引入认知加工模型对考试设计的作用。笔者认为,运用认知加工模型有利于提高试题的质量,控制和调整试题的难度,加强考试的诊断功能,确保考试的效度。在考试设计中强化认知加工模型的理念,将成为教育考试设计的有效框架之一。 相似文献
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伏干 《天津师范大学学报(基础教育版)》2014,(1):44-48
国内外的相关研究表明,眼动研究可以通过对数学问题解决过程中的眼动轨迹进行记录以及对注视时间、注视次数等眼动指标的分析,进而了解数学问题解决过程中,大脑的内部加工机制。数学学科能力主要体现为数学问题的解决能力,通过数学学科教育中的眼动研究文献分析发现,眼动研究有助于探寻数学问题解决过程中注意分配及加工策略选择过程。在数学学科教育中针对这些认知加工的特点进行策略教学旨在:培养高效的注意能力、提取关键的表征信息、激发多知识体系的想象力,更好地提高学科教育的有效性。 相似文献