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As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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Blatto-Vallee G Kelly RR Gaustad MG Porter J Fonzi J 《Journal of deaf studies and deaf education》2007,12(4):432-448
This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers. 相似文献
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Dirk De Bock Wim Van Dooren Dirk Janssens Lieven Verschaffel 《Educational Studies in Mathematics》2002,50(3):311-334
Several recent ascertaining studies revealed a deep-rooted and almost irresistible tendency among 12–16-year old students
to improperly apply the linear or proportional model in word problems involving lengths, areas and volumes of similar plane
figures and solids. While these previous studies showed to what extent students' improper use of linear reasoning is affected
by different characteristics of the task, it remained largely unclear what aspects of their knowledge base are responsible
for the occurrence and strength of this phenomenon and how these aspects relate to other more general misconceptions and buggy
rules identified in the literature. This paper reports an in-depth investigation by means of individual semi-standardised
interviews aimed at analysing the thinking process underlying students' improper linear reasoning and how this process is
affected by their mathematical conceptions, beliefs and habits. During these interviews,students' solution processes were
revealed through a number of well-specified questions by the interviewer with respect to one single non-linear application
problem, as well as through their reactions to subsequent kinds of cognitive conflict. The interviews provided a lot of information
about the actual process of problem solving from students falling into the ‘linearity trap’ and the mechanism behind it. Although
some students seem to really ‘believe’ that quantities are always linked proportionally, their improper use of linearity often
results from superficial and intuitive reasoning, influenced by specific mathematical conceptions, habits and beliefs leading
to a deficient modelling process.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
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Marilyn P. Carlson 《Educational Studies in Mathematics》1999,40(3):237-258
This study investigated the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Their problem-solving behavior was observed while completing complex mathematical tasks, and their beliefs were assessed by administering a written survey. These graduate students report that a mentor, most frequently a high school teacher, facilitated the development of their problem solving abilities and continued mathematical study. The mentors were described as individuals who provided challenging problems, encouragement, and assistance in learning how to approach complex problems. When confronted with an unfamiliar task, these graduate students exhibited exceptional persistence and high confidence. Their initial problem solving attempts were frequently to classify the problem as one of a familiar type, and they were not always effective in accessing recently taught information or monitoring their solution attempts, but were careful to offer only solutions that had a logical foundation. These results provide numerous insights into the complexities of using and extending one's mathematical knowledge and suggest that non-cognitive factors play a prominent role in a student's mathematical success.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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刘义良 《实验室研究与探索》2011,30(2)
学生课堂问题行为不但影响到课堂教学质量,而且也影响到学生健康人格和心理的形成。如何加强学生实验教学课堂行为管理,提高学生自控能力。我们通过对学生计算机文化基础的现状、上机环境、课堂问题行为的分析,针对学生特点、爱好、专业层次进行课堂行为管理方面的研究。通过软硬件相结合的方式,采用技术手段进行科学设置来实施有效管理,促使学生有计划,按步骤的完成计算机上机任务,从而保证了计算机实验教学效果的不断巩固和提高。 相似文献
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数学认知结构是数学知识结构与学生心理结构相互作用的产物.构建数学认知结构是为了完善学生的数学知识体系,提高学生分析问题、解决问题的能力.数学教学策略主要应注重三个方面:熟悉原有的数学认知结构、设计数学问题或问题链、突出适合的数学思想方法. 相似文献
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The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition 总被引：1，自引：0，他引：1
The purpose of the present study is to examine the effects of IMPROVE, a meta-cognitive instructional method, on students'
mathematical knowledge, mathematical reasoning and meta-cognition. Participants were 81 students who studied a pre-college
course in mathematical. Students were randomly assigned into one of two groups and groups were randomly assigned into one
of two conditions: IMPROVE vs. traditional instruction (the control group). Both groups were exposed to the same learning
materials, solved exactly the same mathematical problems, and were taught by the same experienced teacher. The IMPROVE students
were explicitly trained to activate meta-cognitive processes during the solution of mathematical problems. The control group
was exposed to traditional instruction with no explicit exposure to meta-cognitive training. Results indicate that the IMPROVE
students significantly outperformed their counterparts on both mathematical knowledge and mathematical reasoning. In addition,
the IMPORVE students attained significantly higher scores then the control group on the three measures of meta-cognition:
(a) general knowledge of cognition; (b) regulation of general cognition; and (c) domain-specific meta-cognitive knowledge.
The theoretical and practical implications are discussed. 相似文献
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尚莲荣 《伊犁教育学院学报》2005,18(2):101-102
数学教学要密切结合学生的生活经验,从现实中寻找学习的素材,通过学生的自主探索,合作交流,经历知识的形成和应用过程,归纳总结解决问题的数学方法,并能用所学的数学知识解决现实生活中的问题,从而培养学生“应用数学”的意识和能力。 相似文献
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数学建模对学生综合素质的影响分析 总被引：2，自引：0，他引：2
本文从建模及竞赛分析数学建模在学生素质培养中所起的作用,对学生解决实际问题的能力的影响,阐述了数学建模训练是人们解决实际问题必要的训练和准备的观点,说明数学建模对学生的影响是质变的过程,参加过建模训练的学生必定是“终生难忘,终生受益”。 相似文献
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随着职业高等教育的基础化、综合化、社会化、网络化和国际化,如何发展高职学生的个性,完善他们的人格,培养他们良好的心理素质,已成为时代性的课题。通过对高职学生人际交往问题厌学心理问题进行具体的分析,意在帮助他们找到克服的办法,期盼他们能带着良好的意志品质步入社会。 相似文献
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数学表述是学生掌握数学知识与技能的一种手段,也是教师评价学生数学学习能力和水平的一个重要标准.目前,小学生问题解决中数学表述的状况是:不同年级学生采用表述类型的倾向性不同,数学语言的掌握程度是影响学生数学表述的根本原因.而小学数学表述教学方面存在的问题包括:教师对数学表述的重视程度一般,数学表述教学质量不高;学生存在数学语言理解和转换障碍,数学交流能力有待提高.认清数学表述教学的价值、理清数学表述与数学语言和数学交流的关系、构建小学数学表述教学模式,对培养小学生数学表述能力具有重要意义. 相似文献
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李美 《雁北师范学院学报》2004,20(5):62-63
在学习高等数学的过程中,往往会形成一种思维的定势,局限解题思路.本文主要通过实例说明思维 不应该定势,而要充分发挥自己灵活思考,独立解决问题的能力,开发创新思维. 相似文献
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本研究采用自编态度问卷对上海市9所高校的573名在校大学生就残疾学生接受高等融合教育的态度及其影响因素进行了调查。结果表明:在认知维度上,在校大学生对残疾学生及其接受高等教育的态度较为积极,但对高等融合教育形式相对陌生。在情感维度上,在校大学生表现出积极的接纳态度。在行为倾向上,在校大学生的社会行为倾向态度较个体行为倾向态度更为积极。被调查者的性别、专业、与残疾人的接触频率及对高等融合教育的了解程度对其态度有影响作用。调查结果表明,上海实施高等融合教育在同伴接纳这方面的条件已基本具备。 相似文献
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Developing students' ability to interpret the vast amount of quantitative data they encounter on a daily basis has become a major task for today's educators. However, very little attention has been given to students' strategies of analyzing multivariate data. This study investigated how students interpret and analyze multivariate data organized in tables and the nature of external visual displays that they tend to create and use for this purpose. Ten middle school students were asked to think aloud while solving five problems demanding an analysis of data organized in tables. The students were then interviewed. Results indicated that (1) students based their conclusions on only part of the data; (2) students did not use either efficient or sufficient visual representations; (3) students did not apply mathematical operations efficiently; and (4) students referred to or built a context to the problem. The results of the current research may assist educators to design efficient curricula while being aware of and taking into account (1) students' difficulties in employing previously learned mathematical devices to analyze data, (2) students' skills in choosing appropriate and efficient visual representations to present and interpret the data, and (3) strategies employed by students in analyzing multivariate data. 相似文献
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Philip C. Clarkson 《Educational Studies in Mathematics》1992,23(4):417-429
It is argued that bilingual students should not be categorized as a unidimensional group. Their level of competence in each language is important if academic activity is considered. As an example of this, results from the present study indicate that Papua New Guinea bilingual students competent in both their languages scored significantly higher on two different types of mathematical tests compared to collegues who had low competence in their languages. Further, there was some indication that bilingual students competent in both languages performed better than monolingual students, even though the monolingual students attended schools that had many more teaching resources. Such results were seen as support for the new Papua New Guinea govemment policy of using students' original languages in school. The use of the students' original languages may also open the way for easier access to traditional mathematical concepts in classrooms. 相似文献
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数学建模的教学探讨 总被引：1，自引：0，他引：1
李传伟 《成都教育学院学报》2007,21(3):90-91
文章针对高等职业技术院校的学生在学习数学建模课程时都比较吃力、感觉困难的问题,以具体的数学建模试题的解答作为中心,围绕问题求解及如何解的全过程,在教学实践中培养学生学习数学建模的兴趣,引导学生自己求解,重视学生能力的培养,提高教学效果.这对于我们以后数学建模教学有一定的指导意义. 相似文献