再论中小学"数学情境与提出问题"的数学学习

辩证唯物主义认识论，现代数学观和建构主义学习观指导下的“设置数学情境与提出数学问题”教学实验，旨在培养学生的数学问题意识，提高学生的提出数学问题和解决数学问题能力，增强学生的创新意识和实践能力，创设数学情境，就是呈现给学生刺激性数学信息，引起学生学习数学的兴趣，启迪思维，激起学生的好奇心，发现欲，产生认知冲突，诱发质疑猜想，唤醒强烈的问题意识，从而使其发现和提出数学问题，解决数学问题。     

The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success

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.     

关于奥数与小学生数学思维能力发展冲突的思考

近年来,小学“奥数”越来越热。小学生做奥数题是否真的有利于小学生的数学思维能力发展,这一问题成为一些教育界人士与家长关心的重要议题。文章认为,大面积的小学生“奥数”培训热,降低了小学生数学学习的兴趣,不利于提高小学生的数学能力。小学数学教学应该把提升小学生的数学素质作为基本出发点,促进小学生的数学思维能力发展。     

奥赛题与探究性课题相结合的初步构想

为辅导学生参加数学奥林匹克竞赛而产生的各种数学问题(以下简称奥赛题)是一个有待开发的资源.经过筛选和加工,其中有的可以作为“ 探究性课题”,成为数学课堂教学的学习材料.这不仅为培养广大青少年学生独立思考和创新能力,提供了更多的“ 载体”,也为数学课程的开发提供了更丰富的资源.     

Correlations Among Five Demographic Variables and the Performance of Selected Jamaican 11th-graders on Some Numerical Problems on Energy

This study was designed to assess whether the level of performance of selected Jamaican 11th-grade physics students on some numerical problems on the energy concept was satisfactory and if there were significant differences in their performance linked to their gender, socioeconomic background (SEB), school location, English language and mathematical abilities. The 331 sampled students consisted of 213 boys and 118 girls; 197 students were from a high SEB and 134 students from a low SEB; 296 students were from seven urban schools and 35 students from three rural schools; 112, 153 and 66 of the students had high, average and low English language abilities, respectively, while 144, 81 and 106 of the students had high, average and low mathematical abilities, respectively. An Energy Concept Test (ECT) consisting of six structured numerical questions was employed for data collection. The results indicated that although the students’ level of performance was regarded as fairly satisfactory, there was a lot of room for improvement. There were statistically significant differences in the students’ performance on the ECT linked to SEB, and mathematical abilities in favour of students from a high SEB, and high mathematical abilities, respectively. There was a positive, statistically significant but weak correlation between the students’ (a) mathematical abilities, and (b) English language abilities and their performance on the ECT, while there were no correlations among their gender, school location, and SEB and their performance on the ECT.     

The association between working memory and educational attainment as measured in different mathematical subtopics in the Swedish national assessment: primary education

The aim of this study was to examine the relationship between working memory capacity and mathematical performance measured by the national curriculum assessment in third-grade children (n?=?40). The national tests concerned six subareas within mathematics. One-way ANOVA, two-tailed Pearson correlation and multiple regression analyses were conducted. The results showed that working memory could be deemed as a predictor for the overall mathematical ability. However, the significance of working memory contributions varied for the different mathematical domains assessed. Working memory contributed most to basic mathematical competencies. Algorithms were not explained significantly by working memory. The contributions of different working memory resources varied as a function of the mathematical domain, but in certain respects the variance was shared across the elements and both visuo-spatial and phonological abilities seem important for mathematic performance. We suggest that individuals’ working memory capacity is important to take into consideration in learning.     

高职数学实验课教学初探

数学实验课做到理论联系实际,学以致用,能提高学生的综合素质与解决问题的能力,变"把学生教会"为"让学生自己学会",深受学生的欢迎与喜爱.     

试析影响学生数学建模数学化过程的若干因素

为适应新一轮数学课程改革中加强应用性和创新性,重视联系学生生活实际和社会实践要求,开展数学建模教学成为当今数学教育改革的热点之一。如何有效实施数学建模教学是许多数学教师感到困惑的一大难题。而研究学生数学建模过程中所面临的困难及产生原因是教师有效实施数学建模教学的前提与关键。文章拟从初中数学课堂中实施数学建模教学的一则案例出发,初步研究发现学生在数学建模的数学化过程中,学生自身的数学阅读能力、简化实际问题能力、数学语言能力和元认知能力影响着学生的数学建模活动。从而对教师在日常数学课堂中有效开展数学建模教学活动具有积极意义。     

试论数学问题教学中常用的数学思维方式

数学思维是学习数学知识过程中难得的、实用的方法,它同时又是教师在讲授教学理论过程中应当注意加以提炼并引导学生持续掌握、运用进而解决实际问题的一种能力。本文试图通过一些数学问题的分析解答,凸显数学思维及其作用,以达到引起读者关注并试图体验之目的。     

数学模型方法与数学教学

数学模型是数学创造与数学教学中经常使用的一种重要的数学方法．从方法论的角度考虑，让学生了解MM方法的涵义和作用、构建一般的模式等，对促进其数学学习、灵活地应用数学知识和思想方法解决现实问题、提高数学能力都有极其重要的意义。     

小学生数学表述状况调查及数学表述教学模式研究

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.     

依托数学建模竞赛加强大学生实践能力

培养大学生数学实践能力是大学数学教育的根本任务,数学建模竞赛恰好是一条培养高素质具备实践能力人才的重要途径。在实践中依托数学建模竞赛,采取增强实践自信心,增强实践兴趣,提升实践水平,理论与实践相结合的方法,可以达到增强大学生实践能力的目的。     

Visual spatial representation in mathematical problem solving by deaf and hearing students

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.     

《企业经济数学》教材编写设想

《企业经济数学》是职业院校经济类专业必修基础课,该教材以问题———理论———问题的教学思想,提高学生解决实际问题能力,在强调直观教学的基础上,提高学生发现问题和解决问题的能力,使感性概括通过分析、综合上升到理性认识,从而在提高学生创新思维的同时培养学生的实践能力。     

例谈探究式解题课教学

阐述了解题课的基本功能,指出了目前中学数学教育中解题课存在的问题。通过对一道平面几何题的分析,讨论了解题课环节如何创设一系列探究式问题,引导学生从问题的条件出发通过特例、试错等方法猜测一般规律并找到解决问题的方法,反思是如何想到这样的方法的?进一步对解题方法的优劣进行评判。通过方法的探究过程培养学生的元认知以及提升学生对数学方法的价值与审美判断能力。     

开放性数学应用问题解决的差异性研究

数学教育硕士、本科生解决开放性数学应用问题仍然是困难的,具有较高数学理论知识未必天然地能较好解决那些只用较低数学理论知识就能解答的数学应用问题;解决策略开放、结论开放、条件开放数学应用问题的难度逐渐显著增加,数学新课程重视数学应用教育促进了学生数学应用问题解决能力的发展;解决开放性数学应用问题的策略选择具有显著性差异,呈现数学思维的单一性、近迁移性等特征,误解信息、隐喻干扰等因素对被试的策略选择产生影响.     

数学建模竞赛与大学生创新能力提高的研究与实践

本文主要结合我院参加大学生数学建模竞赛的具体实践情况,论述了数学建模竞赛在当代大学生提高创新能力中扮演的重要作用。     

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia)

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth graders, it is shown that students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low, typically, and high achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relation persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low-achieving from typically achieving students, suggesting an ANS deficit that is specific to MLD.     

Core skills assessment to improve mathematical competency

Many engineering undergraduates begin third-level education with significant deficiencies in their core mathematical skills. Every year, in the Dublin Institute of Technology, a diagnostic test is given to incoming first-year students, consistently revealing problems in basic mathematics. It is difficult to motivate students to address these problems; instead, they struggle through their degree, carrying a serious handicap of poor core mathematical skills, as confirmed by exploratory testing of final year students. In order to improve these skills, a pilot project was set up in which a ‘module’ in core mathematics was developed. The course material was basic, but 90% or higher was required to pass. Students were allowed to repeat this module throughout the year by completing an automated examination on WebCT populated by a question bank. Subsequent to the success of this pilot with third-year mechanical engineering students, the project was extended to five different engineering programmes, across three different year-groups. Full results and analysis of this project are presented, including responses to interviews carried out with a selection of the students involved.     

Evaluating the suitability of mathematical thinking problems for senior high-school students by including mathematical sense making and global planning

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an evaluation method by including mathematical sense making and global planning. Eighteen 11th-grade high-school students, divided into three groups of three pairs, solved six mathematical thinking problems that included the finding of a numeric solution and the writing of mathematical texts and arguments. Content analysis of the students’ solution procedures provided for three kinds of hierarchically ordered mathematical sense-making categories. The results showed the expected statistically significant difference between the kinds of problems, though only mathematical sense making enabled the exclusion of the routine problem. The implications for practice are discussed.