数学开放题的评价

数学开放题的评价包括两个方面：一是数学开放题考试的评分标准；二是对数学开放题教学的评价．数学开放题考试的评分标准分3个维度、6个等级来制定．数学开放题教学的评价可以从教师教的角度和学生学的角度两个方面来进行．数学开放题评价应重视形成性评价；要注意评价方式多样化；既应尊重学生的个体差异性，又应依据一定的准则．     

数学开放题在创造能力培养中作用的实验研究

数学开放题是创新教育中一种不可多得的“好”题．本文在简单地回顾了日本、欧美的数学开放题研究概况后，从数学开放题的引进、教学设计到数学开放题的概念、特点、教育价值、开放度以及分类、编制和教学原则等方面对国内数学开放题的研究作了详细的论述，并把数学开放题的特点与创造性能力的某些特性进行了比较．     

数学开放题研究

解决方向不唯一的数学题是数学开放题．当前，教学中使用的数学开放题主要靠教师结合教学内容来编制，可以根据现行教材和资料，把传统数学题．数学命题改编成数学开放题．也可以创制一些新颖别致的数学开放题。     

研究性学习与高中数学教学

“数学研究性学习”是学生数学学习的一个有机组成部分，它更加关注学生的学习过程和学习方式．开放式教学和“研究性学习”的核心是创新教育、能力教育。开放式教学为“研究性学习”提供了一个很好的舞台．开放式教学是以开放题为我体的，所以编制开放题是进行开放式教学的关键，也是在数学学习中开展“研究性学习”的保证。     

数学开放题教学模式初探

开放式教学是相对于封闭式教学而提出的。A70年代，由日本学者首先提出“开放题教学”以来，“开放题教学”与“数学开放教学方法”在国际数学教育界已成为热门话题．二十年来。开放题作为开放式教学的切入点，在我国各地教学试验中广泛进行．     

浅谈高中数学开放性问题及教学分析

对于一名数学教师说来，数学开放题这个同并不陌生，但它却又是一个比较模糊的概念。1977年．日本数学教育学者小组以岛田茂为首的学者在《算术数学课的开放式问题——改善教学的新方案》报告文集中首先提出“数学开放题”这个名词，并提出了“数学开放教学方法”。在美国，开放题起初是在研究“问题解决”热潮中出现的，     

“数学开放题”之我见

早在2003年全国高考数学科命题组就指出：“要考查一些开放问题”．国家教委也将“数学开放题”列为重点科研项目。相对于传统的封闭题严密完整,开放题在构成问题的要素——条件、策略、结论中有一些是不明确的（分别称为条件开放题、策略开放题、结论开放题）。     

浅谈高中数学开放题教学

1 数学开放题的概念 数学开放题是相对于传统的封闭题而言的,数学中的“封闭性问题”一般是指问题的条件和结论都是完全确定的,而且是不多不少的．关于什么是数学开放题,目前还没有统一的认识,但比较一致的观点是：学生在解决开放性问题时,可以有较强的选择性,选择不同的方法,得出不同的结论．因此我们可以给出开放题的描述性定义：数学开放题是指那些答案不唯一确定,并且要求学生多角度、多方面进行探索的一类数学问题．     

论中学数学开放题的编制方法、教学策略与模式

当前，数学开放题已经成为初中数学教学改革的一个热点。数学思维活动的开放性，数学思考过程的多样性，决定了数学教学需要适应这种“开放性”和“多样性”。这是一个值得认真思考的问题。开放题是相对于明确条件和结论的封闭型习题而言的，是指能引起学生发散性思维的一种数学习题，它具有“开放性”和“多样性”的特点，在数学教学中应用数学开放题往往会起到很好的教学效果。数学开放题教学是最富有教育价值的，所以在数学教学中要重视开放题的编制、教学模式和策略探究。     

方格纸上相似的格点三角形

在数学开放题的教学中，如何结合日常的教学内容，将原本封闭的知识设计成开放的内容结构，是进行数学开放题教学的重要途径之一．在第二次“数学开放题及其教学”国际学术研讨会上，我校陈算荣老师开设的一节研讨课在这方面作了较好的探索．下面是这堂课的教学设计和评析．     

Exploring and evaluating differentiated assessment practices of in-service teachers for components of differentiation

Classroom assessment is central to effective teaching and learning, making assessment literacy a core component for teacher education. The present study explores self-reported, differentiated assessment practices of Malaysian in-service teachers. The practices were evaluated using an analytic framework that was developed based upon the existing literature on components of differentiation. Data were collected from 32 in-service teachers using open-ended survey questionnaires. Twelve of the teachers also participated in in-depth interviews. Documents provided by the teachers were also analyzed. Data from the open-ended survey were analyzed using NVivo11 to develop codes for the analytic framework. The findings offer insights into teachers’ knowledge, application, and interpretation of differentiated assessment practices. The discussion explores teachers’ explanations of their own practices and, further, recommends ways to improve knowledge and application of differentiated assessment. The implications of the findings are discussed for assessment literacy-related professional development for teachers, school management and policies to facilitate implementation of differentiated assessment.     

SOLO分类法在教学评价中的应用

SOLO分类法是一种新的评价理论,它在教学评价中的应用值得深入研究。通过研究,在阐述其理论的基础上,探讨了SOLO分类法对学习理论的贡献：把“阶段”观念迁移到具体的学习任务,使之能应用到教学实践;解释了功能方式的转换,克服了布鲁姆教育目标分类学的理论困难。教学评价中的应用：为评价学习的质量提供了一种更为有效的方法;为不同学科的教学评价构建了一个比较学习质量的共同平台;为开放性试题的评分提供了理论依据。     

Parents’ beliefs about assessment: A conceptual framework and findings from Finnish basic education

The viewpoint of parents has been scarcely studied in classroom assessment research. We address this research gap by examining parents’ beliefs about assessment in the context of Finnish basic education (grades 1–9). A socioculturally oriented framework is developed to study the beliefs of parents. With this newly formulated framework, we qualitatively analyse parents' open-ended responses based a large-scale questionnaire study (N = 622). Our findings show that in the low-stakes assessment culture of Finland, parents largely framed assessment through a pedagogical conception that reflects the learning purposes of assessment. A societal conception of assessment was also strongly present, as parents believed that assessment should produce numerical data for the purposes of measurement and comparison. As a major contribution of this study, a six-dimensional conceptual framework for analyzing parents’ beliefs about classroom assessment is formulated and tested.     

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.     

论开放性活动的教育评价文化

作为对封闭性标准化测验的反叛形式与有益补充之一,开放性活动已经走进了国际教育测量与评价工作者的视野,并在我国新课程评价改革中彰显了极强的生命力.从文化层面来剖解开放性活动与标准化测验各自蕴涵的教育评价文化理念,澄清其背后隐寓的社会文化价值观,对于新课程评价改革的深入开展至关重要。     

Two non-traditional measures of chemistry learning: Word association and idea association

Conclusion The word association test and idea association test are open-ended tests which assess students' linking ability and also their accuracy in retrieving the relevant knowledge. These tests break through the “spoon-fed” and “drilled” types of assessment. The earlier study has shown that linkage of knowledge is one of the influential factors in determining problem solving performance (Lee, 1986). A replication study has confirmed the earlier findings that these two non-traditional measures assess learning performance as do the traditional methods. Apart from providing the numerical scores, for the learning performance, the two non-traditional tests also provide teachers with useful qualitative evidence of how students proceed with their learning and with their understanding of concepts. The technical procedures of setting, carrying out and scoring the tests are reasonably easy to handle. On the basis of the evidence shown, it is suggested that the word association and idea association tests should become part of the regular testing of chemistry learning in schools.     

基于数学文化的数学课程改革

通过对数学文化的理解,分析数学课程改革发展的趋势,从教学教育观、教学内容、教学方式、评价方式等诸方面阐述教师寓数学文化于数学课程与教学的思考.     

Meaningful learning,reasoning ability,and students' understanding and problem solving of topics in genetics

The purpose of this study was to explore relationships among school students' (N = 189) meaningful learning orientation, reasoning ability and acquisition of meaningful understandings of genetics topics, and ability to solve genetics problems. This research first obtained measures of students' meaningful learning orientation (meaningful and rote) and reasoning ability (preformal and formal). Students were tested before and after laboratory-based learning cycle genetics instruction using a multiple choice assessment format and an open-ended assessment format (mental model). The assessment instruments were designed to measure students' interrelated understandings of genetics and their ability to solve and interpret problems using Punnett square diagrams. Regression analyses were conducted to examine the predictive influence of meaningful learning orientation, reasoning ability, and the interaction of these variables on students' performance on the different tests. Meaningful learning orientation best predicted students' understanding of genetics interrelationships, whereas reasoning ability best predicted their achievement in solving genetics problems. The interaction of meaningful learning orientation and reasoning ability did not significantly predict students' genetics understanding or problem solving. Meaningful learning orientation best predicted students' performance on all except one of the open-ended test questions. Examination of students' mental model explanations of meiosis, Punnett square diagrams, and relationships between meiosis and the use of Punnett square diagrams revealed unique patterns in students' understandings of these topics. This research provides information for educators on students' acquisition of meaningful understandings of genetics. © 1996 John Wiley & Sons, Inc.     

Generalizability and Validity of a Mathematics Performance Assessment

The QUASAR Cognitive Assessment Instrument (QCAI) is designed to measure program outcomes and growth in mathematics. It consists of a relatively large set of open-ended tasks that assess mathematical problem solving, reasoning, and communication at the middle-school grade levels. This study provides some evidence for the generalizability and validity of the assessment. The results from the generalizability studies indicate that the error due to raters is minimal, whereas there is considerable differential student performance across tasks. The dependability of grade level scores for absolute decision making is encouraging; when the number of students is equal to 350, the coefficients are between .80 and .97 depending on the form and grade level. As expected, there tended to be a higher relationship between the QCAI scores and both the problem solving and conceptual subtest scores from a mathematics achievement multiple-choice test than between the QCAI scores and the mathematics computation subtest scores.