概念图——概率统计教学的新途径

简述了概念图的起源、国内外发展现状,介绍了概念图的三个组成部分:结点、连线和连接语词,指出了相对于传统教学的概念图教学,在概率统计教学中的突出之处:概念图可作为教师教学的先行组织者;可作为学生复习时整理知识的工具;可作为教师检测学生学习的工具,提出了概率统计知识概念图制作的策略,并用实例说明了概念图应用于概率统计教学中的良好效果.     

基于概念图的概率统计课程评价的实证研究

概念图评价的发端可以追溯到奥苏贝尔(Ausubel),特别是诺瓦克(Novak)及其同事在20世纪六、七十年代早期的工作,他们经过12年的研究得出概念图是有效的评估工具,2004年在西班牙召开的第一届概念图国际会议上探讨的第一个主题便是:概念图在教学中的评价.     

高中数学课堂教学新方式的运用——以基本不等式的证明教学为例

1 基本情况 1.1 教学背景简介 为了进一步推进数学课堂教学改革,提高课堂教学实效,改变以往的教师：备课（找题）—上课（讲题）—辅导（讲题加大量练习）;学生：做题（已学内容的大量练习）—听课（听题）—做题（课后练习加各种考试）这样单调、机械、高耗、低效而又违背教学规律的教学方式,徐州市县正积极研讨试推行新的教学方式,我学校结合以往改革实践经验、结合学案教学优良传统、借鉴兄弟学校成功的经验提出了＂活动参与—学案导演＂教学模式,这一模式可以简要概括为＂学案导学、合作探讨、活动参与、生演师导、达标巩固＂,其特点是：＂全方位、精细化、重活动,抓实效＂.模式的几个基本环节是：学案支架预习交流——小组合作探究讨论——生演师导多维互动——全面评价达标检测——反思总结练习巩固.该模式以新课程的三维目标的实现为任务,在教师的精心设计下,以教材和学案为基础,预设与生成相结合,以小组合作、自主学习、展示讲演、教师启导为主要手段和方式,在多维互动的基础上,有效地达成教学目标.     

概念图指向单元整体建构课的教学策略--“二次函数图象与性质”赛课观摩有感

概念图是课堂教学设计的有效工具.为了让学生对一个单元所学知识网络化,建构对单元知识和方法的整体理解,引导学生深度学习,研究者以观摩省赛课“二次函数图象与性质”为例,探究基于概念图的单元整体建构课的教学策略:知识建构,让思维痕迹可视化;方法统领,让思维品质高阶化;深度探究,让思维体验个性化.     

科学设计概念图 提高数学复习效率

高三复习是高中教学中最重要的环节之一,而复习效率不高是高中数学复习过程中较为突出的现象,教师过分依赖教辅资料和题型讲授,大考小考不断,学生只顾埋头做题而不反思总结,复习不注重知识的系统性、准确性和完整性是出现这种现象的原因之一．高三数学复习中,常常遇到这样的情况：做完一道题,问“涉及到什么知识,用了什么方法,它们之间有什么联系？”大多数学生回答不知道,很多学生表示考试时常处于似曾相识却不知如何下笔的困境．切实可行的复习方法是提高教学质量的关键．相关研究表明,基于概念图的复习教学策略能有效提高数学复习效率,如何通过科学设计概念图,有效促进数学复习的教与学,值得探讨研究．     

数学教学中开展小组合作学习的探究

数学来源于生活,同时又反过来应用于生活．合作是我们生活和工作中常用的方式,而在数学教学中它也发挥着不容小觑的作用．学生之间的合作学习不仅有助于提高学生对知识的分析、综合理解能力,还有助于让学生认识个人与集体的关系,增强学生的集体意识合作学习既突出了学生的主体地位,又照顾了学生之间存在的差异,也能更好地根据学生的个性差异因材施教,满足学生的个陛心理需要,使他们认识自身价值,促进其自身情感的发展,大大提高学生的自身素质,缩小学生之间的差异．但是,在教学中如何使小组合作学习的教学模式发挥其真正的作用值得每位教师仔细思考和探讨。     

一般性与特殊性并存的几何概念教学情境设计——以苏教版课例《6.2角》的设计为例

七年级的几何概念和几何证明问题渐渐在数学学习中占有重要的部分,学习的基础来源于对几何概念的深入理解.课堂教学是学习数学概念最主要的途径,几何概念教学情境设计能带领学生构建自己的认知结构,适当的引导能帮助学生构建几何概念学习的一般方法.几何概念能借助三类数学语言（图形语言、文字语言、符号语言）完善概念图;在教学过程中,具体到每一个几何概念（如“角”）,它能够体现几何概念的一般性教学思路,也有着个体的特殊性,当一般与特殊结合融入到教学情境设计过程中去,更能有利于建立学生丰富的思维认知结构.     

构建有效的“双边对话”课堂

一、对数学有效对话的认识 ＂教学对话＂是一种以沟通与交流为基本特征的动态行为.在对话式教学中教师根据具体的教学内容,选择恰当的教学方法,创造良好的教学情境,引导学生积极思维,使学生在自己的思考中获取知识,并使思维能力得到发展.＂教学对话＂既有利于学生主体的凸现,又有利于新型师生关系的培育.师生在对话的同时也在进行着思想与思想的碰撞.     

概念图在数学课中的运用

纵观这几年中考试题的走向，已经由单纯的知识叠加型转化为知识、方法和能力综合型，尤其加强了创新能力型试题，为数学教学方法提出了新的思考，即如何在教学中加入“媒介物”，以使学生将抽象的概念和实践意义进行有机结合，而“概念图”就是这样的一种“媒介物”．     

用心讲好课本习题

教材为帮助学生理解概念的内涵、巩固知识、锻炼应用知识解决某些实际问题的能力,在＂感受理解＂、＂思考运用＂、＂探究拓展＂栏目中分不同层次配置了一定数量的习题.平心而论,题目典型,但难度有的不够,有的重复累赘,所以出现＂教师不屑讲、学生不乐做＂的现象.自从江苏于2005年实行新课改以来,身在教学一线的数学老师在不同的场合发表了许多观点,但笔者结合自己多年的教学实践,对此有着不同的见解：     

Effect of self-constructed concept map with peer feedback on chemistry learning outcome

Concept mapping remains widely used in education. However, little is known about how self-constructed concept maps and peer feedback can improve student learning outcomes in chemistry. We investigated the effects of peer feedback on concept mapping and how it improves students' learning performance in a large second-semester, introductory chemistry course. Three hundred and twenty students were randomly assigned to one of two concept mapping conditions: self-constructed concept map with peer feedback and self-constructed concept map without peer feedback. Each group constructed concept maps that depicted the relationship between concepts on the topic of intermolecular force. The results showed that students in the self-constructed concept map with peer feedback condition outperformed students in the no peer feedback condition in chemistry learning outcome. Overall, this study demonstrates that peer feedback enhances the effectiveness of learning with generative concept maps. The implications and future directions are discussed.     

Exploring college students’ mental representations of inferential statistics

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students’ representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students’ partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.     

Conceptual Representations of Flu and Microbial Illness Held by Students,Teachers, and Medical Professionals

This study describes 5 th, 8th, and 11th‐grade students', teachers', and medical professionals' conceptions of flu and microbial illness. Participants constructed a concept map on “flu” and participated in a semi‐structured interview. The results showed that these groups of students, teachers and medical professionals held and structured their conceptions about microbes differently. A progression toward more accurate and complete knowledge existed across the groups but this trajectory was not always a predictable, linear developmental path from novice to expert. Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses. This knowledge was tightly linked to participants' prior experiences with colds and flu. There were typically large gaps in participants' (children and teachers) understandings of vaccines, immune system responses, treatments (including the mechanisms of pain medications and the functions of antibiotics), and transmission of non‐respiratory microbial illness. A common misconception held by students was the belief that antibiotics can cure viral infections.     

How concept images affect students’ interpretations of Newton's method

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students’ interpretation and application of Newton's method. Results show that some students’ concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.     

Scoring Concept Maps: An Expert Map‐Based Scheme Weighted for Relationships

The use of student‐constructed concept maps in assessment is congruent with the changing emphases set forth by the National Science Education Standards. Authorities have expressed concern about concept map scoring systems and their associated validity and reliability. They favor methods that employ expert/criterion maps as referents and emphasize the use of accurate concept relationships in deriving scores, which have been found to correlate with performance on standardized tests. In this study, student constructed concept maps (n= 17) that emerged from post‐instructional interviews about chlorofluorocarbons were scored against a teacher‐expert map using a scheme weighted for relationships. Interrater reliability for the scoring scheme was high (r= .959). Students' map scores correlated highly with their scores on the California Achievement Test component total (r= .729) and moderately with their Pathfinder index (r= .474), the latter believed to be an excellent measure of structural knowledge. A revised map score, derived only from relationships containing one or more of the concepts employed in Pathfinder analysis, was a statistically significant (p= .031) predictor of the Pathfinder index. The findings of this study support the recommendations of others to use expert referents and emphasize concept relationships in assessing concept maps.     

The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of inquiry‐based science instruction in the elementary classroom, including the benefits of using rigorous science curriculum with general education students. The results of the study revealed a statistically significant gain in science process skills, science concepts, and science‐content knowledge by general education students in the experimental group when compared with students in the comparison group. Moreover, teacher participation in the STEM program had a statistically significant impact on students' variability in posttest scores. These interim student performance data support the implementation of rigorous differentiated science curriculum focused on improving science concept, content knowledge, and process skills.     

Structuring mathematical knowledge and skills by means of knowledge graphs

The aim of the study reported on in this paper was to develop, test and improve a cognitive tool which could help students structure their mathematical knowledge and skills. Mathematics teaching as an auxiliary subject in the context of secondary or tertiary education courses in other disciplines pays too little attention to the structure of the mathematical concepts presented. For the students, therefore, the network of relationships between these concepts does not become a part of their mathematical knowledge and skills, and is consequently not fully available for purposes of reasoning, proving, mathematicizing and solving problems. Knowledge graphs (KGs) can be used by students as a tool to visualize this structure of the concepts and the relations between them. The learning activity of structuring one's mathematical knowledge and skills can be supported by a model, the Mathematical Knowledge Graph Model (MKGM), which serves as a pre-structured heuristic framework. The elements of this model include a central concept, special cases of this concept, operations or actions on the concept, areas of application and properties of the concepts and operations. The present paper reports on a trial among five students of the Open University of the Netherlands (OUNL), who constructed a KG in accordance with the MKGM model. The paper focuses on the graphs produced by the students, their appreciation of the structuring activity and the relation between their graphs and test results.     

STUDENT TEACHERS’ UNDERSTANDING OF RATIONAL NUMBER: PART-WHOLE AND NUMERICAL CONSTRUCTS

Previous research has shown that secondary school students’ understanding of fractions is dominated by the part-whole concept to the possible detriment of their understanding of a fraction as a number in its own right. The present paper reports on an investigation into the understanding of intending primary teachers in this area. Four representatives of a cohort of sixty students on a PGCE course specialising in the lower primary age range were asked detailed questions probing their knowledge of fractions. The conclusion was that the part-whole concept dominates. All of the students were familiar with the numerical concept from their work on the PGCE course, but they reverted to the more familiar part-whole ideas in attempting to solve problems.     

A questionnaire to elicit the mathematical concept images of engineering students

As part of a study into the mathematical understanding of engineering students, a questionnaire has been developed which seeks to elicit from students their concept images attached to key mathematical concepts. The questionnaire seeks to address both the level of understanding of the students and the mode in which the students hold the concept image. The instrument has been used on over 200 students in the schools of mathematics and engineering at the University of Plymouth, and while the details may not be exactly suited to other groups, it is suggested that the method may be helpful to other researchers in the field. Initial results suggest that engineering and mathematics students do have different concept images, and in particular that engineering students gradually adopt mathematical ideas into their engineering knowledge in a way which makes sense of them.