概念图及其在数学学习中的现实意义

概念图是用来组织与表征知识的工具.在数学学习中概念图具有重要的现实意义,它可以激励学习者主动建构概念,培养元认知知识和自主性,激发猜想并检验猜想等.学习制作概念图时,要注意:布置任务的形式由结构化逐渐转向弱结构化;概念图制作时应首先集中在一个主题,然后再与其它概念图或主题相连接.     

关于概念图在数学教学评价中的应用研究问题

概念图是组织和表征知识的工具,它的节点、连线、层级、分支和交叉连接都可以用来检测学生的学习.数学概念之间的关系可以拓展为对象与对象、对象与过程,或是过程与过程等之间的复杂关系,也牵涉到与运算之间的关系.概念图的评价形式有读图改错题、填图题和构图题.不同形式的概念图检验试题可以设计不同的评分标准,有节点连线评分法、编码评分法和等级评分法.     

The Knowledge Arena as an Extension to the Concept Map: Reflection in Action

The concept map is becoming a ubiquitous tool in education. In recent years there has been a growing interest in “diagramming” or “mapping” ideas to be learned (e.g., Jonassen et al., 1998). The approach has been championed by study skills proponents such as Buzan (1993). Maps of concepts and relationships have been used by many researchers and practitioners to help diagnose misunderstanding, improve study methods and glimpse how learners come to know. In other areas, the representation of knowledge in formalisms such as the Net greatly assisted the development of intelligent tutoring systems (e.g., Sowa, 1983). In order to better understand the claims made for its efficacy, reference to how concept maps have been used and defined will lead to a plausible explanation of the process of “off–loading” of concepts during learning or study (McAleese, 1994, 1998). In order to demonstrate the widespread application of supporting learn ers with external “learning spaces” (c.f. ISLEs/ and REALs—Grabinger et al., 1998; Grabinger & Dunlap, 1995; MacFarlane, 1993), consideration will be given in this paper to techniques that formally represent knowledge in Concept–Relationship–Concept “instances” (Fisher et al., 1990). Other techniques such as reflection journals draw on the same process but are not considered in detail here. The importance of self regulation (Zimmerman, 1990) and self-confrontation (McAleese, 1985) is highlighted in this framework. The map as a mirror or an assistant to learners is well documented (e.g., Vizcarro & Leon, 1998); the question of an external representation of thinking, in the form of a map determining what can be learned as well as what might be learned, is not yet fully known.     

概念图在数学教学中应用的实践研究

概念图作为一种有效组织和表征知识的工具,在一些欧美国家已成为了比较盛行的一种教学形式,而在国内却在近几年才开始有学者进行介绍、引进并试图在教学中应用。本文通过在理论成面上深入挖掘概念图与认知思维的内涵关系,进而对在此基础上的结合数学课程开展的概念图教学形式进行探讨与总结,并对概念图在教学过程中的实践效果进行量化分析,以期将来在更广大范围内推广应用,推动基础教育课程改革向深度发展。     

Knowledge presented in concept maps: correlations with conventional cognitive knowledge tests

Our study focuses on the correlation of concept map (CMap) structures and learning success tested with short answer tests, taking into particular account the complexity of the subject matter. Novice sixth grade students created CMaps about two subject matters of varying difficulty. The correlation of the complexity of CMaps with the post-test was small but highly significant in both subject matters. The complexity of the CMaps correlated with the long-term knowledge in the difficult subject matter but not in the context of the easy one. Furthermore, the high number of technical errors makes it close to impossible to estimate students’ knowledge. In summary, CMaps do not provide an adequate alternative to conventional short answer knowledge tests, but together with them they may offer a better comprehension of a student’s knowledge structure and aid in the preparation of further instruction tailored to individual needs.     

Concept maps: Experiments on dynamic thinking

Three experiments were conducted to examine the effects of map structure, concept quantification, and focus question on dynamic thinking during a Concept Map (CMap) construction task. The first experiment compared cyclic and hierarchical structures. The second experiment examined the impact of the quantification of the header concept in the map. The third experiment explored the effect of the focus question on the map. For all three experiments, the content of the CMaps was assessed for the number of dynamic propositions and the number of quantified concepts. The results show that the cyclic structure, the quantification of the header concept, and the focus question “How” significantly increased dynamic thinking. The studies, the theoretical background, and the implications of the findings are discussed. © 2006 Wiley Periodicals, Inc. J Res Sci Teach 44: 448–465, 2007     

Teaching Science in Elementary Schools: a Research Programme by the University of Pavia,Italy

Concept mapping is a technique used to provide a visual representation of an individual’s ideas about a concept or set of related concepts. This paper describes a concept mapping tool using a photograph association technique (CoMPAT) that is considered to be a novel way of eliciting children’s ideas. What children at 11 years of age know about particular concepts related to microbial activity is presented and discussed in relation to the effectiveness of CoMPAT as a tool to draw out their ideas. It is proposed that this tool could be used to explore ideas about this and other science concepts from children in other age groups, and where language may be a barrier to participation.     

Teaching the Self

Abstract

Teaching a business program capstone class presents a double challenge, requiring the educator to integrate different functional areas of business and evaluate student learning. This paper discusses concept maps as an active learning assessment tool in teaching a strategic management capstone course. Concept maps are used to meaningfully depict knowledge and present illustrations of relationships between concepts in a particular course. This study reviews 54 individual and 19 group concept maps collected over three semesters. The analysis affirms that concept maps are a powerful pedagogical tool that requires students to reflect on the knowledge gained during a course.     

Aggregating concept map data to investigate the knowledge of beginning CS students

Concept maps have a long history in educational settings as a tool for teaching, learning, and assessing. As an assessment tool, they are predominantly used to extract the structural configuration of learners’ knowledge. This article presents an investigation of the knowledge structures of a large group of beginning CS students. The investigation is based on a method that collects, aggregates, and automatically analyzes the concept maps of a group of learners as a whole, to identify common structural configurations and differences in the learners’ knowledge. It shows that those students who have attended CS education in their secondary school life have, on average, configured their knowledge about typical core CS/OOP concepts differently. Also, artifacts of their particular CS curriculum are visible in their externalized knowledge. The data structures and analysis methods necessary for working with concept landscapes have been implemented as a GNU R package that is freely available.     

基于概念图工具的地理教科书分析研究——以高中必修1两版本教科书“大气的水平运动”为例

概念图是组织和表示知识的图形工具,可以使用概念图软件Cmap Tools进行绘制。在基础教育研究中运用信息化教育科研方法是教育研究的发展方向。作为一种研究工具,概念图软件可以用于高中地理教科书分析研究。节点频率等5个定量分析指标可以帮助认识教科书和选用适合教学的教科书,某节点与其他节点的联系等3个方面的定性分析可以帮助认识教科书内容和修订教科书中的具体知识。     

The Synthesis Map Is a Multidimensional Educational Tool That Provides Insight into Students’ Mental Models and Promotes Students’ Synthetic Knowledge Generation

Concept mapping was developed as a method of displaying and organizing hierarchical knowledge structures. Using the new, multidimensional presentation software Prezi, we have developed a new teaching technique designed to engage higher-level skills in the cognitive domain. This tool, synthesis mapping, is a natural evolution of concept mapping, which utilizes embedding to layer information within concepts. Prezi’s zooming user interface lets the author of the presentation use both depth as well as distance to show connections between data, ideas, and concepts. Students in the class Biology of Cancer created synthesis maps to illustrate their knowledge of tumorigenesis. Students used multiple organizational schemes to build their maps. We present an analysis of student work, placing special emphasis on organization within student maps and how the organization of knowledge structures in student maps can reveal strengths and weaknesses in student understanding or instruction. We also provide a discussion of best practices for instructors who would like to implement synthesis mapping in their classrooms.     

Semantic networking: The new kid on the block

This article briefly describes the SemNet? software and some of its uses as an educational and research tool, with emphasis on the similarities and differences between concept mapping and semantic networking. A semantic network captures (in part) each concept's position in psychological space, identifying both the other concepts to which it is connected and the nature of the links that bind them. Computer-based semantic networks differ from paper-and-pencil maps in that they are n-dimensional; each concept can be linked to many other concepts; relations are bidirectional; representations can include images, text, and sound; and nets can be very large. Disadvantages of SemNet? networks include (a) the difficulties in obtaining a clear overview and (b) the homogeneous nature of the representations, in which all links look alike. Advantages include the ability to integrate ideas across a large knowledge base, the ease and rapidity of net creation, the ease with which elements (concepts, relations, or propositions) can be found within nets, and the utility of nets as self-study tools. Concept mapping and semantic networking are complementary strategies that can be used effectively in tandem to help students learn, to help teachers teach, and to support cognitive research.     

概念图的布局算法研究

概念图是一种有效的知识可视化工具,而概述图的布局是影响其信息传递能力的重要因素,因此布局算法是实现概念图工具的重要技术基础.本文在Sugiyama层次布局算法的基础上,针对概念图的特点和布局要求,提出了一种概念图的布局算法：首先对概念图的概念节点和关系节点进行简化处理,然后应用Sugiyama层次布局算法的第一步（分层）,并对图中的关系节点进行特殊处理,调整分层,最后应用Sugiyama层次布局算法的“交叉减少”和“坐标分配”模块,得出概念图各个节点（包括概念节点、关系节点和虚拟节点）的坐标,最终得出概念图的布局.该算法已通过编程实现,并成功应用于我们自主研发的概念图工具软件中.     

Propagation from the start: the spread of a concept-based instructional tool

We describe the propagation of a technology-based educational innovation through its first 3 years of public use. The innovation studied is the Concept Warehouse (CW), a database-driven website developed to support the use of concept-based pedagogies. This tool was initially developed for instructors in undergraduate chemical engineering courses, but has spread to other disciplines as well. In this time, it has grown to over 650 registered instructors representing over 170 institutions. While this study is specific to a particular case, the intent of this article is to provide an exemplar of real-time propagation that informs other researchers and developers. We frame our analysis with Diffusion of Innovation Theory and use a design research methodology that focuses on communication channels, types of knowledge, and stages of the innovation-decision process. Data sources include usage records and survey responses which are analyzed with network diagrams and non-parametric statistics. We find that in comparison to mass media, interpersonal communications tended to result in higher proportions of how-to knowledge and implementation. Three types of opinion leaders were identified through user data and network diagrams. All played critical roles in the tool’s propagation, especially the project collaborators—opinion leaders who actively promoted the CW, in part, because it also propagates their own innovations. Finally, users with self-identified prior principles knowledge showed statistically significantly greater progress in gaining how-to knowledge, but no significant difference in progressing to the implementation stage of the innovation-decision process when compared to users without.     

A Hierarchical Biology Concept Framework: A Tool for Course Design

A typical undergraduate biology curriculum covers a very large number of concepts and details. We describe the development of a Biology Concept Framework (BCF) as a possible way to organize this material to enhance teaching and learning. Our BCF is hierarchical, places details in context, nests related concepts, and articulates concepts that are inherently obvious to experts but often difficult for novices to grasp. Our BCF is also cross-referenced, highlighting interconnections between concepts. We have found our BCF to be a versatile tool for design, evaluation, and revision of course goals and materials. There has been a call for creating Biology Concept Inventories, multiple-choice exams that test important biology concepts, analogous to those in physics, astronomy, and chemistry. We argue that the community of researchers and educators must first reach consensus about not only what concepts are important to test, but also how the concepts should be organized and how that organization might influence teaching and learning. We think that our BCF can serve as a catalyst for community-wide discussion on organizing the vast number of concepts in biology, as a model for others to formulate their own BCFs and as a contribution toward the creation of a comprehensive BCF.     

The Status of Genetics Curriculum in Higher Education in the United States: Goals and Assessment

We review the state of genetics instruction in the United States through the lens of backward design, with particular attention to the goals and assessments that inform curricular practice. An analysis of syllabi and leading textbooks indicates that genetics instruction focuses most strongly on foundations of DNA and Mendelian genetics. At the same time, a survey of faculty indicates that other concepts, such as the application of genetics to society or the environment, are viewed as equally or even more important than foundation concepts. This disconnect suggests a need for more explicit goal setting prior to curriculum development. We also review the relationship between concept inventories, multiple-choice tests measuring conceptual understanding, and curricular goals. Existing concept inventories offer a strong foundation on which to build community-developed concept assessments of genetics knowledge. Concept assessments such as these would allow the genetics education community to test hypotheses of curricular change.     

中学物理概念建构策略

物理概念教学是物理教学的核心内容,如何帮助学生建构概念是物理教学方面的热点问题。目前多数教师在课堂上有建构知识的教学意识,但在操作层面上仍存在问题。中学物理概念建构的策略包括分析概念特点,创设多维情境;激发学生认知矛盾,打破思维平衡态;设计"留白"与"讨论",引发学生意义建构;提炼核心要点,强化学生概念表述方法。     

A new model of concept teaching and learning

Current models of instructional design assume that concepts are (a) classifying rules, (b) components of a more complex network or schema in memory, and (c) evaluated/taught by classification performance. Based on current research and theory, however, concepts should be viewed as conceptual tools rather than classification rules. Concepts may be schemas or networks in themselves, as a complex arrangement of declarative, procedural, and inferential knowledge. Concept learning may be measured by concept use and inferences as well as classification and taught via analogies, learning strategies, use/inference practice, and rational-set generators.     

Analysing Concept Maps as an Assessment Tool in Teaching Physics and Comparison with the Achievement Tests

Concept mapping is a technique that paves the way to represent knowledge schematically. In this research, concept mapping was used as an assessment method on the impulse–momentum topic. The purpose of this study was to determine teacher candidates’ knowledge about understanding of the concepts of impulse and momentum by comparing and contrasting two different methods; namely, students’ concept maps and an achievement test. The mean of teacher candidates’ concept map scores are extremely low when compared with the scores of the achievement test. In addition, it was seen that although a great number of concepts were written down, not many relationships were established between these concepts. There is a weak correlation between the achievement test and the concept map scores since concept maps assess the students’ knowledge from a conceptual perspective while the achievement tests measure the level of students’ knowledge on the topic and his/her ability to apply this knowledge on different occasions.     

大学力学概念图的制作

文章首先介绍了一般概念图的六个组成成分:概念、分支、水平层次、同一分支下概念间的连接线和连接语、不同分支下概念间的连接线和连接语、例子;在此基础上,介绍了制作大学力学概念图时对一般概念图所进行的改进措施,而后以大学力学知识概念图实例为基础,总结了制作大学力学概念图的具体步骤;文章以多个大学力学概念图制作的范例为依据,论证了制作大学力学概念图应该遵循的原则.