Overcoming misconceptions via analogical reasoning: abstract transfer versus explanatory model construction

In most work investigating factors influencing the success of analogies in instruction, an underlying assumption is that students have little or no knowledge of the target situation (the situation to be explained by analogy). It is interesting to ask what influences the success of analogies when students believe they understand the target situation. If this understanding is not normative, instruction must aim at conceptual change rather than simply conceptual growth. Through the analysis of four case studies of tutoring interviews (two of which achieved some noticeable conceptual change and two of which did not) we propose a preliminary list of factors important for success in overcoming misconceptions via analogical reasoning. First, there must be a usable anchoring conception. Second, the analogical connection between an anchoring example and the target situation may need to be developed explicitly through processes such as the use of intermediate, bridging analogies. Third, it may be necessary to engage the student in a process of analogical reasoning in an interactive teaching environment, rather than simply presenting the analogy in tetext or lecture. Finally, the result of this process may need to be more than analogical transfer of abstract relational structure. The analogies may need to be used to enrich the target situation, leading to the student's construction of a new explanatory model.     

Conjecturing via reconceived classical analogy

Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners are unable to transfer analogical reasoning to learning situations. This study aims at facilitating analogy use for conjecturing in discourse-rich mathematics classrooms. We reconceptualized one of the traditional perspectives on analogical reasoning, called classical analogy, as a more dynamic one by providing learners with the opportunity to choose a target object and its property. While shifting attention to particular aspects of mathematical activity, we observed and analyzed how students became aware of hidden relational similarities and utilized them while weakening others to make conjectures. The detailed analysis of the constructs and processes of several similarity-making and conjecturing activities supports the significance of reconceived classical analogy use in mathematics classrooms.     

Analogical reasoning in restructuring scientific knowledge

This study presents the results of an experiment which investigated analogical reasoning in knowledge acquisition in a natural school setting. The aims were to evaluate the efficiency of analogy in the conceptual restructuring of a science topic and compare the effects of analogy in different learning conditions. Two analogical topics of physics (water flow and heat flow) were studied by means of two experiments performed in the classroom with concrete objects. Eighty-four 5th graders, divided into three experimental conditions (given analogy, constructed analogy, no analogy), took part in the study. The quantitative analysis mainly confirms the hypothesis that analogy can be a productive way to trigger a process of knowledge restructuring while students learn a new topic. However, the effective use of the analogy was affected by the experimental condition: When the analogy was constructed by the learners themselves, instead of being presented and justified by the teacher, it acted indeed as a more powerful tool in understanding the new topic which required changing their initial conceptions. The qualitative analysis shows the children’s explanations of the heat flow phenomenon and different conceptual outcomes of the learning process. Finally, educational implications are considered.     

Teaching Scientific Analogies: a proposed model

The purpose of this paper is to propose a model for teaching scientific analogies. This model is called: ‘The General Model of Analogy Teaching’ (GMAT). A theoretical framework is developed first for this model. The following points are covered in this framework: (1) definition of the analogy, (2) analogical learning, (3) variables related to the analogical learning, (4) evaluating the outcomes of analogical learning, and (5) limitations of using analogies in teaching. The General Model of Analogy Teaching proceeds in the following nine stages: (1) measure some of the students’ characteristics related to analogical learning in general, (2) assess the prior knowledge of the students about the ‘topic’ to be taught, (3) analyse the learning material of the ‘topic’ to be taught, (4) judge the appropriateness of the analogy to be used, (5) determine the characteristics of the analogy to be used, (6) select the strategy of teaching and the medium of presenting the analogy, (7) present the analogy to the students, (8) evaluate the outcomes of using the analogy in teaching, and (9) revise the stages of the model.     

Effects of teacher training on children's analogical reasoning performance

Two studies were conducted to assess the effects of teacher training in analogical reasoning on students' performance of analogy tasks. Study One focused on elementary school teachers and students, while Study Two involved early childhood teachers. In Study One, 25 fourth-grade teachers were assigned either to Control, or to Level I or Level II treatment conditions. The Level I condition involved the receipt of detailed analogy lessons. The Level II condition encompassed both the receipt of instructional materials and explicit training for teachers in their underlying theory and use. Further, 19 of the 25 treatment and control teachers were observed during the course of the study to determine the influence of observation of teachers on students' analogical reasoning. Students' performance of an analogy task was compared prior to and following teacher-delivered instruction by means of an analysis of covariance procedure. Results indicated that students in Level II classrooms significantly outperformed Level I students, who significantly outperformed students in Control classrooms. Teacher observation was found to be a significant factor in the performance of Level I, but not Level II or Control, students. In Study Two, teachers participating in two summer programs for gifted preschoolers were taught how to deliver instruction in analogical reasoning to young children, ages three to six. Results demonstrated that children receiving explicit instruction in analogical reasoning scored significantly better on an analogy task than the children assigned to control. No effect for age, race, gender, or Socioeconomic studies were found. Implications of the results of these two studies for educational practice are discussed.     

比拟引申初探

该文证明了同比喻、借代一样,比拟也是一种很普遍的词义引申手段,阐明了比拟引申的规律,区分了比拟引申和比喻引申。与此同时,对比拟的性质、分类、范围也提出了一些新的看法。     

Exploring the use of multiple analogical models when teaching and learning chemical equilibrium

This study describes the multiple analogical models used to introduce and teach Grade 12 chemical equilibrium. We examine the teacher's reasons for using models, explain each model's development during the lessons, and analyze the understandings students derived from the models. A case study approach was used and the data were drawn from the observation of three consecutive Grade 12 lessons on chemical equilibrium, pre‐ and post‐lesson interviews, and delayed student interviews. The key analogical models used in teaching were: the “school dance”; the “sugar in a teacup”; the “pot of curry”; and the “busy highway.” The lesson and interview data were subject to multiple, independent analyses and yielded the following outcomes: The teacher planned to use the students' prior knowledge wherever possible and he responded to student questions with stories and extended and enriched analogies. He planned to discuss where each analogy broke down but did not. The students enjoyed the teaching but built variable mental models of equilibrium and some of their analogical mappings were unreliable. A female student disliked masculine analogies, other students tended to see elements of the multiple models in isolation, and some did not recognize all the analogical mappings embedded in the teaching plan. Most students learned that equilibrium reactions are dynamic, occur in closed systems, and the forward and reverse reactions are balanced. We recommend the use of multiple analogies like these and insist that teachers always show where the analogy breaks down and carefully negotiate the conceptual outcomes. © 2005 Wiley Periodicals, Inc. J Res Sci Teach 42: 1135–1159, 2005     

谈工作记忆与类比推理

类比推理是一种特殊的推理形式,也是个体抽象思维的一种主要形式。有些心理学家着重研究与类比推理有关的问题,以期可以找到发展类比推理能力的有效策略,以提高学生学习新知识、新技能等的效率。经过大量研究与调查数据显示,工作记忆的各个子成分与类比推理之间有着密切的联系,工作记忆直接影响着个体类比推理能力的发展。因此,文章主要探讨工作记忆与类比推理的含义,以及工作记忆对类比推理的影响,希望能够为相关研究者提供参考。     

Chemistry and the Pendulum – What Have They to do With Each Other?

Physicists have known for some time that pendulum motion is a useful analogy for other physical processes. Chemists have played with the idea from time to time but the strength of the analogy between pendulum motion and chemical processes has only received prominent published recognition since about 1980, although there are details of the analogy that still remain to be explored. This paper suggests that thinking of the pendulum as a type of energy converter can help students understand the energy conversions involved in molecular collisions associated with a chemical reaction. In particular, the relationship between kinetic and potential energy becomes vital in understanding the process of bond breaking, bond making, and enthalpy change in a chemical reaction. As a result, the principles behind transition state theory become somewhat easier to grasp. However, the use of the pendulum as an analogy for a reaction approaching chemical equilibrium can lead to misconceptions. The paper also discusses the nature of catalytic feedback, periodicity and non-periodicity in oscillating chemical reactions and the extent to which the action of a pendulum might elucidate these phenomena. Identifying the limitations as well as the strengths of an analogy is an important consideration when an analogy is applied to a teaching and learning situation. While one is tempted to think that pendulum action is probably more pertinent to the study of physics, there are important applications in the field of chemistry.     

话语隐喻:类推图式形成的关键

认知语言学家很久以来就对人类思维与话语中的类推感兴趣,但是对语言行为与类推图式之间的关系属性却研究得甚少.话语隐喻是指能在某个话语群引起一致类推的语言表达结构.类推图式是具体的,是围绕特殊的词汇进行的,话语隐喻是类推图式形成的关键因素.     

Using examples and analogies to remediate misconceptions in physics: Factors influencing conceptual change

Examples are often recognized as important in teaching conceptual material, yet little research has been done concerning the best use of examples in attempts to remediate misconceptions. This study questions the effectiveness of a traditional teaching-by-example technique. Results indicate that when students hold a misconception, presenting a principle with supporting examples to show the range of application of the principle may be ineffective. Rather, it appears that examples are more effective when they help students draw on and analogically extend existing valid physical intuitions in constructing a new conceptual model of a target situation. To help students in this constructive effort, first, the examples used must be understandable and believable to the students, not simply to the teacher or textbook author. Second, even when an example is compelling to the student, it may not be seen as analogous to target problems drawing out a misconception. In that case, analogy relations may need to be explicitly developed. Third, qualitative, visualizable models may need to be developed which give mechanistic explanations for phenomena.     

An Analogy‐Based Computer Tutor for Remediating Physics Misconceptions

We describe a computer tutor designed to help students understand physics concepts. The tutor uses a teaching strategy called “bridging analogies” that previous research has demonstrated to be successful in one‐on‐one tutoring. The strategy is designed to remedy misconceptions by appealing to existing correct intuitions, and extending these intuitions by encouraging analogical thinking. Students were videotaped while using the program and were encouraged to think aloud. The strategy was successful in changing beliefs for some students. We outline suggestions for improving the tutor using artificial intelligence technology.     

Cognitive and metacognitive aspects in conceptual change by analogy

This study is a qualitative investigation on the teaching-learning by analogy of complex curriculum concepts in natural and relevant environments, such as classrooms, to improve the ecological validity of the research itself. It aimed at exploring whether students' successful use of analogy in learning science was related a) to the level of their understanding of a specific analogy and b) to their metacognitive awareness of how the analogy was to be used and of the changes produced in their own conceptual structures. During the implementation of a biological curriculum unit, sixty 5th graders were engaged in understanding the ways in which the new concepts (concerning the human circulatory system) were similar to a familiar source (the mail delivery system) by detecting all the relations between the two systems and mapping the relevant information from the source to the target. Learners' preexisting mental models have been taken into account in order to examine their conceptual growth and change via the analogy. Qualitative data are presented for the analysis of elicited and spontaneous analogical inferences, based on structural and semantic similarities, as well as of the identification of where the analogy breaks down. Moreover, qualitative data also concern children's metacognitive awareness of the meaning and the purpose of the analogy, and their personal use of the analogy in changing initial conceptions. As hypothesized, results showed a high correlation between level of conceptual understanding of the new science topic, level of understanding of the analogy itself, and the effective use of the analogy in integrating the new information into the pre-existing conceptual structures. Some implications on the use of analogy for conceptual change are considered from an educational standpoint.     

类比推理的形式化探析

类比推理是一种重要的推理,仅仅由属性的相似性去解释类比是不够的,应该从形式上对类比推理进行深入的探究.类比是源域S和目标域T之间的结构保持映射fM.在类比推理的过程中,对源域S的选择、对结构保持映射的要求以及对类比迁移的控制,都会影响类比推理的关联性和可靠性.     

“地下水动力学”课程教学中类比法的运用

类比法是萌发科学猜想的一种重要思维方法,也是一种重要的教学方法。达西定律是地下水运动的基本规律,是开展地下水定量计算和定性分析一系列水文地质现象的关键。为了提高教学效果,可以充分利用达西定律与传热学中的傅立叶定律、电学中的欧姆定律三者之间的相似性,开展类比法教学。这不仅能够加深学生对达西定律的理解,还有助于培养学生利用其他学科的知识来开展本学科研究的思想方法,是帮助初学者学习新知识的有效方法。     

Exploring undergraduates' understanding of photosynthesis using diagnostic question clusters

We present a diagnostic question cluster (DQC) that assesses undergraduates' thinking about photosynthesis. This assessment tool is not designed to identify individual misconceptions. Rather, it is focused on students' abilities to apply basic concepts about photosynthesis by reasoning with a coordinated set of practices based on a few scientific principles: conservation of matter, conservation of energy, and the hierarchical nature of biological systems. Data on students' responses to the cluster items and uses of some of the questions in multiple-choice, multiple-true/false, and essay formats are compared. A cross-over study indicates that the multiple-true/false format shows promise as a machine-gradable format that identifies students who have a mixture of accurate and inaccurate ideas. In addition, interviews with students about their choices on three multiple-choice questions reveal the fragility of students' understanding. Collectively, the data show that many undergraduates lack both a basic understanding of the role of photosynthesis in plant metabolism and the ability to reason with scientific principles when learning new content. Implications for instruction are discussed.     

Coordinating principles and examples through analogy and self-explanation

Research on expertise suggests that a critical aspect of expert understanding is knowledge of the relations between domain principles and problem features. We investigated two instructional pathways hypothesized to facilitate students’ learning of these relations when studying worked examples. The first path is through self-explaining how worked examples instantiate domain principles and the second is through analogical comparison of worked examples. We compared both of these pathways to a third instructional path where students read worked examples and solved practice problems. Students in an introductory physics class were randomly assigned to one of three worked example conditions (reading, self-explanation, or analogy) when learning about rotational kinematics and then completed a set of problem solving and conceptual tests that measured near, intermediate, and far transfer. Students in the reading and self-explanation groups performed better than the analogy group on near transfer problems solved during the learning activities. However, this problem solving advantage was short lived as all three groups performed similarly on two intermediate transfer problems given at test. On the far transfer test, the self-explanation and analogy groups performed better than the reading group. These results are consistent with the idea that self-explanation and analogical comparison can facilitate conceptual learning without decrements to problem solving skills relative to a more traditional type of instruction in a classroom setting.     

Overcoming Junior High School Students' Misconceptions About Microscopic Views of Phase Change: A Study of an Analogy Activity

This study was conducted to examine the effectiveness of an analogy activity, which was designed to overcome junior high students' misconceptions about the microscopic views of phase change. Eighty Taiwanese 8th graders were randomly assigned to either a control group or an experimental group. For the control group, the subjects were instructed through traditional teaching whereas for the experimental group, an analogy activity was conducted on students. This specific analogy activity was presented in the form of role-playing in which students acted as particles and worked together to perform the conditions of phase changes. Through analyzing these students' drawings of the atom arrangements for the three states of some substances, it was found that the students of experimental group, though in many cases, did not perform statistically better than did those of control group in an immediate posttest. The comparisons of a delay test between these two groups indicated that the analogy activity had clearly positive impacts on students' conceptual change on these scientific concepts in terms of long-term observations.     

类比法在“大学数学”教学中的应用

类比方法是用已有的知识和已掌握的技能去解决新问题,从而加深学生对新知识的理解,促进学生对新规律的认识;找出问题、探究问题、解决问题,有助于思想、方法和技巧的开拓与延伸。类比法对提高教学效果和培养学生的创新意识是十分必要的,也是课程改革所倡导的。介绍类比式教学的基本概念,分别大学数学的基础学科和应用学科两类课程来以类比式教学方法的使用情况。运用好类比式教学法将有助于学生加深对数学课程的认识,形成系统全面的知识体系。