Assessing Students' Misclassifications of Physics Concepts: An Ontological Basis for Conceptual Change

Physics novices and experts solved conceptual physics problems involving light, heat, and electric current and then explained their answers. Novices were ninth-grade students with no background in physics; experts were two postgraduates in physics and two advanced physics graduate students. Problems were multiple choice, with one correct response and three alternative responses representing possible misconceptions. For each conceptual physics problem, an isomorphic material-substance problem was constructed by imagining a materialistic conception of the physics topic and creating the resulting version of the problem. In each physics problem, one of the incorrect choices corresponded to the correct choice in the isomorphic material-substance problem. The empirical question was whether novices would reason about the physics problem as if it were conceptually similar to the substance isomorph. This question was addressed by comparing subjects' responses in the problem pairs, as well as by examining their explanations concerning all problems. A content analysis of subjects' explanations revealed that physics novices were strongly inclined to conceptualize physics concepts as material substances, whereas expert protocols revealed distinctly nonmaterialistic representations. A theory of conceptual change involving ontologically distinct categories is substantiated by these findings.     

Analogical transfer, problem similarity, and expertise

When we encounter a new problem, we are often reminded of similar problems solved earlier and may use the solution procedure from an old problem to solve a new one. Such analogical transfer, however, has been difficult to demonstrate empirically, even within a single experimental session. This article proposes a framework for conceptualizing analogical problem solving that can account for the conflicting findings in the literature. In addition, the framework leads to two predictions concerning the transfer behavior of experts and novices. These predictions concern both positive and negative transfer and are based on the different types of features included in the problem representations of experts and novices. First, when two problems share structural features but not surface features, spontaneous positive transfer should be more likely in experts than in novices. Second, when two problems share surface but not structural features, spontaneous negative transfer should be stronger for novices than for experts. These predictions were supported by the results of three experiments involving college students solving a complex arithmetic word problem.     

线索提示对物理问题表征的影响

考察了复杂物理问题解决中图形线索提示和参数线索提示的作用,结果表明,在难度较大的物理问题中,单一的图形线索提示未给学生带来太大的帮助,而参数线索提示有助于学生搜索到有效算子.讨论了专家在物理问题解决过程中的特点,认为专家的优势之一在于比新手更善于发现关键的线索,能够根据关键线索找到合适的原理来完整地表征问题.     

大学生解决物理问题的表征层次的实验研究

设计了两个实验,探讨优、差生物理问题表征层次的特点。结果表明,优、差生物理问题表征层次有差异。优生侧重于科学理论表征,表现为以物理原理分类,在科学理论表征层次上多为正向推理：差生则受初始表征的影响,以表面特征分类,在科学理论表征层次上多为逆向推理。     

The relation between problem categorization and problem solving among experts and novices

These investigations were conducted to examine the relationship between problem-solving ability and the criteria used to decide that two classical mechanics problems would be solved similarly. We began by comparing experts and novices on a similarity judgment task and found that the experts predominantly relied on the problems' deep structures in deciding on similarity of solution, although the presence of surface-feature similarity had a clear adverse effect on performance. The novices relied predominantly on surface features, but were capable of using the problems' deep structures under certain conditions. In a second experiment, we compared groups of novices, at the same level of experience, who tended to employ different types of reasoning in making similarity judgments. Compared to novices who relied predominantly on surface features, novices who made greater use of principles tended to categorize problems similarly to how experts categorized them, as well as score higher in problem solving. These results suggest that principles play a fundamental role in the organization of conceptual and procedural knowledge for good problem solvers at all levels.     

优、差生解决有机合成的问题表征差异及其影响因素

用两个实验探讨了大学本科化学专业优生和差生解决有机合成问题所运用的问题表征的类型及其差异。结果表明：（１）大学生解决有机合成的问题表征有三种类型;符号表征、方法表征和机理表征。（２）优生能灵活运用上述三类问题表征,特别是运用机理表征抓住问题的关键,进而采用方法表征和符号表征来解题;差生则停留于符号表征和方法表征。很少采用机理表征,而方法表征又往往选择错误,因而不能正确解题。（３）优,差生在问题表征上的差异与其知识总量和知识结构有密切相关。     

专家和新手问题解决认知活动特征的研究

采用口语报告技术对专家和新手解决同类问题的认知活动差异进行分析和评价。结果表明,专家和新手在解决问题时具有不同的编码程序．专家贮存信息以组块化（chunking）方式进行,并能熟练地运用手段─目的分析策略,利用课题中的信息向前解,能正确表征产生式,最大特点是具有概括性和抽象性。新手贮存信息的形式和数量与专家存在着差异,在解决问题时较多进行盲目搜索,一般根据课题中的问题往回解,其内部表征较零乱,具体细节多,解题速度较慢。     

An expert–novice comparison of feature choice

Perceptual experts have learned to rapidly and accurately perceive the structural regularities that define categories and identities within a domain. They extract important features and their relations more efficiently than novices. We used fingerprint examination to investigate expert–novice differences in feature choice. On each fingerprint within our set, experts and novices selected one feature they thought was most useful for distinguishing a particular print and one feature they thought was least useful. We found that experts and novices often differed in the features they chose, and experts tended to agree more with each other. However, any such expert–novice difference appeared to depend on the image at hand typically emerging when salient or more conspicuous features of a fingerprint were unclear. We suggest that perceptual training ought to direct attention to useful features with the understanding that what is useful may change depending on the clarity of the stimuli.     

Outcome trees and baseball: A study of expertise and list-length effects

When people estimate the probability of an event using a list that includes all or most of the possible events, their estimate of that probability is lower than if the other possible events are not explicitly identified on the list (i.e., are collapsed into an all-other-possibilities category). This list-length (or pruning) effect has been demonstrated to occur even for people who have expertise or considerable knowledge in the event domain. We reasoned that the experts used in previous studies would be unlikely to have probabilistic representations of their problem domains (e.g., auto mechanics, auditors, hospitality managers). We used baseball experts (n= 35) and novices (n = 56) on the assumption that expertise in baseball almost certainly involves mental representations of probability for various baseball events. Subjects estimated the frequency of hits, walks, strikeouts, putouts, and “all other” outcomes for an average major league player in 100 times at bat. Other subjects estimated these event outcome frequencies in a short-list condition (e.g., strikeouts, walks, and “all other”). Strong list-length effects were observed with novices; the frequency estimate for strikeouts, for example, was nearly twice as high in the short-list condition as in the long-list condition. Experts, however, showed no list-length effect and their estimated probabilities were very near the actual (normatively correct) probabilities in all conditions. We argue that the omission effect can be overridden by strong mental representations of the family of possible events and/or a clear knowledge of the probabilities associated with the events. As well, we argue that list-length effects seem to result at least in part from an anchoring-and-adjustment strategy.     

Internal Models in Physics Problem Solving

In this paper, we discuss the relations among internal mental models, attentional cues, and knowledge structure in solving elementary physics problems. The notion of semantic sensitivity is introduced as a qualitative measure of problem-solver receptivity to cues for generating, or making a shift to, a new internal model that may lead to the correct answer. Using three physics problems and their variations, the following results were obtained. First, think-aloud protocol data of two experts and one novice, working on those problems, were analyzed to provide empirical examples of internal models, and also to show that generation and shift of internal models generally results from the interplay of two kinds of processes, model construction and model development. Second, protocol data from 15 novices and seven professionals were used to present a more extensive empirical taxonomy of internal models for those problems. Third, seven experiments were used, along with the results from the protocol data, to suggest the following conditions on semantic sensitivity. (1) If the problem solver's present internal model is independent of his knowledge of physics principles underlying the given problem, but if attentional cues are related directly to the knowledge, then his present model is semantically sensitive to the cues, that is, it can be shifted easily to another model that is based on the knowledge. (2) His present model is semantically insensitive, if given cues are encoded based on the same knowledge as used for generating the model. (3) The relevance of cues to knowledge structure is critical for semantic sensitivity of the presently encoded model: Which cues to attend to is guided by the problem solver's knowledge, and if he can focus on those most relevant to the physics principles underlying the problem, then his present model is semantically sensitive to those cues, that is, he is more able to shift the present model to another that would lead to the correct answer.     

简单与复杂物理问题解决及状态元认知

本研究采用认知作业分析及问卷法,研究了中学生简单与复杂物理问题解决的表征机制及状态元认知结构。结果显示：(1)物理问题解决是对问题的表征状态不断转换的过程,其受认知主体信息的提取、转换、整合能力及状态元认知的影响;(2)中学生物理问题解决中的状态元认知主要由他的自我效能感、自我监测、策略系统三种成分构成;(3)复杂问题解决的关链是正确提取范畴性知识以形成对问题的深层表征。     

Chronometric comparisons of imagery to action: visualizing versus physically performing springboard dives

Motor imagery research emphasizes similarities between the mental imagery of an action and its physical execution. In this study, temporal differences between motor imagery and its physical performance as a function of performer expertise, skill complexity, and spatial ability were investigated. Physical execution times for springboard dives were compared with visualized execution times. Results indicate that physical and visualized performance times were not identical: Their relation is a function of dive complexity and diver expertise, but not their interaction. Relative to physical time, visualization time increased with increased complexity, suggesting the involvement of capacity-limited working memory. A nonmonotonic relation was found for expertise: Unlike experts or novices, visualization time for intermediates was significantly slower than physical time. These temporal differences are most consistent with schematic differences in skill representation. Intermediates may be relatively slowed by greater amounts of nonautomatized knowledge, as compared with the automatized knowledge of experts or the sparse knowledge of novices.     

Bothered by abstraction: the effect of expertise on knowledge transfer and subsequent novice performance.

Although experts should be well positioned to convey their superior knowledge and skill to novices, the organization of that knowledge, and particularly its level of abstraction, may make it difficult for them to do so. Using an electronic circuit-wiring task, the authors found that experts as compared with beginners used more abstract and advanced statements and fewer concrete statements when providing task instructions to novices. In a 2nd study, the authors found that beginner-instructed novices performed better than expert-instructed novices and reported fewer problems with the instructions when performing the same task. In Study 2, the authors found that although novices performed better on the target task when instructed by beginners, they did better on a different task within the same domain when instructed by experts. The evidence suggests that the abstract, advanced concepts conveyed by experts facilitated the transfer of learning between the different tasks.     

Decision making and professional experience: an experimental study of generating, evaluating and modifying diagnostic hypotheses

Experimental investigations on generation, evaluation, and modification of diagnostic hypotheses in symptom pattern classification revealed in different domains (e.g. clinical decision making) that reasoning in non-experts and experts differ in the 'content' (e.g. issue-directed substance of concepts) rather than in the 'form' of reasoning (e.g. number, specificity of hypotheses). These results are essentially accounted for by the experts' upper-level flexibility in the interpretation of data. In a two-factorial design (competence x predictive value of data), patients' clinical data with varying predictive value were given singularly in succession to two groups (experts and novices; n = 20) of subjects. The task of the subjects was (a) to name their assumptions and (b) give a summarizing decision on the--probable--diagnostic category of hypothetical cases. Results: Between experts and novices no difference was found in the number and degree of specification of hypotheses; in summarizing decisions, experts considered more categories as plausible than novices; on patient data with low predictive value, experts considered more specific categories. The moment of hypothesis formation depends not on the competence level but on the predictive value of the patient's clinical data.     

Why a Diagram is (Sometimes) Worth Ten Thousand Words

We distinguish diagrammatic from sentential paper-and-pencil representations of information by developing alternative models of information-processing systems that are informationally equivalent and that can be characterized as sentential or diagrammatic. Sentential representations are sequential, like the propositions in a text. Diagrammatic representations are indexed by location in a plane. Diagrammatic representations also typically display information that is only implicit in sentential representations and that therefore has to be computed, sometimes at great cost, to make it explicit for use. We then contrast the computational efficiency of these representations for solving several illustrative problems in mathematics and physics. When two representations are informationally equivalent, their computational efficiency depends on the information-processing operators that act on them. Two sets of operators may differ in their capabilities for recognizing patterns, in the inferences they can carry out directly, and in their control strategies (in particular, the control of search). Diagrammatic and sentential representations support operators that differ in all of these respects. Operators working on one representation may recognize features readily or make inferences directly that are difficult to realize in the other representation. Most important, however, are differences in the efficiency of search for information and in the explicitness of information. In the representations we call diagrammatic, information is organized by location, and often much of the information needed to make an inference is present and explicit at a single location. In addition, cues to the next logical step in the problem may be present at an adjacent location. Therefore problem solving can proceed through a smooth traversal of the diagram, and may require very little search or computation of elements that had been implicit.     

Tall is typical: Central tendency, ideal dimensions, and graded category structure among tree experts and novices

Many accounts of categorization equate goodness-of-example with central tendency for common taxonomic categories; the best examples of a category are average members--those that are most similar to most other category members. In the present study, we asked 24 tree experts and 20 novices to rate goodness-of-example for a sample of 48 trees and found (1) that the internal structure of the category tree differed between novices and experts and (2) that central tendency did not determine goodness-of-example ratings for either group. For novices, familiarity determined goodness-of-example ratings. For experts, the "ideal" dimensions of height and weediness, rather than average similarity to other trees, were the primary predictors of goodness-of-example ratings for experts. The best examples of tree were not species of average height, but of extreme height. The worst examples were the weediest trees. We also found systematic differences in predictors of goodness-of-example as a function of type of expertise. We argue that the internal structure of taxonomic categories can be shaped by goal-related experience and is not necessarily a reflection of the attributional structure of the environment. Implications for models of category structure and category learning are discussed.