Understanding spatial diagram structure: an analysis of hierarchies, matrices, and networks

diagrams are powerful tools for comprehension and problem solving in diverse contexts. Two studies examined the structural properties of (i.e., applicability conditions for) three interrelated spatial diagrams—hierarchies, matrices, and networks. College students from two groups with distinct educational backgrounds and learning histories—advanced computer science students and representative undergraduates—rated the diagnosticity of the hypothesized applicability conditions for each of the 3 diagrams. The results validated 24-26 of the 30 hypothesized applicability conditions and provided evidence regarding the relative importance, or diagnosticity, of the validated properties for each type of diagram. A different set of properties was identified as most highly diagnostic for each type of diagram, indicating that the three spatial diagrams are optimized to serve different representational functions: The matrix stores static information about the kind of relation that exists between pairs of items in different sets, the network conveys dynamic information by showing the local connections and global routes connecting the items being represented, and the hierarchy depicts a rigid structure of power or precedence relations among items. The quantitative and qualitative differences in representational knowledge due to educational background are discussed.     

Context and structure: The nature of students' knowledge about three spatial diagram representations

The authors investigated whether college students possess abstract rules concerning the applicability conditions for three spatial diagrams that are important tools for thinking—matrices, networks, and hierarchies. A total of 127 students were asked to select which type of diagram would be best for organising the information in each of several short scenarios. The scenarios were written using three different story contexts: (a) neutral, presenting a real-life situation but not cueing a particular representation; (b) abstract, presenting only variable names and relations; and (c) incongruent, in which the context and informational structure cued different representations. The results indicated above-chance performance on the abstract scenarios, as well as comparable performance on the abstract and neutral context scenarios. In a follow-up study in which eight students thought out loud while selecting diagrams for the abstract scenarios, there were almost no references to concrete examples. The results of these studies suggest that students possess abstract rules concerning the applicability conditions for matrices, networks, and hierarchies.     

To Matrix, Network, or Hierarchy: That Is the Question

The authors present a structural analysis of three spatial diagrams-matrices, networks, and hierarchies-that specifies 10 properties on which these diagrammatic representations are hypothesized to differ: global structure, building block, number of sets, item/link constraints, item distinguishability, link type, absence of a relation, linking relations, path, and traversal. Each property has a "value" for each diagram, and these property values constitute the applicability conditions for the representations. Twenty-three college students (computer science majors and math educators) selected the type of diagram they thought would be most efficient for organizing the information in each of 18 short scenarios and verbally justified the reasons for their selections. The verbal protocols were coded with respect to the structural analysis. Both the representation selection and verbal justification data provided strong support for the structural analysis. Additionally, a factor analysis of students' justifications indicated that the organization of their knowledge is consistent with the structural analysis. Students' use of the structural properties to select appropriate representations and to justify those selections indicates that the structural analysis has psychological force.     

Implicit diagnosticity in an information-buying task. How do we use the information that we bring with us to a problem?

Past research suggests that people may make use of diagnosticity information when explicit data regarding P(D | H) and P(D | ? H) are given to them. However, people fall victim to pseudodiagnosticity biases and ignore P(D | ? H) when such data must be actively sought. This series of four experiments utilized judgment problems in which subjects have knowledge of P(D | ? H) but must recognize the relevance of that knowledge for the judgment at hand. It was hypothesized that subjects who genuinely understood the role of P(D | ? H) in hypothesis testing would respond to this manipulation of implicit diagnosticity by exhibiting greater confidence and lesser information buying when given evidence of relatively high diagnosticity. In the first three studies, subjects attempted to judge the guilt or innocence of suspects in several fictional crimes. In the fourth experiment, subjects attempted to judge the club membership status of students at their own university. Greater amounts of information were bought when the only available information was of low diagnosticity. Subjects also expressed greater confidence in judgments made using highly diagnostic information. However, within the legal scenario, sensitivity to diagnosticity was dependent upon the implication of the cues received. Results are discussed with respect to Bayesian probability, expected value theory, and a confidence criterion model of information purchasing.     

Diagnosticity,confidence, and the need for information

Recent research has suggested that people prefer to use the most diagnostic available information as the basis for their choices and decisions, and are most confident in those decisions when information is highly diagnostic. However, the effect of information diagnosticity on the need for additional information has yet to be investigated; that is, in an optional stopping task, will the amount of information requested depend upon information diagnosticity? Three models of the role of diagnosticity in information use were examined; expected value, a confidence criterion, and information cost. Subjects attempted to categorize stimuli with the aid of information of varying costs and diagnosticity levels. They requested more information when it was obtained at a low cost. More importantly, across cost conditions, subjects consistently requested greater amounts of information when that information was of a low diagnosticity. These data seem most consistent with use of a confidence criterion that is adjusted for information costs.     

类别使用的特征诊断效应

运用预备实验评定过的鱼轮廓图,考察了类别判断和特征预测这两种类别使用方式下的特征诊断效应。被试是48名大学生,学习材料是两类鱼的类别成员,在测验阶段,实验1判断新项目类别标签,实验2预测新项目的缺失特征。结果表明,类别判断条件下,单个特征诊断力加强和诊断性特征数量增加都对类别判断有促进作用;特征预测条件下,只有单个特征诊断力加强可以促进特征预测,诊断性特征数量增加无助于特征预测     

Time,space, and memory for order

Information about the order of items in a sequence can be conveyed either spatially or temporally. In the present investigation, we examined whether these different modes of presentation map onto compatible mental representations of serial order. We examined this issue in three immediate serial-recall experiments, in which participants recalled lists of letters in the temporal order in which they had appeared. Each letter in a to-be-remembered sequence was presented in a unique spatial position, with the order of these spatial positions progressing from either left to right or right to left. In this way, the visually presented lists contained both temporal and spatial order information. Recall of the temporal order information was more accurate with congruent spatial order information—that is, when the letters progressed from left to right, following the typical reading direction of English—than when the spatial order information was incongruent. These results suggest compatible representations of serial order when sequences are conveyed spatially and temporally.     

Evidence for abstract, schematic knowledge of three spatial diagram representations

Spatial diagram representations such as hierarchies, matrices, and networks are important tools for thinking. Our data suggest that college students possess abstract schemas for these representations that include at least rudimentary information about their applicability conditions. In Experiment 1, subjects were better able to select the appropriate spatial diagram representation for a problem when cued to use general category information in memory about those representations than when cued to use specific example problems given during the experiment. The results of Experiment 2 showed that the superior performance in the general category condition was not based on a comparison of the test problems with examples in memory. The results of Experiment 3 showed that the superior performance was not due to learning that occurred during the experiment or to transfer appropriate processing. The General Discussion section considers the nature of students' representation schemas and the question of why college students have only rudimentary schemas for common and widely applicable diagrammatic representations.     

Representational Translation With Concrete Models in Organic Chemistry

In representation-rich domains such as organic chemistry, students must be facile and accurate when translating between different 2D representations, such as diagrams. We hypothesized that translating between organic chemistry diagrams would be more accurate when concrete models were used because difficult mental processes could be augmented by external actions on the models. In three studies, the task was to translate between different diagrams of molecules with or without a model. The model groups outperformed control groups, and students who received and used models outperformed those who received but did not use models. Uses of the model suggested that participants were performing external actions to support or replace difficult mental spatial processes. Spatial ability was a much weaker predictor of performance than model use. Results suggest that concrete molecular models can be an effective learning tool but some students need direct instruction to be able to take advantage of models.     

信息呈现方式与学习者的个性特征对多媒体环境下学习效果的影响

采用两个实验:实验一以陈述性知识为学习内容,实验二以程序性知识为学习内容,在这两种情况下,分别用组间设计探讨信息呈现方式对不同认知风格和空间能力的学习者在多媒体环境下学习效果的影响。结果表明:(1)认知风格对陈述性知识在多媒体环境下的学习效果产生影响,而选择的多媒体信息呈现方式和被试的空间能力则对其不产生影响;(2)对于程序性知识的保持,多媒体信息呈现方式和被试认知风格都会对学习效果产生影响,被试空间能力则不会产生影响,而且被试不同的认知风格在不同的多媒体信息呈现方式上会产生不同的影响;(3)对程序性知识的迁移,多媒体信息呈现方式、被试认知风格和空间能力都会对多媒体环境下的学习效果产生影响,而且被试不同的认知风格和空间能力在不同的多媒体信息呈现方式上都会产生不同的影响。     

The role of color diagnosticity in object recognition and representation

The role of color diagnosticity in object recognition and representation was assessed in three Experiments. In Experiment 1a, participants named pictured objects that were strongly associated with a particular color (e.g., pumpkin and orange). Stimuli were presented in a congruent color, incongruent color, or grayscale. Results indicated that congruent color facilitated naming time, incongruent color impeded naming time, and naming times for grayscale items were situated between the congruent and incongruent conditions. Experiment 1b replicated Experiment 1a using a verification task. Experiment 2 employed a picture rebus paradigm in which participants read sentences one word at a time that included pictures of color diagnostic objects (i.e., pictures were substituted for critical nouns). Results indicated that the “reading” times of these pictures mirrored the pattern found in Experiment 1. In Experiment 3, an attempt was made to override color diagnosticity using linguistic context (e.g., a pumpkin was described as painted green). Linguistic context did not override color diagnosticity. Collectively, the results demonstrate that color information is regularly utilized in object recognition and representation for highly color diagnostic items.     

Developmental changes in the embodied self of spatial perspective taking

Spatial perspective taking consists of mental self‐rotation and other cognitive information processing. Mental self‐rotation is a process of rotating an embodied representational self through mental simulation of the sensorimotor mechanisms underlying actual self‐movement. It was predicted that physical development would affect the operation of the representational self. One hundred and twenty‐five individuals aged 5–80 years (57 children, 35 students, and 33 elderly people) executed a video game task of spatial perspective taking in three conditions of sensorimotor activation: A restrained, stable, and unstable condition. In the linear function formulas considering the degree of rotation and response times, the gradient represented the theoretical speed of mental self‐rotation and the intercept represented other cognitive processing. A significant interaction was found between age group and condition on the gradients, indicating that the response times in the unstable condition were faster than in the other conditions for the children, the restrained condition was slower than the other conditions for the students, while no difference was found for the elderly adults. The results suggest that the influence of sensorimotor activation on the embodied representational self depends on developmental changes in physical control.     

Predicting others’ knowledge: Knowledge estimation as cue utilization

Predicting what others know is vital to countless social and educational interactions. For example, the ability of teachers to accurately estimate what knowledge students have has been identified as a crucial component of effective teaching. I propose the knowledge estimation as cue-utilization framework, in which judges use a variety of available and salient metacognitive cues to estimate what others know. In three experiments, I tested three hypotheses of this framework: namely, that participants do not automatically ground estimates of others’ knowledge in their own knowledge, that judgment conditions shift how participants weight different cues, and that participants differentially weight cues based upon their diagnosticity. Predictions of others’ knowledge were dynamically generated by judges who weighed a variety of available and salient cues. Just as the accuracy of metacognitive monitoring of one’s own learning depends upon the conditions under which judgments of self are elicited, the bases and accuracy of metacognitive judgments for others depends upon the conditions under which they are elicited.     

Representations in Distributed Cognitive Tasks

In this article we propose a theoretical framework of distributed representations and a methodology of representational analysis for the study of distributed cognitive tasks—tasks that require the processing of information distributed across the internal mind and the external environment. The basic principle of distributed representations Is that the representational system of a distributed cognitive task is a set of internal and external representations, which together represent the abstract structure of the task. The basic strategy of representational analysis is to decompose the representation of a hierarchical task into its component levels so that the representational properties at each level can be independently examined. The theoretical framework and the methodology are used to analyze the hierarchical structure of the Tower of Hanoi problem. Based on this analysis, four experiments are designed to examine the representational properties of the Tower of Hanoi. Finally, the nature of external representations is discussed.     

Identifying Representational Competence With Multi-Representational Displays

Increasingly, multi-representational educational technologies are being deployed in science classrooms to support science learning and the development of representational competence. Several studies have indicated that students experience significant challenges working with these multi-representational displays and prefer to use only one representation while problem solving. Here, we examine the use of one such display, a multi-representational molecular mechanics animation, by organic chemistry undergraduates in a problem-solving interview. Using both protocol analysis and eye fixation data, our analysis indicates that students rely mainly on two visual–spatial representations in the display and do not make use of two accompanying mathematical representations. Moreover, we explore how eye fixation data complement verbal protocols by providing information about how students allocate their attention to different locations of a multi-representational display with and without concurrent verbal utterances. Our analysis indicates that verbal protocols and eye movement data are highly correlated, suggesting that eye fixations and verbalizations reflect similar cognitive processes in such studies.     

Drawing is Integrating: An Examination of Students’ Graphic Representations of Multiple Texts

In this study, integration, or students’ connection formation across texts, was examined across two tasks: when undergraduates were asked to complete a writing assignment and a novel, diagram construction task. While the writing assignment asked students to compose an argument based on multiple texts, the diagram construction task asked students to visually represent a set of eight conflicting texts and the relations among them. The Documents Model Framework (DM) was used to code undergraduates’ written responses and diagrams for the type of multiple text representations they featured (i.e., mush models, separate representations models, and documents models of multiple texts). Moreover, written responses and diagrams were coded for the specificity at which they integrated texts, corresponding to the formation of evidentiary, thematic, and contextual relations. Limited associations were found between college students’ written responses and the diagrams constructed. Implications for understanding multiple text integration are discussed.     

When seeing what's wrong makes you right: The effect of erroneous examples on 3D diagram learning

Comprehending 3D diagrams is critical for success in scientific practice and research demonstrates that understanding of 3D geology diagrams can be improved by making predictive sketches. In mathematics, explaining erroneous examples can support learning. This study combined these approaches to better understand how to effectively support 3D geologic diagram understanding. Participants generated sketches, explained erroneous example sketches, or copied and explained correct sketches. It was hypothesized that generating sketches or explaining erroneous cases would improve understanding, but an open question was whether these conditions would differ from each other. Explaining erroneous examples and sketching improved understanding whereas explaining correct sketches did not. Further, explaining erroneous examples was a more efficient strategy than sketching. These results indicate that erroneous examples can be effective for supporting 3D diagram comprehension and may be a practical substitute for some traditional sketching activities in the context of real classrooms where class time is limited.     

Cross-cultural similarity in the love attitudes scale: short form.

Recently, Hendrick, Hendrick, and Dicke presented two short forms of the Love Attitudes Scale, the first using 24 items with 4 items for each subscale and the second using 18 items with 3 items for each subscale. Their data indicated that the two short versions have even stronger psychometric properties than the original scale. This study reports an 18-item short form of the scale developed independently in Taiwan using 460 graduate and undergraduate students in the fall semester of 1997. The results demonstrated a remarkable cross-cultural similarity in the development and response to the short form of the scale and its applicability to a broader cultural setting.     

The functional and developmental organization of cognitive developmental sequences

This study examines the organization and development of 5 domains of reasoning (categorical, quantitative, spatial, causal, and propositional) and the construct validity of a test designed to measure development from early adolescence to early adulthood. The theory underlying the test is first summarized and the conceptual design of the test is then illustrated. Each domain was addressed by tasks tapping abilities known to be acquired in this age period. The test was administered to 629 adolescents ranging in age from 12 to 18 years. Confirmatory factor analysis validated the 5 domains of reasoning and revealed a common factor underlying all domains. The Rasch model was used to scale the items and specify the reliability of the test across the whole sample and within different groups of participants (female, male, students of gymnasium, and students of lyceum). This model showed that the test is highly reliable and invariant across groups. Cluster analysis and the saltus model were applied to uncover successive developmental stage‐like levels of difficulty and showed the presence of five such levels. The procedural and representational characteristics of these levels were also specified and their implications for developmental and cognitive theory were discussed.