Sequential processing in comprehension of hierarchical graphs

Hierarchical graphs represent the relationships between non-numerical entities or concepts (like computer file systems, family trees, etc). Graph nodes represent the concepts and interconnecting lines represent the relationships. We recorded participants' eye movements while viewing such graphs to test two possible models of graph comprehension. Graph readers had to answer interpretive questions, which required comparisons between two graph nodes. One model postulates a search and a combined search-reasoning stage of graph comprehension (two-stage model), whereas the second model predicts three stages, two stages devoted to the search of the relevant graph nodes and a separate reasoning stage. A detailed analysis of the eye movement data provided clear support for the three-stage model. This is in line with recent studies, which suggest that participants serialize problem solving tasks in order to minimize the overall processing load. Copyright © 2004 John Wiley & Sons, Ltd.     

Towers of Hanoi and London: contribution of working memory and inhibition to performance

The Tower of Hanoi and Tower of London have become well-established executive function tasks that presumably tap cognitive skills mediated by the frontal cortex. It has been assumed that the two tower tasks are more or less interchangeable and that both measure working memory and inhibition processes. These assumptions were tested in a study involving 37 normal college volunteers (M age = 20 years). Participants were administered the Tower of Hanoi (TOH), Tower of London-Revised (TOL-R), two working memory tests, and two tests of inhibition. The two tower tasks correlated significantly (r = .39), but only moderately. The working memory and inhibition variables explained over one-half of the variance in TOL-R performance; however, there was a relatively weaker contribution of inhibition to TOH performance.     

A constrained Rasch model of trace redintegration in serial recall

The notion that verbal short-term memory tasks, such as serial recall, make use of information in long-term as well as in short-term memory is instantiated in many models of these tasks. Such models incorporate a process in which degraded traces retrieved from a short-term store are reconstructed, or redintegrated (Schweickert, 1993), through the use of information in long-term memory. This article presents a conceptual and mathematical model of this process based on a class of item-response theory models. It is demonstrated that this model provides a better fit to three sets of data than does the multinomial processing tree model of redintegration (Schweickert, 1993) and that a number of conceptual accounts of serial recall can be related to the parameters of the model.     

数学焦虑个体近似数量加工的神经机制:一项EEG研究

近似数量加工是对大数目物体数量在不依赖逐个数数前提下的估计。行为学研究提示高数学焦虑人群近似数量加工能力下降, 但神经机制未明。本研究探讨高数学焦虑个体近似数量加工的神经机制, 比较高低数学焦虑脑电活动的差异:(1)行为上无显著组间差异; (2)高数学焦虑组的P2p成分波幅增加; (3) δ频段ERS及β频段ERD无显著数量比例效应, 而低数学焦虑组在上述指标的数量比例效应显著。本研究为高数学焦虑人群近似数量加工能力下降提供了电生理学的证据。     

What dot clusters and bar graphs reveal: subitizing is fast counting and subtraction

In two studies, we found that dot enumeration tasks resulted in shallow-sloped response time (RT) functions for displays of 1-4 dots and steep-sloped functions for displays of 5-8 dots, replicating results implicating subitizing and counting processes for low and high ranges of dots, respectively. Extracting number from a specific type of bar graph within the same numerical range produced a shallow-sloped but scallop-shaped RT function. Factor analysis confirmed two independent subranges for dots, but all bar graph values defined a unitary factor. Significantly, factor scores and asymmetries both showed correlations of bar graph recognition to dot subitizing but not to dot counting, strongly suggesting that subitizing was used in both enumeration of low numbers of dots and bar graph recognition. According to these results, subitizing appears to be a nonverbal process operating flexibly in either additive or subtractive fashion on analog quantities having spatial extent, a conclusion consistent with a fast-counting model of subitizing but not with other models of the subitizing process.     

Signed difference analysis: Theory and application

Psychological constructs can only be measured indirectly in terms overt behavior, often by means of changes in the level of performance on tasks they are presumed to affect. However, the exact relationship between constructs and the tasks they are presumed to affect is usually not known, which often requires non-essential auxiliary assumptions to be added to a psychological model to allow it to contact the data. Signed difference analysis is a method of deriving testable consequences from psychological models under the general assumption that the relationship between task performance and the constructs or combinations of constructs postulated by the model is at least monotonic. The predictions derived using signed difference analysis do not depend upon estimation of either model parameters or explicit functional relationships. In the present paper, the mathematical theory of signed difference analysis is presented and applied to illustrative problems drawn from research in memory, spatial attention, and reading. The relationships between signed difference analysis and related inferential procedures such as conjoint measurement, state-trace analysis, and double dissociation are discussed.     

Eye movements reveal distinct search and reasoning processes in comprehension of complex graphs

Hierarchical graphs (e.g. file system browsers, family trees) represent objects (e.g. files, folders) as graph nodes, and relations (subfolder relations) between them as lines. In three experiments, participants viewed such graphs and carried out tasks that either required search for two target nodes (Experiment 1A), reasoning about their relation (Experiment 1B), or both (Experiment 2). We recorded eye movements and used the number of fixations in different phases to identify distinct stages of comprehension. Search in graphs proceeded like search in standard visual search tasks and was mostly unaffected by graph properties. Reasoning occurred typically in a separate stage at the end of comprehension and was affected by intersecting graph lines. The alignment of nodes, together with linguistic factors, may also affect comprehension. Overall, there was good evidence to suggest that participants read graphs in a sequential manner, and that this is an economical approach of comprehension. Copyright © 2010 John Wiley & Sons, Ltd.     

不同类型数学任务的PASS认知加工发展特点

PASS理论是由Das和Naglieri提出的关于智力理论的一种认知过程理论。研究采用以PASS理论为基础编制而成的认知评估系统（第二版简版,CAS-2B）为研究工具,选取226名二年级、四年级以及七年级的学生,探讨PASS过程在数学计算流畅性,数学问题解决及数学推理等不同数学任务中的作用。研究结果显示：PASS模型各过程在三个年级的不同数学任务上各有侧重。在数学推理任务中,同时性加工对三个年级的数学推理任务预测显著,解释率为15%~17%,注意过程只在二年级对学生的数学推理任务预测;在数学计算流畅性任务中,注意过程随着年级的升高,其预测作用逐渐减退,解释率为5%~24%,计划功能的作用随年级的升高而逐渐突显;在数学问题解决任务中,继时性加工与注意功能对二年级预测显著,四年级时突显了计划和同时性加工的作用。不同复杂性的数学任务具有不同的认知特点,编码加工过程对于较复杂数学任务作用明显;计划与注意过程对简单数学任务作用明显。研究结果为今后不同年级学生开展有针对性的数学学习训练提供了理论基础。     

How do mothers know? infants' chronological age or infants' performance as determinants of adaptation in maternal instruction?

In the present study a longitudinal disign was adopted to determine development as compared to age-related changes in maternal task instruction to children in their second year. The interactions of 12 mother-infant pairs doing simple tasks (tower building, form sorting), were video-recorded at bimonthly intervals between the infants' 14th and 22nd month. Relative frequency of infants' task attempts was chosen as an indicator of the competence to pursue complex action intentions—an essential component of action competence. For purpose of analysis the age of the infants was cross-tabulated with the rate of infants' task attempts as potential predictors for maternal efforts to motivate the child. The analysis was performed using log-linear modeling and contrasting a development-centered with an age-centered model. The development-centered model assumes that the effect of infant's age is restricted to its influence on infant's current performance rate which, in turn, affects kind and rate of maternal attempts to elicit task action in the child, and the differential effect of tasks. The development-centered model was shown to be superior to the age-centered model. Implications of the results are discussed with regard to the current debate on substituting chronological age as an independent variable by psychologically significant developmental variables.     

Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non‐symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta‐analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two‐level random‐effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non‐symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non‐symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school‐aged children and for adults.     

A mathematical model of the interaction between bottom-up and top-down attention controllers in response to a target and a distractor in human beings

Top-down and bottom-up attention are two systems that allocate our neuronal resources for processing different stimuli. To do the tasks efficiently, it is required to suppress irrelevant information. In the presence of both target and distractor, synchronization or desynchronization between the activities of neuronal responses has been observed in different regions of the brain. In the current study, we have proposed a mathematical model to show how the interaction between top-down and bottom-up attention, through synchronization and desynchronization, can lead to the suppression of distractor effects in human beings. The model structure was inspired by the results of neurological studies. The model consists of several oscillating units as a representation of top-down and bottom-up neuronal processing resources. These units communicate with each other through synchronization and desynchronization procedures.Results of simulations showed that how the mutual interaction between top-down and bottom-up units, which was done using synchronization and desynchronization procedures, led to the selective or divided attention between the target and distractor. It was shown that the activity of responsive units to the distractor could be suppressed by a desynchronous signal transmitted from the top-down attention unit. This model suggests a justification for brain waves synchronization or desynchronization during attentionally demand tasks. The proposed model also provides a tool to investigate the effect of some influencing factors such as the distractor intensity or similarity between the distractor and the target on the function of top-down and bottom-up systems.     

Integration processes during frequency graph comprehension: Performance and eye movements while processing tree maps versus pie charts

Frequency graph types differ in the way how data are translated into visual representations. We compared 2 visualization methods, a traditional circular representation (pie chart) and a rectangular representation (constant column width tree map), which were hypothesized to differ regarding the cognitive ease of visual comparison processes. Performance was evaluated in tasks involving proportion and comparison judgments under both highly controlled and more realistic circumstances. The results showed performance benefits (in terms of reduced response times or error rates) for rectangular representations. Additional eye movement analyses revealed that this benefit was mainly due to a facilitation of scanning the graph for relevant information. The results suggest that facilitating comparison processes by representing the critical variable in less complex visual dimensions (i.e., straight length with constant orientation instead of surface area or curved length) eventually enhances the efficiency of integration processes during graph comprehension.     

Graph‐Framing Effects in Decision Making

This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate‐to‐differentiate approach, we proposed a two‐process model of graph‐framing effects. In the first mental process, the graph‐editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate‐to‐differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other‐dimensional difference to be the determinant of the final choice. Four experiments were tested for graph‐framing effects. Experiment 1 found a graph‐framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph‐framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph‐framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph‐framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph‐framing effects. Copyright © 2011 John Wiley & Sons, Ltd.     

Task bias and the accuracy of judgment: Setting a baseline for expected group performance

When a judgment task evokes unbiased estimates (i.e. the errors in individual judgments are distributed randomly around the true value), mathematical aggregation of individual estimates, even by a simple arithmetic mean, often will outperform all group members. However, when a task evokes biased estimates, mathematical aggregation does not perform so well. In this study, simulated data were accumulated to specify the expected' accuracy of mathematical aggregation relative to the accuracy of observed judgment of individual group members under varying conditions of task bias. Three types of judgment tasks were employed: (1) single-estimate, holistic tasks, (2) multiple-estimate, ranking tasks, and (3) multi-cue, decomposed tasks. Findings indicated across all task types that a large percentage of judgment-making group estimates formed strictly by computing the arithmetic mean of individual estimates performed better than their most capable members when a judgment task evoked little or no bias, a result particularly pronounced for ranking tasks. When the task was more greatly bias-evoking, a large percentage of parallel groups performed more poorly than average (or median) members, again a pattern more starkly evident for ranking tasks. These results suggest that the extent to which a judgment task evokes bias in a population of prospective group members is an important explanatory variable deserving much greater attention in the study of group performance. For example, an assertion about the efficacy of a particular group intervention based on a reliable demonstration of group performance as accurate as the most capable members may be unfounded when a task evokes no bias, since the baseline standard under such conditions should be much higher. By selecting tasks and populations that jointly produced highly biased estimates, researchers can lower the performance floor enough to detect (with reasonably small samples of groups) experimental effects should they occur.     

Type of stimulus mediates the relationship between working-memory performance and type of precocity

The relationship between type of stimulus (numeric and verbal) and type of precocity (mathematical and verbal) was examined in tasks designed to tap three aspects of working memory: encoding, capacity, and manipulation of information. The tasks included semantic categorization, odd-even categorization, recall of five-item lists after semantic categorization, and recall of items in a continuous paired-associates task. Correlations between task performance and the mathematical and verbal portions of the Scholastic Aptitude Test (SAT-M and SAT-V) were computed for gifted youth. There were no sex differences in the performance measures or in the pattern of correlations between performance and SAT scores. The analysis revealed positive relationships between SAT-M scores and numeric categorization latency, recall in the continuous paired-associate task with words and digits, and recall of digit lists. SAT-V scores were related only to word recall in the continuous paired-associate task and recall of word lists. In the working-memory tasks used, mathematical precocity is more strongly related to performance than is verbal precocity. The relationship is especially strong with numeric stimuli, even when the numeric stimuli are simply items to be remembered. The relationship between type of stimulus and type of precocity suggests underlying differences between verbally and mathematically precocious youth in how different types of stimuli are represented in memory.     

Effects of auditory context cues and training on performance of a point estimation sonification task

Research on auditory graph interpretation has investigated mappings, scalings, and polarities, as well as the addition of some contextual design features like clicks. However, little has been done to quantify the benefits of those or other design features, or to investigate training in specific sonification tasks such as point estimation. In Study 1, 160 undergraduates listened to auditory graphs and estimated exact dollar values at specific points in the graph. X‐axis context (clicks) improved performance by aiding time calibration. Y‐axis context (reference tones) that provided scaling cues improved performance. In Study 2, listeners performed similar tasks with continuous as opposed to discrete stimuli, and with or without training. X‐axis clicks did not help in this case. Training improved performance overall. When there was no training, y‐axis context improved performance to the level of trained listeners, suggesting the effects of training and y‐axis were comparable, but not additive. Copyright © 2005 John Wiley & Sons, Ltd.     

A graph theory model of the semantic structure of attitudes

The semantic structure underlying the attitudes of pretreatment and posttreatment drug addicts was modeled using a network analysis of free word associations. Measures of graph theoretic properties were used to assess structural differences in the associative networks of the two populations. These measures modeled the information processes of associative networks proposed in the spreading activation theory of semantic processing. As expected based on graph theory, the structure of the associative networks of post-treatment subjects was more dense, less constrained, and more hierarchically organized by the self concept. In a test of the network model, the subjects' evaluations of concepts in the associative network were found to be a function of their evaluations of semantically similar concepts. Although preliminary and limited, the results suggest that graph theory may provide a broad mathematical foundation for diverse models of cognitive systems.The research was funded by a grant from the National Institute for Drug Abuse to the Institute of Cultural Studies, Inc.Daytop Village.     

工作记忆训练及对数学能力的迁移作用

工作记忆缺陷会影响个体数学能力发展。通过记忆策略、广度、刷新、转换等功能的工作记忆训练,可以改善个体认知功能。然而,工作记忆训练对个体的阅读、数学、流体智力等方面的远迁移效果并不一致。研究表明,工作记忆训练可以改善数感、视觉空间能力、推理能力等数学一般技能;也会通过改善语音工作记忆以及空间能力促进数学计算能力,或者通过改善中央执行系统,提升数学问题表征、模式识别、解题迁移、策略选择等复杂的过程,从而促进数学问题解决能力。因此,区分不同数学任务的认知过程,可以获得工作记忆训练对数学能力迁移效果的进一步证据。今后,神经影像学的证据或许也是未来工作记忆训练对数学能力提高的又一佐证。     

The area above the ordinal dominance graph and the area below the receiver operating characteristic graph

Receiver operating characteristic graphs are shown to be a variant form of ordinal dominance graphs. The area above the latter graph and the area below the former graph are useful measures of both the size or importance of a difference between two populations and/or the accuracy of discrimination performance. The usual estimator for this area is closely related to the Mann-Whitney U statistic. Statistical literature on this area estimator is reviewed. For large sample sizes, the area estimator is approximately normally distributed. Formulas for the variance and the maximum variance of the area estimator are given. Several different methods of constructing confidence intervals for the area measure are presented and the strengths and weaknesses of each of these methods are discussed. Finally, the Appendix presents the derivation of a new mathematical result, the maximum variance of the area estimator over convex ordinal dominance graphs.