Understanding spatial transformations: similarities and differences between mental rotation and mental folding

Mental rotation and mental folding, two widely used measures of spatial ability, both require the dynamic spatial transformation of objects with respect to their internal spatial structure. Traditionally, however, these two skills have been considered quite distinct, based primarily on factor analyses of psychometric data. This paper reviews the similarities and differences between mental rotation and mental folding from a variety of perspectives, including their definitions, component cognitive processes, neurological bases, developmental trajectories, malleability, predictive validity, and psychometric properties. We conclude that mental rotation and mental folding are similar in many respects. However, the tasks differ in whether they require rigid or non-rigid transformations of objects. In addition, mental rotation shows robust sex-related differences whereas mental folding does not. We also identify specific questions for which research is lacking.     

Individual differences in cognitive arithmetic

Unities in the processes involved in solving arithmetic problems of varying operations have been suggested by studies that have used both factor-analytic and information-processing methods. We designed the present study to investigate the convergence of mental processes assessed by paper-and-pencil measures defining the Numerical Facility factor and component processes for cognitive arithmetic identified by using chronometric techniques. A sample of 100 undergraduate students responded to 320 arithmetic problems in a true-false reaction-time (RT) verification paradigm and were administered a battery of ability measures spanning Numerical Facility, Perceptual Speed, and Spatial Relations factors. The 320 cognitive arithmetic problems comprised 80 problems of each of four types: simple addition, complex addition, simple multiplication, and complex multiplication. The information-processing results indicated that regression models that included a structural variable consistent with memory network retrieval of arithmetic facts were the best predictors of RT to each of the four types of arithmetic problems. The results also verified the effects of other elementary processes that are involved in the mental solving of arithmetic problems, including encoding of single digits and carrying to the next column for complex problems. The relation between process components and ability measures was examined by means of structural equation modeling. The final structural model revealed a strong direct relation between a factor subsuming efficiency of retrieval of arithmetic facts and of executing the carry operation and the traditional Numerical Facility factor. Furthermore, a moderate direct relation between a factor subsuming speed of encoding digits and decision and response times and the traditional Perceptual Speed factor was also found. No relation between structural variables representing cognitive arithmetic component processes and ability measures spanning the Spatial Relations factor was found. Results of the structural modeling support the conclusion that information retrieval from a network of arithmetic facts and execution of the carry operation are elementary component processes involved uniquely in the mental solving of arithmetic problems. Furthermore, individual differences in the speed of executing these two elementary component processes appear to underlie individual differences on ability measures that traditionally span the Numerical Facility factor.(ABSTRACT TRUNCATED AT 400 WORDS)     

The role of experience in spatial test performance: A meta-analysis

The hypothesis that spatial ability is, in part, experientially determined, and that sex differences in spatial ability can be explained by sex differences in spatial experience, can be studied in a correlational manner by examining the relationship between spatial activity participation and spatial ability test performance for males and females. Alternatively, an experimental training situation, comparing male and female susceptibility to training, has been proposed to test the hypothesis that environment has an impact on spatial skills and sex differences in ability. Both lines of research are reviewed here, through the use of meta-analytic techniques. The first meta-analysis reveals a weak but reliable relationship between spatial activity participation and spatial ability. This relationship appears similar for males and females. The second meta-analysis reveals that spatial ability test performance can be improved by training for both sexes. This improvement does not appear different for males and females, however, contrary to a predominant hypothesis in the literature. Training to asymptote may be a better test of the relevance of differential experience to sex differences. Content and duration of training are also discussed as important factors in the effectiveness of training.This research was supported by Grant No. MH39671 from the National Institute of Mental Health. A version of this paper was presented at the biennial meetings of the Society for Research in Child Development, Baltimore, Maryland, April 1987. We are grateful to Margaret Signorella and Susan Resnick for providing data. We would also like to thank Judith Dubas, Susan Resnick, Ralph Rosnow, Carolyn Spies, Lance Weinmann, and Marsha Weinraub for helpful comments on earlier drafts of this article.     

Mental rotation and real-world wayfinding

Sex differences in mental rotation skills are a robust finding in small-scale laboratory-based studies of spatial cognition. There is almost no evidence in the literature, however, relating these skills to performance on spatial tasks in large-scale, real-world activities such as navigating in a new city or in the woods. This study investigates the connections between mental rotation skills as measured by the Vandenburg-Kuse Mental Rotations test and the performance of college students (n=211) navigating a 6-km orienteering course. The results indicate that mental rotation skills are significantly correlated with wayfinding performance on an orienteering task. The findings also replicate sex differences in spatial ability as found in laboratory-scale studies. However, the findings complicate the discussion of mental rotation skills and sex because women often performed as well as men despite having lower mean test scores. This suggests that mental rotation ability may not be as necessary for some women's wayfinding as it is for men's navigation.     

Sex differences in intellectual functioning: How much of a difference do genes make?

An X-linkage theory of inheritance of genes controlling sex differences in major intellectual traits is critically examined. A review of the research suggests that the mechanism of inheritance of differences in spatial visualization ability is X-linked recessive and its expression is probably testosterone-limited. However, the evidence concerning inheritance of differences in IQ does not support an X-linkage theory. Several characteristics of heritability estimates are discussed, including their specificity to a particular population at a certain point in time, their fluctuation with changes in amount of environmental variation, and the necessity of unconfounding sex and treatment in order to better determine the relationship between heritability and changeability of sex differences in specific intellectual trait expression.Parts of this paper were presented at the Western Psychological Association Convention, 1974.     

Gender, level of spatial ability, and lateralization of mental rotation

The present study indicates that some of the inconsistencies in studies of the lateralization of mental rotation may be a consequence of uncontrolled individual differences in the general level of spatial ability. In order to investigate the relation between spatial ability and the lateralization of mental rotation, 48 subjects (24 males and 24 females) were divided into three groups based on their performance on a standardized test of spatial ability. They then performed a lateralized two-dimensional mental rotation task. The results showed the typical mental rotation function in that angle of rotation and reaction time were linearly related. A significant spatial ability by visual field interaction indicated that subjects with low spatial ability had a left field advantage, whereas subjects with medium spatial ability showed no field advantage and subjects with high spatial ability showed a right field advantage. Gender also interacted with visual field, with males showing a left visual superiority and females an insignificant right visual field advantage. A significant three-way interaction of gender, spatial ability, and angle of rotation reflected the fact that low spatial males were more profoundly affected by rotation than the other groups. The results suggest that at least some of the inconsistent findings in studies of lateralization of mental rotation may be accounted for by differences in the level of spatial ability.     

运算动量效应的理论解释及其发展性预测因素

了解运算偏差的形成与发展对探索算数运算系统的内在机制具有重要意义,早期的算数运算能力是儿童理解和进行复杂数学运算的基础。运算动量偏差是指个体在进行基本数学运算时倾向于高估加法运算结果而低估减法运算结果的一种运算偏差,主要包括三种理论解释,即注意转移假说、启发式解释和压缩解释。鉴于运算动量效应在成年群体中相对稳定却在不同发展阶段儿童中存在不一致的证据,数学能力的提高与空间注意的成熟可结合不同的理论解释来阐明儿童发展过程中运算动量效应的变化趋势。未来可以进一步整合多种研究任务以揭示运算动量效应的发展轨迹,考察数量表征系统与运算动量效应间的关联,探究运算动量效应在不同运算符号中的稳定性,探讨不同因素共同作用对运算动量效应的影响,并设计有关数学能力的干预措施以减少运算动量效应这一运算偏差。     

The relationship between mental rotation and arithmetic: do number line estimation,working memory,or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.     

An investigation of cognitive test performance across conditions of silence,background noise and music as a function of neuroticism

The present study investigates the role of trait neuroticism on cognitive performance under distraction. Seventy participants were given a personality test and then undertook a number of different cognitive tasks in silence, in the presence of popular music and in background noise. It was predicted that performance on a general intelligence test, a test of abstract reasoning, and a mental arithmetic task would be adversely affected by background sounds. It was predicted that neuroticism would be negatively correlated with performance on the mental arithmetic task but only when the individuals were working in the presence of background sound. Stable vs. unstable participant's performance on a mental arithmetic task during noise was significantly higher as predicted. The results provided partial support for the hypotheses and are discussed with respect to previous findings in the literature on personality (particularly introversion–extraversion) and distraction on cognitive task performance. Limitations are noted.     

Sex differences in emotion recognition ability: The mediating role of trait emotional awareness

Although previous research on emotion recognition ability (ERA) has found consistent evidence for a female advantage, the explanation for this sex difference remains incompletely understood. This study compared males and females on four emotion recognition tasks, using a community sample of 379 adults drawn from two regions of the United States (stratified with respect to age, sex, and socioeconomic status). Participants also completed the Levels of Emotional Awareness Scale (LEAS), a measure of trait emotional awareness (EA) thought to primarily reflect individual differences in emotion concept learning. We observed that individual differences in LEAS scores mediated the relationship between sex and ERA; in addition, we observed that ERA distributions were noticeably non-normal, and that—similar to findings with other cognitive performance measures—males had more variability in ERA than females. These results further characterize sex differences in ERA and suggest that these differences may be explained by differences in EA—a trait variable linked primarily to early learning.     

A genetic explanation for no sex difference in spatial ability among Eskimos.

Superior spatial ability may be inherited as an X-linked recessive trait. Since the sex ratio for an X-linked recessive trait depends on the gene frequency of the recessive allele, the absence of a sex difference in Eskimo spatial ability may reflect an unusually high frequency of the recessive allele in the Eskimo population.     

Mental rotation of letters,pictures, and three-dimensional objects in German dyslexic children

This study examines mental rotation ability in children with developmental dyslexia. Prior investigations have yielded equivocal results that might be due to differences in stimulus material and testing formats employed. Whereas some investigators found dyslexic readers to be impaired in mental rotation, others did not report any performance differences or even superior spatial performance for dyslexia. Here, we report a comparison of mental rotation for letters, three-dimensional figures sensu Shepard and Metzler, and colored pictures of animals or humans in second-grade German dyslexic readers. Findings indicate that dyslexic readers are impaired in mental rotation for all three kinds of stimuli. Effects of general intelligence were controlled. Furthermore, dyslexic children were deficient in other spatial abilities like identifying letters or forms among distracters. These results are discussed with respect to the hypotheses of a developmental dysfunction of the parietal cortex or a subtle anomaly in cerebellar function in dyslexic readers.     

Mental rotation of letters, pictures, and three-dimensional objects in German dyslexic children.

This study examines mental rotation ability in children with developmental dyslexia. Prior investigations have yielded equivocal results that might be due to differences in stimulus material and testing formats employed. Whereas some investigators found dyslexic readers to be impaired in mental rotation, others did not report any performance differences or even superior spatial performance for dyslexia. Here, we report a comparison of mental rotation for letters, three-dimensional figures sensu Shepard and Metzler, and colored pictures of animals or humans in second-grade German dyslexic readers. Findings indicate that dyslexic readers are impaired in mental rotation for all three kinds of stimuli. Effects of general intelligence were controlled. Furthermore, dyslexic children were deficient in other spatial abilities like identifying letters or forms among distracters. These results are discussed with respect to the hypotheses of a developmental dysfunction of the parietal cortex or a subtle anomaly in cerebellar function in dyslexic readers.     

Spatial ability in secondary school students: Intra‐sex differences based on self‐selection for physical education

Past research has demonstrated consistent sex differences with men typically outperforming women on tests of spatial ability. However, less is known about intra‐sex effects. In the present study, two groups of female students (physical education and non‐physical education secondary students) and two corresponding groups of male students explored a large‐scale virtual shopping centre. In a battery of tasks, spatial knowledge of the shopping centre as well as mental rotation ability were tested. Additional variables considered were circulating testosterone levels, the ratio of 2D:4D digit length, and computer experience. The results revealed both sex and intra‐sex differences in spatial ability. Variables related to virtual navigation and computer ability and experience were found to be the most powerful predictors of group membership. Our results suggest that in female and male secondary students, participation in physical education and spatial skill are related.     

Sex differences in episodic memory: minimal influence of estradiol

Sex differences exist for several cognitive tasks and estrogen has been suggested to influence these differences. Eighteen men and 18 women were matched on age and estradiol level. Potential sex differences were assessed in episodic memory, semantic memory, verbal fluency, problem solving, and visuospatial ability. Significant sex differences, favoring women, were found for tasks assessing episodic memory. Correlations between estradiol level and cognitive performance were significant for face recognition in females. Since sex differences remained in verbal episodic memory tasks and face recognition despite matched levels of estradiol, circulating estradiol does not appear to be of paramount consequence for observed sex differences in episodic memory.     

Spatial congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval

It is known that number and space representations are connected to one another in numerical and arithmetic abilities. Numbers are represented using the metaphor of a mental number line, oriented along horizontal and vertical space. This number line also seems to be linked to mental arithmetic, which is based partly on arithmetic fact retrieval. It seems that number representation and mental arithmetic are linked together. The present study tested the effect of spatial contextual congruency between stimulus presentation and response key arrangements in arithmetic fact retrieval, using number-matching and addition verification tasks. For both tasks in Experiment 1, a contextual congruency effect was present horizontally (i.e., horizontal presentation of stimuli and horizontal response key alignments) but not vertically (i.e., vertical presentation of stimuli but horizontal response key alignments). In Experiment 2, both tasks showed a contextual congruency effect for both spatial conditions. Experiment 1 showed that the interference and distance effects were found in the horizontal condition, probably because of the spatial congruency between stimulus presentation and response key arrangements. This spatial congruency could be related to the activation of the horizontal number line. Experiment 2 showed similar interference and distance effects for both spatial conditions, suggesting that the congruency between stimulus presentation and response alignment could facilitate the retrieval of arithmetic facts. This facilitation could be related to the activation of both horizontal and vertical number lines. The results are discussed in light of the possible role of a mental number line in arithmetic fact retrieval.     

A lateralization of function approach to sex differences in spatial ability: a reexamination

The current study assessed the lateralization of function hypothesis (Rilea, S. L., Roskos-Ewoldsen, B., & Boles, D. (2004). Sex differences in spatial ability: A lateralization of function approach. Brain and Cognition, 56, 332–343) which suggested that it was the interaction of brain organization and the type of spatial task that led to sex differences in spatial ability. A second purpose was to evaluate explanations for their unexpected findings on the mental rotation task. In Experiment 1, participants completed the Water Level, Paper Folding, and mental rotation tasks (using an object-based or self-based perspective), presented bilaterally. Sex differences were only observed on the Water Level Task; a right hemisphere advantage was observed on Water Level and mental rotation tasks. In Experiment 2, a human stick figure or a polygon was mentally rotated. Men outperformed women when rotating polygons, but not when rotating stick figures. Men demonstrated a right hemisphere advantage when rotating polygons; women showed no hemisphere differences for either stimulus. Thus, hemisphere processing, task complexity, and stimulus type may influence performance for men and women across different spatial measures.     

Spatial visualization and sex differences in quantitative ability

The hypothesis that sex differences in spatial visualization ability might account for sex differences in mathematical ability was supported for a group of 183 male and 81 female college students. With spatial visualization statistically controlled, no significant sex differences in Quantitative Scholastic Aptitude Test (QSAT) scores was found; including sex as a predictor variable increased the variance explained by less than 1%. Although the slope of the regression of mathematics on spatial visualization did not differ as a function of sex, males were somewhat more predictable than females. As the OSAT of both males and females high on spatial visualization was more predictable than the QSAT of those scoring less well, it appears that the sex difference in predictability is due to males having higher spatial ability than females.     

Sex differences in parietal lobe morphology: relationship to mental rotation performance

Structural magnetic resonance imaging (MRI) studies of the human brain have reported evidence for sexual dimorphism. In addition to sex differences in overall cerebral volume, differences in the proportion of gray matter (GM) to white matter (WM) volume have been observed, particularly in the parietal lobe. To our knowledge there have been no studies examining the relationship between the sex differences in parietal lobe structure and function. The parietal lobe is thought to be involved in spatial ability, and particularly involved in mental rotation. The purpose of this study is to examine whether sex differences in parietal lobe structure are present, and if present to relate these differences to performance on the mental rotations test (MRT). We found that women had proportionately greater gray matter volume in the parietal lobe compared to men, and this morphologic difference was disadvantageous for women in terms of performance on the MRT. In contrast, we found that men compared to women had proportionately greater parietal lobe surface area, and this morphologic difference was associated with a performance advantage for men on mental rotation. These findings support the possibility that the sexual dimorphism in the structure of the parietal lobe is a neurobiological substrate for the sex difference in performance on the mental rotations test.     

DÉPENDANCE-INDÉPENDANCE À L'ÉGARD DU CHAMP ET RÉSOLUTION DE SYLLOGISMES LINÉAIRES*

A formal analysis of a set of linear syllogisms led the author to a definition of two factors involved in the construction of these syllogisms: (a) a logical factor linking the two premises (I, identical relation; R, reciprocal relation), (b) a linguistic factor concerning the formulation of the premises (affirmative or negative propositions). Thirty-six French adolescents were given a set of 48 problems in which the logical and the linguistic factors were combined in the same proportion. These subjects were of equal ability with regard to the functioning of the formal operatory systems, but of different abilities with respect to field dependence–independence. The results show a significant correlation between latencies and field dependence–independence. The analysis of this correlation leads to the conclusion that the restructuration processes worked more slowly in the dependent subjects than in the independent subjects. It appears from the analysis of the results that the differences observed in the subjects' reasoning processes may be interpreted in terms of mobility of intellectual operations.