Joint attention has been extensively studied in the developmental literature because of overwhelming evidence that the ability to socially coordinate visual attention to an object is essential to healthy developmental outcomes, including language learning. The goal of this study was to understand the complex system of sensory-motor behaviors that may underlie the establishment of joint attention between parents and toddlers. In an experimental task, parents and toddlers played together with multiple toys. We objectively measured joint attention—and the sensory-motor behaviors that (...) underlie it—using a dual head-mounted eye-tracking system and frame-by-frame coding of manual actions. By tracking the momentary visual fixations and hand actions of each participant, we precisely determined just how often they fixated on the same object at the same time, the visual behaviors that preceded joint attention and manual behaviors that preceded and co-occurred with joint attention. We found that multiple sequential sensory-motor patterns lead to joint attention. In addition, there are developmental changes in this multi-pathway system evidenced as variations in strength among multiple routes. We propose that coordinated visual attention between parents and toddlers is primarily a sensory-motor behavior. Skill in achieving coordinated visual attention in social settings—like skills in other sensory-motor domains—emerges from multiple pathways to the same functional end. (shrink)

From the perspective of evolutionary theory, we believe it makes more sense to view the sex differences in spatial cognition as being an evolutionary by-product of selection for optimal rates of fetal development. Geary does not convince us that his proposed selective factors operated with “sufficient precision, economy, and efficiency.” Moreover, the archaeological evidence does not support his proposed evolutionary scenario.

To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within variable environments. This raises the question, how do cognitive systems achieve similarly high degrees of robustness? The aim of this study was to identify a set of mechanisms that enhance robustness (...) in cognitive systems. We identify three mechanisms that enhance robustness in biological and engineered systems: system control, redundancy, and adaptability. After surveying the psychological literature for evidence of these mechanisms, we provide simulations illustrating how each contributes to robust cognition in a different psychological domain: psychomotor vigilance, semantic memory, and strategy selection. These simulations highlight features of a mathematical approach for quantifying robustness, and they provide concrete examples of mechanisms for robust cognition. (shrink)

The central problem in Geary's theory is how differences are conceptualized. Recent research has shown that between-sex differences on certain tasks are a consequence of averaging within sex differences. A mixture distribution models between-sex differences on several tasks well and does not appear congenial to a sexual-selection perspective.

I have provided evidence that Geary's model does not explain male dominance in spatial abilities by sexual selection. The current literature concerning the relations of nonverbal IQ to testosterone, hand preference, and right- and left-hand skill, as well as the organizing effects of testosterone on cerebral lateralization during the perinatal period, does not support Geary's arguments.

Achievement test differences between boys and girls and between young men and young women, mostly favoring males, extend far beyond mathematics. Such pervasive differences, illustrated here, may require an explanatory theory broader than Geary's.

ABSTRACTAdults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude comparison and estimation. Adults with higher mathematics anxiety had lower accuracy on the comparison task and greater percentage absolute error on the estimation task. Unexpectedly, mathematics anxiety was not related to variable strategy use. However, variable strategy use was linked to more accurate (...) magnitude comparisons, especially among adults with lower working memory performance or those who use mathematics less frequently, as well as lower PAE on the estimation task. These findings shed light on the role of strategy variability in fraction problem solving and demonstrate a link between mathematics anxiety and fraction magnitude reasoning, a key predictor of general mathematics achievement. (shrink)

Spatial visualization as a key variable in sex-related differences in mathematical problem solving and spatial aspects of geometry is traced to the 1960s. More recent relevant data are presented. The variability debate is traced to the latter part of the nineteenth century and an explanation for it is suggested. An idea is presented for further research to clarify sex-related brain laterality differences in solving spatial problems.

Spatial and mathematical abilities may be “sex-limited” traits. A sex-limited trait has the same determinants of variation within the sexes, but the genetic or environmental effects would be differentially expressed in males and females. New advances in structural equation modeling allow means and variation to be estimated simultaneously. When these statistical methods are combined with a genetically informative research design, it should be possible to demonstrate that the genes influencing spatial and mathematical abilities are sex-limited in their expression. This approach (...) would give an empirical confirmation of Geary's evolutionary speculations. (shrink)

Geary's is the traditional view of the sexes. Yet each part of his argument – the move from sex differences in spatial ability and social preferences to a sex difference in mathematical ability, the claim that the former are biologically primary, and the sociobiological explanation of these differences – requires considerable further work. The notion of a biologically secondary ability is itself problematic.

We evaluate three of Geary's claims, finding that there is little evidence for sex differences in object- vs. person-orientation; sex differences in competition, even if biologically caused, lead to sex differences in mathematics only given a certain style of teaching; and sex differences in mental rotation, though real, are not well explained in a sociobiological framework or by the proximate biological variables assumed by Geary.

Griffiths and Tenenbaum (2006) asked individuals to make predictions about the duration or extent of everyday events (e.g., cake baking times), and reported that predictions were optimal, employing Bayesian inference based on veridical prior distributions. Although the predictions conformed strikingly to statistics of the world, they reflect averages over many individuals. On the conjecture that the accuracy of the group response is chiefly a consequence of aggregating across individuals, we constructed simple, heuristic approximations to the Bayesian model premised on the (...) hypothesis that individuals have access merely to a sample of k instances drawn from the relevant distribution. The accuracy of the group response reported by Griffiths and Tenenbaum could be accounted for by supposing that individuals each utilize only two instances. Moreover, the variability of the group data is more consistent with this small‐sample hypothesis than with the hypothesis that people utilize veridical or nearly veridical representations of the underlying prior distributions. Our analyses lead to a qualitatively different view of how individuals reason from past experience than the view espoused by Griffiths and Tenenbaum. (shrink)

Working memory resources are needed for processing and maintenance of information during cognitive tasks. Many models have been developed to capture the effects of limited working memory resources on performance. However, most of these models do not account for the finding that different individuals show different sensitivities to working memory demands, and none of the models predicts individual subjects' patterns of performance. We propose a computational model that accounts for differences in working memory capacity in terms of a quantity called (...) source activation, which is used to maintain goal‐relevant information in an available state. We apply this model to capture the working memory effects of individual subjects at a fine level of detail across two experiments. This, we argue, strengthens the interpretation of source activation as working memory capacity. (shrink)

Geary's model is a worthy effort, but ambiguous on important issues. It ignores differential resource allocation, although this follows directly from sexual selection via differential parental investment. Dimorphism in primary traits is arbitrarily attributed to sexual selection via intramale competition, rather than direct evolutionary pressures. Dubious predictions are made about the consequences of raising mathematics achievement.

The purpose of the two studies reported here was to develop an integrated model of the scientific reasoning process. Subjects were placed in a simulated scientific discovery context by first teaching them how to use an electronic device and then asking them to discover how a hitherto unencountered function worked. To do this task, subjects had to formulate hypotheses based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, (...) we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search memory and the other was to generalize from the results of previous experiments. We described the former group as searching an hypothesis space, and the latter as searching an experiment space. In a second study, with 10 adults, we investigated how subjects search the hypothesis space by instructing them to state all the hypotheses that they could think of prior to conducting any experiments. Following this phase, subjects were then allowed to conduct experiments. Subjects who could not think of the correct rule in the hypothesis generation phase discovered the correct rule only by generalizing from the results of experiments in the experimental phase.Both studies provide support for the view that scientific reasoning can be characterized as search in two problem spaces. By extending Simon and Lea's (1974) Generalized Rule Inducer, we present a general model of Scientific Discovery as Dual Search (SDDS) that shows how search in two problem spaces (an hypothesis space and an experiment space) shapes hypothesis generation, experimental design, and the evaluation of hypotheses. The model also shows how these processes interact with each other. Finally, we interpret earlier findings about the psychology of scientific reasoning in terms of the SDDS model. (shrink)

The purpose of the two studies reported here was to develop an integrated model of the scientific reasoning process. Subjects were placed in a simulated scientific discovery context by first teaching them how to use an electronic device and then asking them to discover how a hitherto unencountered function worked. To do this task, subjects had to formulate hypotheses based on their prior knowledge, conduct experiments, and evaluate the results of their experiments. In the first study, using 20 adult subjects, (...) we identified two main strategies that subjects used to generate new hypotheses. One strategy was to search memory and the other was to generalize from the results of previous experiments. We described the former group as searching an hypothesis space, and the latter as searching an experiment space. In a second study, with 10 adults, we investigated how subjects search the hypothesis space by instructing them to state all the hypotheses that they could think of prior to conducting any experiments. Following this phase, subjects were then allowed to conduct experiments. Subjects who could not think of the correct rule in the hypothesis generation phase discovered the correct rule only by generalizing from the results of experiments in the experimental phase.Both studies provide support for the view that scientific reasoning can be characterized as search in two problem spaces. By extending Simon and Lea's (1974) Generalized Rule Inducer, we present a general model of Scientific Discovery as Dual Search (SDDS) that shows how search in two problem spaces (an hypothesis space and an experiment space) shapes hypothesis generation, experimental design, and the evaluation of hypotheses. The model also shows how these processes interact with each other. Finally, we interpret earlier findings about the psychology of scientific reasoning in terms of the SDDS model. (shrink)

Geary's emphasis on hunting ignores the possible importance of other human activities, such as scavenging and gathering, in the evolution of spatial abilities. In addition, there is little evidence that links spatial abilities and math skills. Furthermore, such links have little practical importance given the small size of most differences and girls' superior performance in mathematics classrooms.

Cognitive science has wholeheartedly embraced functional brain imaging, but introspective data are still eschewed to the extent that it runs against standard practice to engage in the systematic collection of introspective reports. However, in the case of executive processes associated with prefrontal cortex, imaging has made limited progress, whereas introspective methods have considerable unfulfilled potential. We argue for a re-evaluation of the standard ‘cognitive mapping’ paradigm, emphasizing the use of retrospective reports alongside behavioural and brain imaging techniques. Using all three (...) sources of evidence can compensate for their individual limitations, and so triangulate on higher cognitive processes. (shrink)

To the extent that Geary's theory concerning biologically primary and secondary behaviors depends on factor analytic methods and findings, it is woefully weak. Factors have been mistakenly called primary mental abilities, but the adjective “primary” represents reification of a mathematical dimension defined by correlations. Fleshing out a factor beyond its mathematical properties requires much additional quantitative experimental and correlational research that goes far beyond mere factoring.

Criticism of sex differences in mathematical ability and sex roles in sociobiology and the pernicious influence of these ideas on education.

Although Geary's partitioning of mathematical abilities into those that are biologically primary and secondary is an advance over most sociobiological theories of cognitive sex differences, it remains untestable and ignores the spatial nature of women's traditional work. An alternative model based on underlying cognitive processes offers other advantages.

The framework of plateaus, dips, and leaps shines light on periods when individuals may be inventing new methods of skilled performance. We begin with a review of the role performance plateaus have played in experimental psychology, human–computer interaction, and cognitive science. We then reanalyze two classic studies of individual performance to show plateaus and dips which resulted in performance leaps. For a third study, we show how the statistical methods of Changepoint Analysis plus a few simple heuristics may direct our (...) focus to periods of performance change for individuals. For the researcher, dips become the marker of exploration where performance suffers as new methods are invented and tested. Leaps mark the implementation of a successful new method and an incremental jump above the path plotted by smooth and steady log–log performance increments. The methods developed during these dips and leaps are the key to surpassing one's teachers and acquiring extreme expertise. (shrink)

Geary proposes a sociobiological hypothesis of how sex differences in math and spatial skills might have jointly arisen. His distinction between primary and secondary math skills is noteworthy, and in some ways analogous to the closed versus open systems postulated to exist for language. In this commentary issues concerning how genes might affect complex cognitive skills, the interpretation of heritability estimates, and prior research abilites are discussed.

In Darwinian terminology, “sexual selection” refers to purely reproductive competition and is conceptually distinct from natural selection as it affects reproduction generally. As natural selection may favor the evolution of sexual dimorphism by virtue of the division of labor between males and females, this possibility needs to be taken very seriously.

The principles of sexual selection were used as an organizing framework for interpreting cross-national patterns of sex differences in mathematical abilities. Cross-national studies suggest that there are no sex differences in biologically primary mathematical abilities, that is, for those mathematical abilities that are found in all cultures as well as in nonhuman primates, and show moderate heritability estimates. Sex differences in several biologically secondary mathematical domains are found throughout the industrialized world. In particular, males consistently outperform females in the solving (...) of mathematical word problems and geometry. Sexual selection and any associated proximate mechanisms influence these sex differences in mathematical performance indirectly. First, sexual selection resulted in greater elaboration in males than in females of the neurocognitive systems that support navigation in three-dimensional space. Knowledge implicit in these systems reflects an understanding of basic Euclidean geometry, and may thus be one source of the male advantage in geometry. Males also use more readily than females these spatial systems in problem-solving situations, which provides them with an advantage in solving word problems and geometry. In addition, sex differences in social styles and interests, which also appear to be related in part to sexual selection, result in sex differences in engagement iii mathematics-related activities, thus further increasing the male advantage in certain mathematical domains. A model that integrates these biological influences with sociocultural influences on the sex differences in mathematical performance is presented in this article. (shrink)

The male advantage in certain mathematical domains contributes to the difference in the numbers of males and females that enter math-intensive occupations, which in turn contributes to the sex difference in earnings. Understanding the nature and development of the sex difference in mathematical abilities is accordingly of social as well as scientific concern. A more complete understanding of the biological contributions to these differences can guide research on educational techniques that might someday produce more equal educational outcomes in mathematics and (...) other academic domains. (shrink)

We challenge the notion that differences in spatial ability are the best or only explanation for observed sex differences in mathematical word problems. We suggest two ideas from the study of autism: sex differences in theory of mind and in central coherence.

Geary's project faces the severe methodological difficulty of tracing the biological effects of gender on mathematical ability in a system that is massively open. Two methodological stratagems he uses are considered. The first is that pancultural sex differences are biological in nature, which is dubious in the domain of mathematics, since it is completely culture-bound. The second is that sociosexual differences are partly caused by biosexual differences, which renders his thesis unfalsifiable and empirically empty.

The target article draws on evolutionary theory to formulate a biosocial model of sex differences in quantitative abilities. Unfortunately, the data do not support some of the crucial hypotheses. The male advantage in geometry is not appreciably greater than the male advantagi in algebra, and the greater male variability in mathematics cited by Gear is not cross-culturally invariant.

Making adaptive choices between solution strategies is a central element of contemporary mathematics education. However, previous studies signal that students make suboptimal choices between mental and written strategies to solve division problems. In particular, some students of a lower math ability level appear inclined to use mental strategies that lead to lower performance. The current study uses a pretest-training-posttest design to investigate the extent to which these students’ choices for written strategies and performance may be increased. Sixth graders of below-average (...) mathematics level (N = 147) participated in one of two training conditions: an explicit-scaffolding training designed to promote writing down calculations or a practice-only training where strategy use was not explicitly targeted. Written strategy choices and performance increased considerably from pretest to posttest for students in both training conditions, but not in different amounts. Exploratory results suggest that students’ strategy choices may also be affected by their attitudes and beliefs and the sociocultural context regarding strategy use. (shrink)

Analyses of bodies of data usually omit some relevant studies. Geary omits some studies looking at functional correlates of basic biological data, studies of developmental implications for functioning, and the recent achievement of acceleration of cognitive development.

Behavioral evidence for the COVIS dual‐process model of category learning has been widely reported in over a hundred publications (Ashby & Valentin, ). It is generally accepted that the validity of such evidence depends on the accurate identification of individual participants' categorization strategies, a task that usually falls to Decision Bound analysis (Maddox & Ashby, ). Here, we examine the accuracy of this analysis in a series of model‐recovery simulations. In Simulation 1, over a third of simulated participants using an (...) Explicit (conjunctive) strategy were misidentified as using a Procedural strategy. In Simulation 2, nearly all simulated participants using a Procedural strategy were misidentified as using an Explicit strategy. In Simulation 3, we re‐examined a recently reported COVIS‐supporting dissociation (Smith et al., ) and found that these misidentification errors permit an alternative, single‐process, explanation of the results. Implications for due process in the future evaluation of dual‐process theories, including recommendations for future practice, are discussed. (shrink)

Huttenlocher et al. (J Exp Psychol Gen 129:220–241, 2000) introduce the category adjustment model (CAM). Given that participants imperfectly remember stimuli (which we refer to as “targets”), CAM holds that participants maximize accuracy by using information about the distribution of the targets to improve their judgments. CAM predicts that judgments will be a weighted average of the imperfect memory of the target and the mean of the distribution of targets. Huttenlocher et al. (2000) report on three experiments and conclude that (...) CAM is “verified”. We attempt to replicate the conditions in Experiment 3 from Huttenlocher et al. (2000). We analyze judgment-level data rather than averaged data. We find evidence of a bias toward a set of recent targets rather than a bias toward the running mean. We do not find evidence of learning. The judgments in our dataset are not consistent with CAM. We discuss other defects in HHV—including dividing by zero. It seems that evidence for CAM is a statistical artifact that appears when researchers analyze data averaged across trials and do not consider a recency bias. (shrink)

This commentary focuses on one of the many issues raised in Geary's target article: the importance of gender differences in spatial ability to gender differences in mathematics. I argue that the evidence for the central role of spatial ability in mathematical ability, or in gender differences in it, is tenuous at best.

Geary suggests that implicit mathematical principles exist across human cultures and transcend sex differences. Is such knowledge present in animals as well, and is it sufficient to account for performance in all species, including our own? I attempt to trace the implications of Gearys target article for comparative psychology, questioning the exclusion of “subitizing” in describing human mathematical performance, and asking whether human researchers function as cultural agents with animals, elevating their implicit knowledge to secondary domains of numerical performance.

Working memory resources are needed for processing and maintenance of information during cognitive tasks. Many models have been developed to capture the effects of limited working memory resources on performance. However, most of these models do not account for the finding that different individuals show different sensitivities to working memory demands, and none of the models predicts individual subjects' patterns of performance. We propose a computational model that accounts for differences in working memory capacity in terms of a quantity called (...) source activation, which is used to maintain goal‐relevant information in an available state. We apply this model to capture the working memory effects of individual subjects at a fine level of detail across two experiments. This, we argue, strengthens the interpretation of source activation as working memory capacity. (shrink)

Most research on risk aversion in behavioral science with human subjects has focused on a component of risk aversion that does not adapt itself to context. More recently, studies have explored risk aversion adaptation to changing circumstances in sequential decision-making tasks. It is an open question whether one can identify evidence, at the single subject level, for such risk aversion adaptation. We conducted a behavioral experiment on human subjects, using a sequential decision making task. We developed a model-based approach for (...) estimating the adaptation of risk-taking behavior with single-trial resolution by modelling a subject’s goals and internal representation of task contingencies. Using this model-based approach, we estimated the subject-specific adaptation of risk aversion depending on the current task context. We found striking inter-subject variations in the adaptation of risk-taking behavior. We show that these differences can be explained by differences in subjects’ internal representations of task contingencies and goals. We discuss that the proposed approach can be adapted to a wide range of experimental paradigms and be used to analyze behavioral measures other than risk aversion. (shrink)

Male superiority in mathematical ability (along with female superiority in verbal fluency) may reflect the operation of an X-Y homologous gene (the right-shift-factor) influencing the relative rates of development of the cerebral hemispheres. Alleles at the locus on the Y chromosome will be selected at a later mean age than alleles on the X, and only by females.