Investigations of metacognition – and also the application of the storehouse and correspondence metaphors – seem as appropriate for laboratory research as for naturalistic research. In terms of measurement, the only quantitative difference between the “input-bound percent correct” and “output-bound percent correct” is the inclusion versus exclusion (respectively) of omission errors in the denominator of the percentages.

Koriat & Goldsmith propose that the correspondence metaphor captures the essence of everyday memory research. We suggest that correspondence is often not at issue because objective assessments of everyday events are frequently lacking. In these cases, other questions arise, such as how individuals evaluate the validity of memories and the significance they attach to those evaluations.

The research guided by the correspondence metaphor is lauded for its emphasis on functional analysis, but the term “correspondence” itself needs clarification. Of the two terms in the relationship, only one is well defined. It is suggested that behavior at acquisition needs to be analyzed and that molecular principles from the learning laboratory might be useful in doing so.

The correspondence metaphor is useful in developing functional models of memory. However, the storehouse metaphor is still useful in developing structural and process models of memory. Traditional research techniques explore the structure of memory; everyday techniques explore the function of memory. We illustrate this point with two examples: amnesia and metamemory. In each phenomenon, both metaphors are useful.

Classical antiquity provides not just the storehouse metaphor, which postdates Plato, but also parts of the correspondence metaphor. In the fifth century B.C., Thucydides (1.22) considered the role of gist and accuracy in writing history, and Aristotle (Poetics 1451b, 1460b 8–11) offered an explanation. Finally, the Greek for truth (alêtheia) means “that which is not forgotten.”

The correspondence view is consistent with a theory of direct remembering that assumes continuity between perception and memory. Two implications of direct remembering for correspondence are suggested. It is assumed that forgetting is exponential, and that remembering at one time is independent of factors influencing remembering at another. Elaboration of the correspondence view in the same terms as perception offers a novel approach to the study of memory.

Koriat & Goldsmith provide an excellent analysis of the flexibility of retrieval processes and how they are situationally dependent. I agree with their emphasis on functional considerations and argue that the traditional laboratory experiment motivates the subject to be accurate. However, I disagree with their strong claim that the quantity–accuracy distinction implies an essential discontinuity between traditional and naturalistic approaches to the study of memory.

Koriat & Goldsmith's distinction between the correspondence and storehouse metaphors is valuable for both memory theory and methodology. It is questionable, however, whether this distinction underlies the heated debate about so called “everyday memory” research. The distinction between experimental and naturalistic methodologies better characterizes this debate. I compare these distinctions and discuss how the methodological distinction, between experimental and naturalistic designs, could give rise to different theoretical approaches.

Our response to the commentators covers four general issues: (1) How useful is our proposed conceptualization of the real-life/laboratory controversy in terms of the contrast between the correspondence and storehouse metaphors? (2) What is the relationship between these two metaphors? (3) What are the unique implications of the correspondence metaphor for memory assessment and theory? (4) What are the nature and role of memory metaphors in memory research? We stress that the correspondence metaphor can be usefully exploited independent of the real-life/laboratory controversy, but that a variety of other metaphors, including the storehouse, should also be utilized in order to more fully capture the myriad facets and functions of memory in everyday life.

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 (i.e., those that emerge primarily in school) 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 (e.g., sex hormones) 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.

Based on Geary's theory, intelligence may determine which males utilize innate spatial knowledge to inform their mathematical solutions. This may explain why math gender differences occur mainly with higher abilities. In support, we found that mental rotation ability served as a mediator of gender differences on the math Scholastic Assessment Test for two high-ability samples. Our research suggests, however, that environment and biology interact to influence mental rotation abilities.

Geary is highly selective in his use of the literature on gender differences. His assumption of consistent female inferiority in mathematics is not necessarily supported by the facts.

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.

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.

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.

Analyses of bodies of data usually omit some relevant studies. Geary omits (1) some studies looking at functional correlates of basic biological data, (2) studies of developmental implications for functioning, and (3) the recent achievement of acceleration of cognitive development.

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.

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.

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.

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.