A reexamination of mental arithmetic models and data: A reply to Ashcraft

In a review of the chronometric literature, M. Ashcraft (1982, Developmental Review, 2, 213–236) concludes that adults store each basic arithmetic fact in a table-like retrieval network. In my commentary (1983, Developmental Review, 3, 225–230), I argued that procedural knowledge (stored rules, principles, or heuristics) might be a cognitively more economical basis for generating many number combinations. In this paper, I draw an analogy between this alternative model of number fact representation and how computers efficiently reconstruct arithmetic combinations, note that the research findings do not clearly support any one model of mental arithmetic, and attempt to address Ashcraft's (1983, Developmental Review, 3, 231–235) criticisms of my model.     

Affordances and infant learning: A reply to Horowitz

We reply to three major points made by F. Horowitz (1983, Developmental Review, 3, 405–409) in her commentary on the ecological approach to infant knowing presented by E. Goldfield (1983, Developmental Review, 3, 371–404). We first clarify the relation between perceiving and acting from an ecological perspective, and distinguish between affordances as environmental properties scaled to the perceiver/performer and representations as mental structures. We then present a critique of the process of association offered by Horowitz as an explanation of infant learning. Association fails to specify the constraints on what is learned, while the ecological process of noticing affordances, presented by Goldfield, considers such constraints. We conclude by presenting operational criteria for measuring affordances and evidence that perception is scaled to the perceiver/performer.     

The development of procedural knowledge: An alternative explanation for chronometric trends of mental arithmetic

In a review of the Chronometrie literature, M. H. Ashcraft (Developmental Review, 1982, 2, 213–236) concluded that the development of number fact efficiency is due to a shift from relying on procedural knowledge such as counting to relying on declarative knowledge (a stored network of facts). This model assumes that all procedural processes are slow or remain slow, which is probably not the case. An alternative account posits that the key change in number fact efficiency involves a shift from slow counting procedures to principled procedural knowledge. As rules, heuristics, and principles become more familiar and interconnected, their use, for example, in producing the number facts becomes more automatic. The use of such procedural knowledge would be cognitively more economical than storing individual facts in long-term memory. Finally, existing Chronometric data can readily be interpreted in terms of this alternative model.     

The case of the disappearing disagreements: A reply to Yussen

S. R. Yussen (1984, Developmental Review, 4, 139–144) and I have few disagreements. The major one seems to be in what the purpose of my article (R. J. Sternberg, 1984, Developmental Review, 4, 113–138) should have been. I believe the article fulfills my own purpose, if not Yussen's.     

A failure to differentiate

The K. J. Rust and T. S. Kendler paper (1987, Developmental Review, 7, 326–362) makes two claims to publication: (1) it claims to show (and implicitly, to show for the first time) that a nonselective learning model such as Spence's can fit the basic phenomenon of independent subproblem learning, and (2) it claims two experimental tests of the nonselective theory versus the differentiation theory interpretations of independent subproblem learning. Neither claim is valid and both claims reflect a failure to differentiate the literature. Moreover, Kendler's basic assumption of a developmental difference in the nature of learning is questionable.     

Procedural knowledge versus fact retrieval in mental arithmetic: A reply to Baroody

Based on a review of reaction time studies, a model of mental arithmetic performance which emphasizes the process of fact retrieval from organized memory representations was proposed (M. H. Ashcraft, Developmental Review, 1982, 2, 213–236). In contrast to this view A. J. Baroody (Developmental Review, 1983, 3, 225–230) proposes that most mental arithmetic performance depends on procedural knowledge such as rules, heuristics, and principles. While Baroody's idea is both intriguing and potentially important, its exposition is quite vague and speculative. Without concrete suggestions as to the nature of the proposed rules and heuristics, especially for routine problems like 4 + 3 and 8 × 5, Baroody's proposal appears to be pertinent only to special cases like N + 0 and N + 1. Lacking this sort of elaboration, the alternative does not provide a useful or compelling explanation of the existing Chronometric results, and seems, at best, to be premature.     

Elkind on egocentrism

The purpose of this paper is to respond to D. Elkind's (1985, Developmental Review, 5, 218–226) reply to D. Lapsley and M. Murphy's (1985, Developmental Review, 5, 201–217) critique of the adolescent egocentrism theory. After a reprise of the issues in contention, we address the problem of theoretical consistency and self-other differentiation in Dr. Elkind's (1967, Child Development, 38, 1025–1034) theory. The role of formal operations in the Lapsley and Murphy (1985) account of the imaginary audience and personal fable is revised, and the empirical support for Elkind's theory is reviewed. We conclude that there are good conceptual and empirical grounds for doubting the major assumptions of the adolescent egocentrism theory, and that the Lapsley and Murphy (1985) framework has promise in suggesting theoretical integration with other approaches to the self.     

Acquiring new word meaning: What does it tell us about development

R. J. Sternberg (1984, Developmental Review, 4, 113–138) offers a thoughtful and provocative essay on how individuals acquire meanings for novel or unfamiliar nouns. The Sternberg essay, however, is incomplete on a number of grounds. By stressing general processes and specific knowledge as critical components in the acquisition of verbal concepts, for example, it overlooks two logically complementary categories—specific processes and general knowledge—and the role these play in the acquisitions in question. A second concern is that the paper blurs distinctions among development, short-term learning, and the origin/acquisition of individual differences. Finally, Sternberg is encouraged to frame the specific phenomenon described here within the context of a larger theory of intellectual development and to indicate what else this specific model can be used to explain.     

Meaning and learning: Response to Moerk

In response to Moerk (1986, Developmental Review, 6, 365–385) the following points are discussed: (a) Semantic and conceptual development must be conceived in terms of systems that undergo developmental change, (b) Objects are viewed as embedded in events and as being conceptualized first within a syntagmatic and later a paradigmatic system, (c) While the nature of the input to the child is important, its effects cannot be considered independently of the state of the child's conceptual and linguistic system. (d) The neurological considerations discussed by Moerk are not relevant to the particular developmental issues discussed in my book.     

Intervention and sleeper effects: A reply to Victoria Seitz

Victoria Seitz (Developmental Review, 1981, 1, 361–373) has misperceived and misunderstood our position (A. D. B. Clarke & A. M. Clarke, Developmental Review, 1981, 344–360). For example, our argument endorsed a transactional and not a main-effect model, nor was our aim to argue that early intervention has no important later consequences, nor did we dispute Consortium findings (I. Lazar & R. Darlington, Lasting effects after preschool, Washington, D.C.: DHEW Publication No. (OHDS) 79-30178, 1978). In fact, agreements with Seitz greatly exceed disagreements. Our skepticism about whether a behavioral treatment can have long-range effects without also having earlier ones remains. Long-term changes appear to result from ongoing long-term processes.     

The Home Observation for Measurement of the Environment: A comment on Zimmerman's critique

This paper is a reply to an article in this journal by M. Zimmerman titled “The Home Observation for Measurement of the Environment: A Comment on Elardo and Bradley's Review”. We found Zimmerman's critique of our original review article (Developmental Review, 1981, 1, 113–145) to contain points which were well taken, and several which seemed pedantic. Specifically, we address his concerns about our discussion of the HOME scale's interrater reliability, test-retest stability, concurrent validity, and predictive validity; and we reply to his comments about the uses of the HOME scale for purposes of screening and matching environments.     

Genetic mediation of sex differences in horizontality: A rejoinder

Neither M. G. McGee (Developmental Review, 1981, 1, 289–295) nor M. J. Allen, M. A. Wittig, and K. Butler (Developmental Review, 1981, 1, 284–288) suggest any alternative explanation for our finding that water-level performance appears to have an X-linked genetic basis. The power calculations of Allen et al. are found to be faulty, and McGee confuses the hypothesis we tested with a weaker hypothesis. Although the X-linked genetic model is not an adequate model of water-level performance the water-level data fit the X-linked model far better than color blindness and HCN data McGee presents as exemplars of X-linked characteristics.     

Subproblem learning: A misnomer

Among other things, K. J. Rust and T. S. Kendler (1987, Developmental Review, 7, 326–362) tested and disconfirmed the Tighes' independent subproblem learning hypothesis experimentally. The Tighes defended themselves by claiming that independent subproblem learning (ISPL) is a label, not a hypothesis and that our tests were invalid. In this reply we showed that ISPL is either an erroneous hypothesis or a misnomer because our tests were valid demonstrations that for young children the so-called “subproblems” are dependent rather than independent.     

The production and verification tasks in mental addition: An empirical comparison

We respond to A. Baroody's comment (1984, Developmental Review, 4, 148–156) with an empirical comparison of the production and verification tasks. With the exception of performance at the first grade level, the two tasks yield essentially identical conclusions. The results of an adjunct task, in which the rate of mental counting was assessed, suggest that children as young as second grade are relying on memory retrieval to a significant degree. In contrast to Baroody's speculation, there appear to be no widespread difficulties associated with results from the verification task. Furthermore, the task permits a more analytic examination of performance and underlying mental process than is afforded by the production task. We conclude by reiterating the empirical support for a model of fact retrieval, and suggesting that accessibility of the arithmetic facts is the basic factor which underlies both fact retrieval and procedural knowledge performance.     

Is it just reading?: Comments on the papers by Mann,Morrison, and Wolford and Fowler

Comments on the stimulating papers by V. A. Mann (Reading skill and language skill. Developmental Review, 1984, 4, 1–15), F. Morrison (Reading disability: A problem in rule learning and word decoding. Developmental Review, 1984, 4, 36–47), and G. Wolford and C. A. Fowler (Differential use of partial information by good and poor readers. Developmental Review, 1984, 4, 16–35) come under four headings. First, their differences with respect to the organizing themes are identified. Second, the central difficulty, for theories of reading disability, posed by the high correlation between reading and IQ, and ways of dealing with this difficulty, are discussed. In the third and fourth sections, comments on the individual papers and a summary of the main lessons to be learned from this collection are presented.     

Why Reading? Because it's there

Three papers (V. A. Mann, Reading skill and language skill. Developmental Review, 1984, 4, 1–15; G. Wolford & C. A. Fowler, Differential use of partial information by good and poor readers. Developmental Review, 1984, 4, 16–35; F. J. Morrison, Reading disability: A problem in rule learning and word decoding. Developmental Review, 1984, 4, 36–47) are critiqued from the standpoint of their adequacy in advancing our understanding of a problem as complex as reading disability. Experimenters should be explicit about their guiding theoretical assumptions, and should think through the relations, if any, between their laboratory tasks and the actual processes of reading. The reading protocol of a dyslexic child is provided, and is interpreted within the frameworks of the Mann, Wolford and Fowler, and Morrison viewpoints.     

The Home Observation for Measurement of the Environment: A rejoinder to Elardo and Bradley''s comment

The published and unpublished research pertaining to Caldwell's Home Observation for Measurement of the Environment (HOME) inventory was recently reviewed by R. Elardo and R. H. Bradley (Developmental Review, 1981, 1, 113–145). Their review was unfortunately deficient in a number of respects. For example, certain methodological issues bearing on the interpretation of the available data were either unrecognized or dismissed without adequate consideration. In addition, some of the data in the studies cited which contradicted or clouded their conclusions were omitted. An extension and reanalysis of the conclusions reached by Elardo and Bradley in light of recently published studies which were not included in their review, and data not discussed in the studies which were reviewed, is provided. Methodological problems are highlighted, and directions for future research are suggested.     

Epistemological Contextualism and the Knowledge Account of Assertion

In this paper, I take up an argument advanced by Keith DeRose (Philosophical Review, 111:167–203, 2002) that suggests that the knowledge account of assertion provides the basis of an argument in favor of contextualism. I discuss the knowledge account as the conjunction of two theses—a thesis claiming that knowledge is sufficient to license assertion KA and one claiming that knowledge is necessary to license assertion AK. Adducing evidence from Stalnaker’s account of assertion, from conversational practice, and from arguments often raised in favor of the knowledge account, I suggest that neither the AK nor the KA theses are plausible. That is, I argue that the knowledge account of assertion to which DeRose appeals is in fact not suitable as an account of assertion. Given that DeRose’s argument stands and falls with the knowledge account, I claim that the argument therefore fails.

On resolving conflicting views of cognitive conflict

F. B. Murray's (Developmental Review, 1983, 3, 54–61) conclusion that a theoretically ambiguous relationship exists between cognitive conflict and Piaget's notion of equilibration was considered. It was suggested that theoretical clarity can be achieved if a distinction is drawn between conflict induction (disequilibrium) and conflict resolution (equilibration). Murray's suggestion that in Piaget's theory internal (cognitive) conflict can be mentally created was disputed. G. N. Cantor's (Developmental Review, 1983, 3, 39–53) concerns about the adequacy of the measures of internal conflict in B. J. Zimmerman & D. E. Blom's (Developmental Review, 1983, 3, 18–38) study due to their independence from external conflict manipulations was discussed. We agreed with Cantor that such findings obviate direct disconfirmation of an internal conflict construct; however, we suggested that evidence of conservation learning in the absence of either external or internal conflict renders Piaget's account less tenable.     

Egocentrism redux

This commentary addresses itself to D.K. Lapsley and M.N. Murphy's critique (1985, Developmental Review, 5, 201–217) of my theory of egocentrism (D. Elkind, 1967, Child Development, 38, 1025–1034). These authors argue that the theory of egocentrism is inconsistent, that self-other differentiation occurs earlier than the theory suggests, and that self-consciousness does not require egocentrism. They conclude that perspective taking provides a more consistent and clear explanation of the adolescent phenomena of the imaginary audience and the personal fable than does egocentricism. I disagree and counter their arguments with my own.