Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across Grades 2-3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. (PsycINFO Database Record (c) 2012 APA, all rights reserved).     

A probabilistic theory of second order causation

Larry Wright and others have advanced causal accounts of functional explanation, designed to alleviate fears about the legitimacy of such explanations. These analyses take functional explanations to describe second order causal relations. These second order relations are conceptually puzzling. I present an account of second order causation from within the framework of Eells' probabilistic theory of causation; the account makes use of the population-relativity of causation that is built into this theory.     

The second order approximation to sample influence curve in canonical correlation analysis

A second order approximation to the sample influence curve (SIC) in canonical correlation analysis has been derived in the literature. However, it does not seem satisfactory for some cases. In this paper, we present a more accurate second order approximation. As a particular case, the proposed method is exact for the SIC of the squared multiple correlation coefficient. An example is given. The authors are most grateful to the associate editor and three reviewers for valuable comments and suggestions which improved the presentation of the paper considerably. The first author was partly supported by a RGC earmarked research grant of Hong Kong.     

Cross-cultural second order factor structures of the 16PF

Cross-cultural personality research has generated a great amount of data on individual difference patterns in diverse cultures. One of the major instruments used in this research has been Cattell's 16PF. A major question in this research is whether the underlying personality structure is equivalent for different cultures. The present study evaluated the second order factor structure of the 16PF in 101 subjects of European ancestry and 117 subjects of Japanese ancestry. The factor structure for the Japanese was significantly different from that of the caucasian group. The caucasian results did not differ from those reported by Cattell and his associates. The implications of these results for personality theory and for cross-cultural evaluation were briefly discussed.     

Proving theorems of the second order Lambek calculus in polynomial time

In the Lambek calculus of order 2 we allow only sequents in which the depth of nesting of implications is limited to 2. We prove that the decision problem of provability in the calculus can be solved in time polynomial in the length of the sequent. A normal form for proofs of second order sequents is defined. It is shown that for every proof there is a normal form proof with the same axioms. With this normal form we can give an algorithm that decides provability of sequents in polynomial time.The author was sponsored by project NF 102/62–356 (Structural and Semantic Parallels in Natural Languages and Programming Languages), funded by the Netherlands Organization for the Advancement of Research (NWO).Presented byCecylia Rauszer     

About why there is a shift from cardinal to ordinal processing in the association with arithmetic between first and second grade

Digit comparison is strongly related to individual differences in children's arithmetic ability. Why this is the case, however, remains unclear to date. Therefore, we investigated the relative contribution of three possible cognitive mechanisms in first and second graders’ digit comparison performance: digit identification, digit–number word matching and digit ordering ability. Furthermore, we examined whether these components could account for the well‐established relation between digit comparison performance and arithmetic. As expected, all candidate predictors were related to digit comparison in both age groups. Moreover, in first graders, digit ordering and in second graders both digit identification and digit ordering explained unique variance in digit comparison performance. However, when entering these unique predictors of digit comparison into a mediation model with digit comparison as predictor and arithmetic as outcome, we observed that whereas in second graders digit ordering was a full mediator, in first graders this was not the case. For them, the reverse was true and digit comparison fully mediated the relation between digit ordering and arithmetic. These results suggest that between first and second grade, there is a shift in the predictive value for arithmetic from cardinal processing and procedural knowledge to ordinal processing and retrieving declarative knowledge from memory; a process which is possibly due to a change in arithmetic strategies at that age. A video abstract of this article can be viewed at: https://youtu.be/dDB0IGi2Hf8     

The role of reversal frequency in learning noisy second order conditional sequences

The hallmark of implicit learning is that complex knowledge can be acquired unconsciously. The second order conditionals (SOCs) of Reed and Johnson (1994) were developed to be complex, and they are popular materials for implicit learning research. Recently, it was demonstrated that in a sequence made noisy (by combining two SOCs), shared features of the SOCs may be learned explicitly (Fu, Fu, & Dienes, 2008). What are these shared features? We hypothesized that low reversal frequency may play a significant role. We have varied reversal frequency, and discovered that reversal frequency affected response times, inclusion exclusion behavior, and recognition ratings. Not only does it appear to be important to distinguish implicit and explicit knowledge, but also to distinguish what the knowledge is of.     

任务呈现方式、双任务反应顺序影响算术估算策略选择与执行

采用选择/无选范式,通过操纵任务呈现方式(估算题目的数字消失与否)与主次任务反应顺序(先反应算术任务或先反应字母任务),考察了双任务协调在算术策略选择与执行中的潜在作用。结果显示:(1)不同双任务呈现情境中个体的算术策略表现有明显区别。算术题目数字不消失相比消失时,个体对主、次任务的回答正确率都比较低,在策略选择上更倾向于选择较简单策略,在策略执行上准确性偏低;(2)双任务反应顺序会影响算术策略运用表现。先反应算术任务时,双任务情境只影响策略执行的准确性;而先反应字母任务时,双任务情境对策略执行的准确性和反应速度均发挥干扰作用,且估算题目的数字消失与否对策略选择准确性的影响更大,策略选择适应性之间的差异亦更加明显。上述发现对于深入理解双任务协调功能在策略运用中的作用机制具有重要意义。     

An empirically feasible approach to the epistemology of arithmetic

Recent years have seen an explosion of empirical data concerning arithmetical cognition. In this paper that data is taken to be philosophically important and an outline for an empirically feasible epistemological theory of arithmetic is presented. The epistemological theory is based on the empirically well-supported hypothesis that our arithmetical ability is built on a protoarithmetical ability to categorize observations in terms of quantities that we have already as infants and share with many nonhuman animals. It is argued here that arithmetical knowledge developed in such a way cannot be totally conceptual in the sense relevant to the philosophy of arithmetic, but neither can arithmetic understood to be empirical. Rather, we need to develop a contextual a priori notion of arithmetical knowledge that preserves the special mathematical characteristics without ignoring the roots of arithmetical cognition. Such a contextual a priori theory is shown not to require any ontologically problematic assumptions, in addition to fitting well within a standard framework of general epistemology.     

Animals and artifacts may not be treated equally: differentiating strong and weak forms of category-specific visual agnosia

We examined a categorical dissociation hypothesis of category-specific agnosia using hierarchical regression to predict the naming responses of three agnosia patients while controlling a wide variety of perceptual and conceptual between-category differences. The living-nonliving distinction remained a significant predictor for two of the patients after controlling for all the other factors. For one remaining patient, the categorical variable was not significant once the form-function correlation of different objects was controlled. We argue that the visual system may use various subprocesses at different stages, some of which reflect true categorical organization and some of which reflect a unitary feature-based system that distinguishes kinds.     

Applications of weak Kripke semantics to intermediate consequences

Section 1 contains a Kripke-style completeness theorem for arbitrary intermediate consequences. In Section 2 we apply weak Kripke semantics to splittings in order to obtain generalized axiomatization criteria of the Jankov-type. Section 3 presents new and short proofs of recent results on implicationless intermediate consequences. In Section 4 we prove that these consequences admit no deduction theorem. In Section 5 all maximal logics in the 3 ^rd counterslice are determined. On these results we reported at the 1980 meeting on Mathematical Logic at Oberwolfach. This paper concerns propositional logic only.     

Priming effects of arithmetic signs in 10- to 15-year-old children

In this research, 10- to 12- and 13- to 15-year-old children were presented with very simple addition and multiplication problems involving operands from 1 to 4. Critically, the arithmetic sign was presented before the operands in half of the trials, whereas it was presented at the same time as the operands in the other half. Our results indicate that presenting the ‘x’ sign before the operands of a multiplication problem does not speed up the solving process, irrespective of the age of children. In contrast, presenting the ‘+’ sign before the operands of an addition problem facilitates the solving process, but only in 13 to 15-year-old children. Such priming effects of the arithmetic sign have been previously interpreted as the result of a pre-activation of an automated counting procedure, which can be applied as soon as the operands are presented. Therefore, our results echo previous conclusions of the literature that simple additions but not multiplications can be solved by fast counting procedures. More importantly, we show here that these procedures are possibly convoked automatically by children after the age of 13 years. At a more theoretical level, our results do not support the theory that simple additions are solved through retrieval of the answers from long-term memory by experts. Rather, the development of expertise for mental addition would consist in an acceleration of procedures until automatization.