Affine representations in psychophysics and the near-miss to Weber’s law

A theoretical account for the near-miss to Weber’s law in the form of a power function, with a special emphasis on the interpretation of the exponent, was proposed by Falmagne [Falmagne, J.-C. (1985). Elements of psychophysical theory. New York: Oxford University Press] within the framework of a subtractive representation, P(x,y)=F(u(x)−g(y)). In this paper, we examine a more general affine representation, P(x,y)=F(u(x)h(y)+g(y)). We first obtain a uniqueness theorem for the affine representation. We then study the conditions that force an affine representation to degenerate to a subtractive one. Part of that study involves the case for which two different affine representations co-exist for the same data. We also show that the balance condition P(x,y)+P(y,x)=1 constrains an affine representation to be a special kind of subtractive representation, a Fechnerian one. We further show that Falmagne’s power law takes on a special form for a so-called weakly balanced system of probabilities, in which case the affine representation is Fechnerian. Finally, following Iverson [Iverson, G.J. (2006a). Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences. Journal of Mathematical Psychology, 50, 271-282], we generalize the Fechner method to construct the sensory scales in a weakly balanced affine representation by integrating (derivatives of) just noticeable differences.     

Number line estimation in highly math‐anxious individuals

In this study, we aimed to investigate the difficulties highly math‐anxious individuals (HMA) may face when having to estimate a number's position in a number line task. Twenty‐four HMA and 24 low math‐anxiety (LMA) individuals were presented with four lines with endpoints 0–100, 0–1,000, 0–100,000, and 267–367 on a computer monitor on which they had to mark the correct position of target numbers using the mouse. Although no differences were found between groups in the frequency of their best‐fit model, which was linear for all lines, the analysis of slopes and intercepts for the linear model showed that the two groups differed in performance on the less familiar lines (267–367 and 0–100,000). Lower values for the slope and higher values for the intercept were found in the HMA group, suggesting that they tended to overestimate small numbers and underestimate large numbers on these non‐familiar lines. Percentage absolute error analyses confirmed that HMA individuals were less accurate than their LMA counterparts on these lines, although no group differences were found in response time. These results indicate that math anxiety is related to worse performance only in the less familiar and more difficult number line tasks. Therefore, our data challenge the idea that HMA individuals might have less precise numerical representations and support the anxiety–complexity effect posited by Ashcraft and colleagues.     

The guise of the good and the problem of partiality

According to the guise of the good thesis, we desire things under the ‘guise of the good.’ Here I sympathetically articulate a generic formulation of the guise of the good thesis, and address a problem for the view, which I call the problem of partiality. The problem is, roughly, that our partial pro-attitudes –for example, our special concern for ourselves –do not correspond to what is absolutely good. I criticize three solutions to the problem, and propose an alternative strategy, on which partial pro-attitudes constitute a species of illusion.     

No grammatical gender effect on affective ratings: evidence from Italian and German languages

In this study, we tested the linguistic relativity hypothesis by studying the effect of grammatical gender (feminine vs. masculine) on affective judgments of conceptual representation in Italian and German. In particular, we examined the within- and cross-language grammatical gender effect and its interaction with participants’ demographic characteristics (such as, the raters’ age and sex) on semantic differential scales (affective ratings of valence, arousal and dominance) in Italian and German speakers. We selected the stimuli and the relative affective measures from Italian and German adaptations of the ANEW (Affective Norms for English Words). Bayesian and frequentist analyses yielded evidence for the absence of within- and cross-languages effects of grammatical gender and sex- and age-dependent interactions. These results suggest that grammatical gender does not affect judgments of affective features of semantic representation in Italian and German speakers, since an overt coding of word grammar is not required. Although further research is recommended to refine the impact of the grammatical gender on properties of semantic representation, these results have implications for any strong view of the linguistic relativity hypothesis.     

Perception2

The article is an overview of some central philosophical problems associated with perception. It discusses what distinguishes perception from other sensory capacities and from conception. It discusses anti‐individualism, a view according to which the nature of a perceptual state is dependent not just causally but for its identity or ‘essence’ on relations to a normal environment in which systems containing that state were formed. It discusses different views about epistemic warrant. By emphasising the deep ways in which human and animal perceptual systems, especially visual systems, are similar, it criticises a dominant view of the last century, in both philosophy and large parts of psychology, according to which a range of sophisticated supplementary abilities have to be learned before a child can perceive objective features of the physical world.     

Representation of Game Algebras

We prove that every abstractly defined game algebra can be represented as an algebra of consistent pairs of monotone outcome relations over a game board. As a corollary we obtain Goranko's result that van Benthem's conjectured axiomatization for equivalent game terms is indeed complete.     

Investigating and facilitating children's graphic, geographic, and spatial development: An illustration of Rodney R. Cocking's legacy

Presented here is a case history of an interdisciplinary program of research on children's graphic, geographic, and spatial development that integrates approaches from developmental psychology, geography, and education. Some of the theoretical and historical roots of this work are discussed, with a particular emphasis on the roles that Rodney R. Cocking played in the evolution of this work. Described are findings from basic research on children's developing understanding of place representations, such as maps, educational interventions designed for public television and elementary school classrooms, and efforts aimed at national educational reform. Taken together, the work illustrates Rodney Cocking's profound, diverse, and continuing legacy to the scholarship of the academy and to the lives of children.     

关于数学应用题心理表征策略的新理论

本文主要阐述了数学应用题心理表征中的两种策略一直接转换策略和问题模型策略,介绍了两种策略的认知过程,并对两种策略的区分方法进行了探讨,最后总结说明了研究数学心理表征在理论和实践中的意义。     

Maternal distancing and event memory at 20 months

Maternal distancing strategies (Sigel, 1993 in The Development and Meaning of Psychological Distance , Cocking R, Renninger KA (eds). Erlbaum: Hillsdale, NJ; 141–158) with 20‐month‐olds were analysed during a mother–child interaction in a free play situation. Then, they were related to memory performance of the children as assessed by the elicited imitation paradigm with 4 three‐step sequences of actions (Bauer, Hertsgaard, Child Dev. 1993; 64 :1204). The aim of this work was to (1) confirm that the Sigel's model of distancing could be used with very young children under two; (2) study relationships between maternal distancing that stimulate representational competence of the child and memory performance of the children. Results showed two different patterns of correlations depending on the sequence type: for enabling sequences, significant positive correlations were obtained for the first two distancing levels whereas for arbitrary sequences no correlation was found whatever the distancing level. As discussed, the first pattern brings new arguments in support of declarative memory before the age of 2 years and reframes the memory development in a Vygotskyian interactionist perspective. The second pattern of correlations calls for replication and more investigation about the processes implied in memory of very young children for different sequence types. Copyright © 2003 John Wiley & Sons, Ltd.     

汉字字组时间顺序的内隐记忆研究

采用再认与偏好测验的内隐记忆方法,以文字相同而字序不同的三类汉字字组为刺激材料,对汉字字组进行启动效应的实验研究,探讨汉字字组内隐的时间顺序表征存在的可能性及其加工特点。结果表明：汉字字组中字与字之间存在内隐的时间顺序表征,这种内隐的时间顺序表征是对刺激项目知觉特征中时间维度的一种反映,受知觉表征系统支配,具有自动加工和提取的特点。