Specyficzne typy reprezentacji umysłowych : reprezentacje linearne

By mówić o reprezentacjach specyficznych, należy najpierw doprecyzować, co rozumie się przez pojęcie reprezentacji "klasycznych", niespecyficznych. W dużym uproszczeniu można powiedzieć, że zaliczają się do nich trzy rodzaje reprezentacji: a) słowo (kod werbalny), b) obraz (kod niewerbalny) i c) sąd o relacjach (kod propozycjonalny). Cały czas należy pamiętać, że wśród ekspertów nie został osiągnięty konsensus co do natury reprezentacji. Część badaczy, na przykład Paivio, twierdzi, że do zawarcia całej wiedzy o świecie, jaką posiada człowiek, nie wystarczy jeden rodzaj reprezentacji (jeśliby nawet wystarczył, byłby on nieekonomiczny). Z tego powodu zakłada on, że występuje zarówno kod werbalny, jak i niewerbalny [por. Nęcka, Orzechowski, Szymura 2006]. Reprezentacje specyficzne to takie, za pomocą których może być reprezentowana tylko część wiedzy o świecie zewnętrznym, obejmują one zatem tylko pewien fragment tego, co człowiek spostrzega i o czym myśli

Czym jest liczba?

What is a number?The concept of number is an abstract concept. Numbers do not exist itself in the nature. On the other hand, they carry a wide variety of significant information about the environment and are present in the life of human being in almost all fields. The origins of numbers as well as its nature were considered in numerous ways by mathematicians, philosophers, psychologists etc. The classical theories of number are briefly discussed and opposed to the psychological and neuroscientific findings regarding number representations. It seems that the ability use information carried by number is not exclusive to educated human mind, contrary its origins are innate and common to humans and several other species

Specyficzne typy reprezentacji umysłowych: reprezentacje linearne

By mówić o reprezentacjach specyficznych, należy najpierw doprecyzować, co rozumie się przez pojęcie reprezentacji „klasycznych”, niespecyficznych. W dużym uproszczeniu można powiedzieć, że zaliczają się do nich trzy rodzaje reprezentacji: a) słowo (kod werbalny), b) obraz (kod niewerbalny) i c) sąd o relacjach (kod propozycjonalny). Cały czas należy pamiętać, że wśród ekspertów nie został osiągnięty konsensus co do natury reprezentacji. Część badaczy, na przykład Paivio, twierdzi, że do zawarcia całej wiedzy o świecie, jaką posiada człowiek, nie wystarczy jeden rodzaj reprezentacji (jeśliby nawet wystarczył, byłby on nieekonomiczny). Z tego powodu zakłada on, że występuje zarówno kod werbalny, jak i niewerbalny [por. Nęcka, Orzechowski, Szymura 2006]. Reprezentacje specyficzne to takie, za pomocą których może być reprezentowana tylko część wiedzy o świecie zewnętrznym, obejmują one zatem tylko pewien fragment tego, co człowiek spostrzega i o czym myśli

What is a number?

The concept of number is an abstract concept. Numbers do not exist itself in the nature. On the other hand, they carry a wide variety of significant information about the environment and are present in the life of human being in almost all fields. The origins of numbers as well as its nature were considered in numerous ways by mathematicians, philosophers, psychologists etc. The classical theories of number are briefly discussed and opposed to the psychological and neuroscientific findings regarding number representations. It seems that the ability use information carried by number is not exclusive to educated human mind, contrary its origins are innate and common to humans and several other species

No fingers, no SNARC? : neither the finger counting starting hand, nor its stability robustly affect the SNARC effect

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively) is considered to be strong evidence for the link between numbers and space. Studies have shown considerable variation in this effect. Among the factors determining individual differences in the SNARC effect is the hand an individual uses to start the finger counting sequence. Left-starters show a stronger and less variable SNARC effect than right-starters. This observation has been used as an argument for the embodied nature of the SNARC effect. For this to be the case, one must assume that the finger counting sequence (especially the starting hand) is stable over time. Subsequent studies challenged the view that the SNARC differs depending on the finger counting starting hand. At the same time, it has been pointed out that the temporal stability of the finger counting starting hand should not be taken for granted. Thus, in this preregistered study, we aimed to replicate the difference in the SNARC between left- and right-starters and explore the relationship between the self-reported temporal stability of the finger counting starting hand and the SNARC effect. In line with the embodied cognition account, left-starters who declare more temporarily stable finger counting habits should reveal a stronger SNARC effect. Results of the preregistered analysis did not show the difference between left- and right-starters. However, further exploratory analysis provided weak evidence that this might be the case. Lastly, we found no evidence for the relationship between finger counting starting hand stability and the SNARC effect. Overall, these results challenge the view on the embodied nature of the SNARC effect

Mathematics anxiety—where are we and where shall we go?

In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical clarifications on what MA is and what constitutes its opposite pole; discussion of construct validity, specifically relations between self-descriptive, neurophysiological, and cognitive measures; exploration of the discrepancy between state and trait MA and theoretical and practical consequences; discussion of the prevalence of MA and the need for establishing external criteria for estimating prevalence and a proposal for such criteria; exploration of the effects of MA in different groups, such as highly anxious and high math–performing individuals; classroom and policy applications of MA knowledge; the effects of MA outside educational settings; and the consequences of MA on mental health and well-being

Finger counting and its role in the development of math competence

Finger counting plays an important role in mathematical cognition, especially in the acquisition of the concept of number and elementary math competence. Fingers are spontaneously used to count because of their constant availability and easiness of manipulation. Stable counting order within hand facilitates the acquisition of ordinal as well as cardinal numbers. Additionally, using fi ngers to count alleviates working memory load and allows constant control of counting accuracy. Apart from the usefulness for counting practice, cognitive representations of fi ngers are strongly interconnected with representations of numbers. Finger gnosis (the quality of the brain representations of fi ngers) is a good predictor of current as well as future math achievement. There is also evidence that the training of fi nger differentiation leads to improvements in math achievement

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes

A large-scale survey on finger counting routines, their temporal stability and flexibility in educated adults

A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the (default) FC habits are over time and how flexible they can be. To investigate these questions, 380 Polish participants completed a questionnaire on their FC routines, the stability of these routines, and the context of FC usage, preceded by the request to count on their fingers from 1 to 10. Next, the test–retest stability of FC habits was examined in 84 participants 2 months following the first session. To the best of our knowledge, such a study design has been adopted for the first time. The results indicate that default FC routines of the majority of participants (75%) are relatively stable over time. At the same time, FC routines can flexibly adapt according to the situation (e.g., when holding an object). As regards prevalence, almost all participants, in line with previous findings on Western individuals, declared starting from the closed palm and extending consecutive fingers. Furthermore, we observed relations between FC preferences and handedness (more left-handers start from the left hand) and that actual finger use is still widespread in healthy adults for a variety of activities (the most prevalent uses of FC are listing elements, presenting arguments and plans, and calendar calculations). In sum, the results show the practical relevance of FC in adulthood, the relative stability of preferences over time along with flexible adaptation to a current situation, as well as an association of FC routines with handedness. Taken together our results suggest that FC is the phenomenon, which is moderated or mediated by multiple embodied factors