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Numerical cognition has long been considered the perfect example of abstract information processing. Nevertheless, there is accumulating evidence in recent years suggesting that the representation of number magnitude may not be entirely abstract but might present a specific case of embodied cognition rooted in the sensory and bodily experiences of early finger counting and calculating. However, so far none of the existing models of numerical development considers the influence of finger-based representations. Therefore, we make first suggestions on (i) how finger-based representations may be integrated into a current model of numerical development and (ii) how they might corroborate the acquisition of basic numerical competencies at different development levels.

The purpose of this study is to observe some factors that may affect the understanding of subtraction with borrowing. The study is done in a foreign environment, in Kenya. Factors that will be looked into are: the classroom environment, the situation of learning in a second language. The study will also observe factors that can cause an erroneous answer and what those may look like. Within this area manipulatives will be mentioned. The study has used a qualitative as well as quantitative approach. The qualitative method has been accomplished through interviews and observations, the quantitative method through tests given to the learners. For the analysis of the observations, Cobb’s and Yackel’s model (1995) of the mathematical classroom has been used. The study is interpreted from a sociocultural perspective focusing interaction. The result in this study shows that the interaction in the classroom is important to the individual learning, perceptions of mathematics and the expectations on the individual. Learning in a second language can be a barrier. The use of manipulatives can work as a scaffold, but it can also hinder the learner to develop a deeper understanding. Syftet med studien är att studera faktorer som kan påverka förståelsen av subtraktion med växling. Studien är gjord i en annan lärmiljö, i Kenya. Faktorer som kommer att uppmärksammas är lärmiljön i klassrummet och att inlärningen sker på ett för eleven andra språk. Studien kommer också att uppmärksamma faktorer som kan bidra till ett felaktigt svar och hur de kan se ut. Inom detta område kommer laborativt material nämnas. Studien har både ett kvalitativt och kvantitativt tillvägagångssätt. Den kvalitativa metoden har genomförts genom intervjuer och observationer, den kvantitativa metoden med hjälp av elevtester. Cobbs och Yackels (1995) modell över matematik klassrummet har använts som analysmaterial. Studien tolkas utifrån ett sociokulturellt perspektiv. Focus är på interaktionen. Resultaten i studien visar att interaktionen I klassrummet är viktigt för det individuella lärandet, uppfattningen om matematik och förväntningar på individen. Undervisning på ett andra språk kan bli ett hinder. Användandet av laborativt material kan fungera som ett stöd, men kan också hindra utvecklandet av en djupare förståelse.

Contains fulltext : 121863.pdf (Publisher’s version ) (Open Access) Evidence for an approximate analog system of numbers has been provided by the finding that the comparison of two numerals takes longer and is more error-prone if the semantic distance between the numbers becomes smaller (so-called numerical distance effect). Recent embodied theories suggest that analog number representations are based on previous sensory experiences and constitute therefore a common magnitude metric shared by multiple domains. Here we demonstrate the existence of a cross-modal semantic distance effect between symbolic and tactile numerosities. Participants received tactile stimulations of different amounts of fingers while reading Arabic digits and indicated verbally whether the amount of stimulated fingers was different from the simultaneously presented digit or not. The larger the semantic distance was between the two numerosities, the faster and more accurate participants made their judgments. This cross-modal numerosity distance effect suggests a direct connection between tactile sensations and the concept of numerical magnitude. A second experiment replicated the interaction between symbolic and tactile numerosities and showed that this effect is not modulated by the participants' finger counting habits. Taken together, our data provide novel evidence for a shared metric for symbolic and tactile numerosities as an instance of an embodied representation of numbers. 8 p.

Fingers offer a practical tool to represent and manipulate numbers during the acquisition of arithmetic knowledge, usually with a greater involvement in addition and subtraction than in multiplication. In adults, brain-imaging studies show that mental arithmetic increases activity in areas known for their contribution to finger movements. It is unclear, however, if this truly reflects functional interactions between the processes and/or representations controlling finger movements and those involved in mental arithmetic, or a mere anatomical proximity. In this study we assessed whether finger movements interfere with basic arithmetic problem solving, and whether this interference is specific for the operations that benefit the most from finger-based calculation strategies in childhood. In Experiment 1, we asked participants to solve addition, subtraction, and multiplication problems either with their hands at rest or while moving their right-hand fingers sequentially. The results showed that finger movements induced a selective time cost in solving addition and subtraction but not multiplication problems. In Experiment 2, we asked participants to solve the same problems while performing a sequence of foot movements. The results showed that foot movements produced a nonspecific interference with all three operations. Taken together, these findings demonstrate the specific role of finger-related processes in solving addition and subtraction problems, suggesting that finger movements and mental arithmetic are functionally related.

The spontaneous use of finger counting has been for long recognized as critical to the acquisition of number skills. Recently, the great interest on space–number associations shifted attention to the practice of finger counting itself, and specifically, to its spatial components. Besides general cross-cultural differences in mapping numbers onto fingers, contrasting results have been reported with regard to the directional features of this mapping. The key issue we address is to what extent directionality is culturally mediated, i.e., linked to the conventional reading–writing system direction, and/or biologically determined, i.e., linked to hand dominance. Although the preferred starting-hand for counting seems to depend on the surveyed population, even within the same population high inter-individual variability minimizes the role of cultural factors. Even if so far largely overlooked, handedness represents a sound candidate for shaping finger counting direction. Here we discuss adults and developmental evidence in support of this view and we reconsider the plausibility of multiple and coexistent number–space mapping in physical and representational space.

Children typically learn basic numerical and arithmetic principles using finger-based representations. However, whether or not reliance on finger-based representations is beneficial or detrimental is the subject of an ongoing debate between researchers in neurocognition and mathematics education. From the neurocognitive perspective, finger counting provides multisensory input, which conveys both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis, or “finger sense,” enhances mathematical skills. Therefore neurocognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development. However, research in mathematics education recommends fostering mentally based numerical representations so as to induce children to abandon finger counting. More precisely, mathematics education recommends first using finger counting, then concrete structured representations and, finally, mental representations of numbers to perform numerical operations. Taken together, these results reveal an important debate between neurocognitive and mathematics education research concerning the benefits and detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be discussed.

In the present study, we experimentally tested the role of hand motor circuits in simple-arithmetic strategies. Educated adults solved simple additions (e.g., 8 + 3) or simple subtractions (e.g., 11 3) while they were required to retrieve the answer from long-term memory (e.g., knowing that 8 + 3 = 11), to transform the problem by making an intermediate step (e g., 8 + 3 = 8 + 2 + 1 = 10+1 = 11) or to count one-by-one (e.g., 8 + 3 = 8...9... 10...11). During the process of solving the arithmetic problems, the experimenter did or did not move the participants' hand on a four-point matrix. The results show that passive hand movements disrupted the counting strategy while leaving the other strategies unaffected. This pattern of results is in agreement with a procedural account, showing that the involvement of hand motor circuits in adults' mathematical abilities is reminiscent of finger counting during childhood.

Like number words and written numerals, fingers can be used to represent numbers. In fact, due to their ubiquitous availability, agility, and discrete quantity, they are considered the most natural tool for counting, which renders them attractive for theories of embodied (numerical) cognition (Andres et al., 2008; Di Luca and Pesenti, 2011). As they are so closely linked to the human body, finger counting sequences may appear to be universal, but both their composition (Bender and Beller, in preparation) and their existence (Butterworth et al., 2011; Crollen et al., 2011) depend on culture. In this paper we will argue that it is crucial for any (embodied) theory of numerical cognition to take this cultural variability into account. To substantiate this claim, we depict some of the cultural variability in finger counting, followed by a brief representational analysis, from which directions for future research will be derived.

Spatial-numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Theoretical implications of this “manumerical cognition” stance for the distinction between grounded, embodied, and situated cognition are discussed.

Frontiers in psychology 2, 389 (2011). doi:10.3389/fpsyg.2011.00389, Published by Frontiers Research Foundation, Lausanne