The influence of finger-counting strategies (pointing, keep track, montring) on number representations is supported by several empirical facts. However, even the above mentioned strategies have been object of studies during childhood, little is known about how finger-counting could interact with the semantic representation of numbers in adulthood. To address this issue, we conducted a first experiment in which participants had to identify Arabic digits by pressing the keyboard with one between their ten fingers. Results showed that responses were faster and more accurate when the finger assigned to each digit was congruent with the finger-counting habits of the participants (Di Luca, Granà, Semenza, Seron and Pesenti, 2006). Subsequently, in a numerosity detection task, we showed that the numerosities expressed by canonical configurations are named faster than those expressed by non-canonical ones, even when no motors responses were needed (Di Luca and Pesenti, in press). Moreover, when used as unconsciously presented primes, both types of configurations speeded up comparative judgments of Arabic digits, but only the priming effect induced by canonical configurations generalized to new, never consciously seen, numerosities, which implies an automatic semantic access for these one only. Finally, we showed that these differences cannot be ascribed to simple visual features, but they stem from two distinct semantic processes. Specifically, canonical configurations are processed as a symbolic system and activate a place coding semantic representation of magnitude, whereas non-canonical configurations activate a summation coding semantic representation.

The influence of finger-counting strategies (pointing, keep track, montring) on number representations is supported by several empirical facts. However, even the above mentioned strategies have been object of studies during childhood, little is known about how finger-counting could interact with the semantic representation of numbers in adulthood. To address this issue, we conducted a first experiment in which participants had to identify Arabic digits by pressing the keyboard with one between their ten fingers. Results showed that responses were faster and more accurate when the finger assigned to each digit was congruent with the finger-counting habits of the participants (Di Luca, Granà, Semenza, Seron and Pesenti, 2006). Subsequently, in a numerosity detection task, we showed that the numerosities expressed by canonical configurations are named faster than those expressed by non-canonical ones, even when no motors responses were needed (Di Luca and Pesenti, in press). Moreover, when used as unconsciously presented primes, both types of configurations speeded up comparative judgments of Arabic digits, but only the priming effect induced by canonical configurations generalized to new, never consciously seen, numerosities, which implies an automatic semantic access for these one only. Finally, we showed that these differences cannot be ascribed to simple visual features, but they stem from two distinct semantic processes. Specifically, canonical configurations are processed as a symbolic system and activate a place coding semantic representation of magnitude, whereas non-canonical configurations activate a summation coding semantic representation.

Studiens syfte är att beskriva hur elever i de lägre åldrarna använder handgester när de löser aritmetikuppgifter. Den teoretiska utgångspunkten i studien är embodied cognition, där det centrala i teorin är att vi lär oss genom kroppen. Tio elever i sjuårsåldern i Sydafrika har observerats med fokus på deras användning av handgester. Resultatet visade att flera av eleverna använder handgester när de löser additions- och subtraktionsuppgifter och att det finns ett antal olika handgester de använder sig av. De olika handgesterna delades in i taktila och icke-taktila gester, som i sin tur kopplades till konkreta och abstrakta gester. Slutsatsen av studien är att elever använder sig av olika handgester i olika kombinationer när de löser aritmetikuppgifter. Deras gester med händer och fingrar kan vara ett uttryckssätt för deras utvecklingsprocess och kan fungera som en bro mellan konkret och abstrakt tänkande. / The aim of the study is to describe how students of the lower ages use hand gestures when solving arithmetic tasks. The theoretical basis of the study is embodied cognition. The viewpoint of embodied cognition holds that the body is a tool for learning. Ten students in South Africa, aged seven, have been observed based on their use of hand gestures. The result showed that several students use hand gestures when solving addition and subtraction tasks and there were a number of different hand gestures being used. The various hand gestures were divided into tactile and non-tactile gestures. These could in turn be linked to concrete and abstract gestures. The conclusion of the study is that students use different types of hand gestures and also in various combinations when solving arithmetic tasks. Their hand gestures can be a way of expressing their development process and to function as a bridge between concrete and abstract thinking.

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.