A pre-test questionnaire was conducted in a kindergarten and it showed that, although the children were able to give various examples of objects, from their everyday lives, that are similar to solid shapes, the examples they gave for plane figures were also tangible objects. Since it is suggested that geometry instruction has to begin early, children need rich experiences of the connections between plane figures and solid shapes. The researchers provided a picture book as an impetus for kindergartners' mathematical thinking. We developed and shared a picture book, The Prints, as an auxiliary means for helping kindergarten children identify the print of a solid shape. Through the picture book-which presents plane figures as prints of solids real life objects-children could link plane figures and solid shapes. The research questions we posed were: (a) Can kindergarten children identify the origin of the plane figures presented? (b) Can they relate the objects presented to the plane figures presented? After sharing the picture book-through the storytelling tradition-and completing the related activities, the identification of the print of a solid shape became more accessible and more engaging to children. They were also able to give appropriate examples of plane figures from their everyday lives. This finding was affirmed by the post-test conducted.

Recent research suggests that children could be engaged in probability tasks at an early age and task characteristics seem to play an important role in the way children perceive an activity. To this direction in the present article we investigate the role of some basic characteristics of probabilistic tasks in their design and implementation. In order to do so, we present the structure and the content of a series of tasks that were implemented in a kindergarten school focusing on two characteristics: the context and the materials used. In our case, the performance of the experiment together with the use of dice and spinners seemed to be critical in children's development of probabilistic thinking.

In this paper we analyse the language used by kindergarten children and their teacher while they discuss the fairness of two games that involved the concept of chance. Their discussions show that the children are able to overcome their primary intuitions concerning the fairness of a game and to comprehend the important role of materials. The children mostly used counting strategies in order to justify their opinion; this reveals the establishment of a primary discursive community based on the premise that each opinion should be justified in order to be accepted by the other children and the teacher.

ChrysanthiSkoumpourdi kara@rhodes.aegean.gr C. Skoumpourdi niños. A través del análisis de 20 respuestas, dadas por niños, con respecto a la secuencia numérica así como a simples problemas de adición y sustracción, parece que aunque los niños utilizaron principalmente cubos, no siempre los utilizaron de forma sistemática ni obtuvieron éxito. El uso efectivo de la línea numérica se limitó a la definición de la secuencia numérica.

In this paper, the design of a multi-material, the 'modern' abacus ('modabacus'), for developing early childhood mathematics, is proposed. Presenting the main theories for the design of educational materials as well as similar materials and their educational use, it appears that a new material is needed. The 'modabacus' would be an apparatus which could serve as a multi-material for acting out mathematical tasks as well as a material that could hopefully overcome the limits and restrictions of traditional abacuses and counting boards. Key words and phrases: 'modabacus', early childhood mathematics, educational materials, top-down process of design, bottom-up process of design, abacus, counting board, AL abacus, arithmetic rack.