Hands-On Math in Kindergarten

Introduction

International research has amply demonstrated that the abstraction process starts from an early age (Butterworth, 1999; Iannece et al., 2010) and it is therefore during kindergarten (K) that the child’s mental models begin to form in order that they may logically organize the world around themselves. (D’Amore et al., 2004) However prejudice remains and the K period continues to be deemed too early for children to begin their education in numeracy. This chapter describes a part of an innovative project, in two schools in the Italian region of Marche, whose aim is to introduce children to mathematics in a fun way. It also invited the teachers involved to reflect on possible processes for numeracy in K. In particular we suggest proto-mathematical activities in K to facilitate the positional notation of numbers in subsequent Primary School (PS) years. In fact, international literature shows that children of eight years have difficulty in the positional notation of numbers, which is often done without explicit reference to the value of digits (Iannitti & Vettore, 2007).

The idea to focus on improving education for numeracy during K originated from the training activities and final thesis as part of a degree in Primary Education at the University of Macerata, Italy, studied by the author of this chapter. In fact, thanks to observation, research and comparative studies with colleagues in the Primary School (PS) of the Province of Macerata (MC), Italy, it was possible to record the major difficulties found in PS children in writing numbers and in their recognition of the semantic value of the positional decimal number system. This is in addition to the perception of a general lack of interest in the discipline, which is considered as boring and pointless. These educational experiments were carried out at the Teaching Circles Regina Elena Civitanova Marche (MC) and Ascoli Piceno Center (AP). Both schools are located in an area of an above average socioeconomic status. The teachers involved have been interested in the educational intervention proposed during the training activities of two students in Primary Education. The study described in this chapter refers to the K level of AP.

The main objective of the whole project was to develop a positive attitude towards mathematics among children and to make them reflect on how a given quantity can have different representations (iconic, verbal, symbolic etc.), starting from their original concepts (Vygostkij, 1987).

The development of the educational courses had the specific objectives of encouraging children to have a positive attitude towards mathematics and towards sharing their thoughts with peers and teachers.

In particular we have tried to create educational activities at K to promote:

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  The need to group the various numerical bases and to organize them in a more simple way.

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  The recognition of the semantic value of the positional decimal system.

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  The development of different languages (iconic and linguistic), including the mathematical language.

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  Cooperative learning.

Other objectives involved decisively impacting the training of the teachers involved, providing them with the grounds to reflect on the usefulness and efficiency of the course and of the teaching ideas.

The methodology that we used was intended to focus on the problematizing of everyday experiences, stimulating the curiosity of children by investigating and resolving issues in a playful and pleasant way.

The instruments used included Contafacile (see “Gioco del due,” or “The Game with Two,” Rinaldelli et al., 2008), a structured tool, and common materials such as flowers, pasta, string, stones, sticks, leaves, dough, cups, posters and colors.

The didactical cycle was useful to monitor the children’s learning process, Centred on semiotic mediation, developed by Bartolini-Bussi & Mariotti (1999), it consisted of the realization of a cyclic path centred on the use of structured tools as mediators of everyday objects.