Abstract
In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 304). A confirmatory factor analysis showed that the four-factor structure fitted the empirical data from the Netherlands. For the Cyprus data a one-factor structure was found to have a more adequate fit. Regarding the effect of country on performance, a comparison at item level showed that the kindergartners in the Netherlands outperformed those in Cyprus in the majority of quantitative competence items. Analyses of variance revealed for each country a significant effect of kindergarten year on performance, with children in K2 (second kindergarten year) outperforming those in K1 (first kindergarten year). A statistical implicative analysis at item level revealed that in both countries the relevant implicative chain, showing what successful solving of an item implies for correct solving of another item, reflects by and large the sequential steps mostly followed in teaching kindergartners early number. This sequence starts with counting and subitizing, then continues with additive reasoning and finally multiplicative reasoning. These implicative chains also clearly show that the development of early quantitative competence is not linear. There are many parallel processes and cross-connections between the components of quantitative competence.
Highlights
Mathematics education for young children has a long history
Based on the reviewed studies concerning early number skills, we focused on the components counting, subitizing, additive reasoning and multiplicative reasoning, and examined how they are connected and develop
To know more about the structure of children’s quantitative competence before they have been formally taught numbers and operations, we set up a study in the Netherlands and Cyprus assessing kindergartners’ early number skills by administering a paper-and-pencil test consisting of two booklets with items about counting, subitizing, additive reasoning and multiplicative reasoning
Summary
Its beginning is found already in the first half of the seventeenth century (Saracho and Spodek 2009) It was only in 2000 that the National Council of Teachers of Mathematics (NCTM 2000) first included this age group in their standards for mathematics education. Much awareness has grown that young learners’ future understanding of mathematics requires an early foundation based on a high-quality, challenging, and accessible mathematics education (NCTM 2013). Necessary for developing this education is a good understanding of what mathematics we want beginning learners of mathematics to get acquainted with and need to teach them. In this study we focus on the early number strand and unravel its components, their relations and their generality for kindergartners in different countries
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