Scandinavian Journal of Psychology, 1999, 40, 65 – 71 Milestones in the development of infant numeracy BERNADETTE A. M. VAN DE RIJT and JOHANNES E. H. VAN LUIT Department of Educational Science, Utrecht Uniersity, The Netherlands Van de Rijt, B. A. M. & Van Luit, J. E. H. (1999). Milestones in the development of infant numeracy. Scandinaian Journal of Psychology, 40, 65–71. This article deals with the development of numeracy among young children of the four to seven year age group. The research investigation described had two aims: to see how early numeracy develops in children of different ages; and to see whether there are fixed points which might serve as milestones in the development of infant numeracy. The results of this investigation involving 96 children indicate a strong development of numeracy skills during this period. With reference to the literature, it is also shown that certain items of a test previously developed for this purpose may be taken as core items that do indeed represent milestones in the development of infant numeracy. Key words: Infant numeracy, milestones, item response theory, development, counting. Ms. dr. Bernadette A.M. Van de Rijt, Department of Educational Science, Utrecht Uniersity, P.O. Box 80.140, 3508 TC Utrecht, The Netherlands INTRODUCTION The development of infant numeracy is a subject that has increasingly aroused the interest of both researchers and those working in the field of education. This interest also is stimulated by the fact it is assumed that, by the stage of infant school, it should be possible to detect any arrest in the development of particular cognitive skills and where possible to intervene in order to prevent later problems in mathematical development. A test has been developed in a research project to look at infant numeracy which allows the numeracy skills of chil- dren between the ages of 4 and 7 years to be measured. This test, the Utrecht Numeracy Test (UNT) (Van Luit et al., 1994), consists of eight sections each containing ten items: Comparison, Classification, Making Correspon- dences, Seriation, Using Numerals, Structured Counting, Resultative Counting and the Application of a Knowledge of Numbers. In this test, the Piagetian operations of seria- tion, classifying and making correspondences are opera- tionalized in items of numbers and counting. The eight sections represent eight infant numeracy skills which have been defined on the basis of the relevant literature (Fuson, 1988; Geary, 1994; Gelman & Gallistel, 1978; Ginsburg, 1989; Van de Rijt & Van Luit, 1994; Van de Rijt & Van Luit, 1998). The test consists of two parallel forms, Form A and Form B, each with five items per section. In the construction of the test the authors made use of item response theory (Wright & Stone, 1979). A significant advantage of tests based on item response theory is the ability to place both the difficulty of an item and the skill of the person on one scale. The investigation described below, conducted with Form A, had two aims, for both of which we took advantage of item response models vis-a `-vis classical test theory. The first aim of the research was to determine the extent to which the above-mentioned eight sections were mastered by the first three year-groups of infant school (kindergarten 1, kindergarten 2 and Grade 1). On the basis of average scores for skill, and using linear transforms of raw scores, we can determine for school year and for age groups which items children master either well, moderately or inadequately. On the basis of the infant numeracy scores of the different age categories, one can also see whether children are able to master the so-called ‘core items’. These core items are items which relate structurally to the studies in experimental developmental psychology conducted, for example by Fu- son (1988) and Geary (1995). These authors describe a developmental sequence in children’s ability to count and to master the functions of numerals. They also indicate the ages at which particular milestones — the mastery of (our) core items — are reached. The second aim of this investigation was to test the validity of the developmental sequences and milestones (referred to as core items) i.e. to see to what extent these can be recognized in our sample and at which age they are mastered. MILESTONES IN THE DEVELOPMENT OF INFANT NUMERACY SKILLS The deelopment of counting and functional mastery of numerals There is currently considerable interest in counting as a precondition for an understanding of number (Van de Rijt, 1996). Recent work on numeracy (e.g. Baroody, 1992; Frank, 1989; Sophian, 1992) has shown that in addition to the well-known Piagetian operations, various counting skills are also important in the development of numeracy. For this reason, the test includes both Piagetian and vari- ous other tasks that relate to counting. The Piagetian tasks themselves, as far as possible, are those which deal with counting. © 1999 The Scandinavian Psychological Associations. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA. ISSN 0036-5564.