Scielo RSS <![CDATA[South African Journal of Childhood Education]]> vol. 3 num. 1 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b>Children's conceptual development of mathematics</b>]]> <![CDATA[<b>Core knowledge and working memory as prerequisites of early school arithmetic</b>]]> Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic operations. Children solved these problems significantly above chance. In Study 2, 66 first graders were tested for their approximate arithmetic achievement, working memory capacity, groupitizing, phonological awareness, naming speed and early arithmetic concepts at the beginning of first grade and again at the beginning of second grade. It appears that approximate arithmetic achievement is independent from most other cognitive variables and correlates most with other variables of the mathematical domain. Furthermore, regression analyses revealed that school success was only predicted by groupitizing and central executive capacity, but not approximate arithmetic achievement, when controlling for other cognitive variables. <![CDATA[<b>Development of numerical concepts</b>]]> The development of numerical concepts is described from infancy to preschool age. Infants a few days old exhibit an early sensitivity for numerosities. In the course of development, nonverbal mental models allow for the exact representation of small quantities as well as changes in these quantities. Subitising, as the accurate recognition of small numerosities (without counting), plays an important role. It can be assumed that numerical concepts and procedures start with insights about small numerosities. Protoquantitative schemata comprise fundamental knowledge about quantities. One-to-one-correspondence connects elements and numbers, and, for this reason, both quantitative and numerical knowledge. If children understand that they can determine the numerosity of a collection of elements by enumerating the elements, they have acquired the concept of cardinality. Protoquantitative knowledge becomes quantitative if it can be applied to numerosities and sequential numbers. The concepts of cardinality and part-part-whole are key to numerical development. Developmentally appropriate learning and teaching should focus on cardinality and part-part-whole concepts. <![CDATA[<b>Development of mathematical concepts as basis for an elaborated mathematical understanding</b>]]> A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key numerical concepts and arithmetic skills from age 4 to 8, is proposed. Two studies will be presented. In the first study, 1095 preschool children completed a mathematics test (MARKO-D0) based on a 5-level model. The test fitted with a one-dimensional Rasch model. The extension of the model to a sixth level was verified in a new study: 312 first-graders took part in a mathematics test based on the six levels (MARKO-D1). In order to check whether the data of both samples adhered to the principle of unidimensionality, the data of MARKO-0 and MARKO-1 were used in a common analysis for comparative purposes. The applicability of these findings for a qualitative diagnostics and an adaptive training will be discussed. <![CDATA[<b>Realising pre-school mathematical education - a development-oriented math programme with special consideration of phonological language processing aspects</b>]]> Mathematical development processes begin long before school starts and the importance of previous mathematical knowledge for later school achievements is beyond dispute. For a suitable pre-school education, the focus of interest must be to find out which early learning processes prepare children best. In this article, the acquisition of the key concepts of numeracy is presented in a developmental model, which served as framework for a supportive programme for 4-8 year-old children. The research into this intervention shows how development-oriented support of key arithmetic concepts can be constructed and taught systematically. The immediate and sustainable effect of the programme Mina and the Mole on the mathematical competencies of children has already been demonstrated in an evaluation study of 248 children aged 5-7. Considering the strong language-orientation of the programme, the present study focused on aspects of phonological awareness and of phonological working memory. It was evident that these phonological language processing aspects correlated with mathematic skills. Furthermore, it was found that the dominant linguistic focus of the training did not constitute a disadvantage - even linguistically weak children significantly improved their mathematical skills. Moreover, children with poor or average phonological performance could profit from the supportive programme also regarding their phonological language processing. <![CDATA[<b>Natural differentiation in the teaching of mathematics to children starting school</b>]]> This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concrete learning environment should fulfil several requirements. On the one hand, the environment has to represent core mathematical principles, and, on the other hand, they have to be suitable for all learners in an inclusive classroom. The concrete formats themselves serve a specific conceptual purpose, while, at the same time, addressing, in an integrated way, the needs of a variety of learners with different levels of competence. <![CDATA[<b>Evaluation of maths training programme for children with learning difficulties</b>]]> In the German school system, children are seen as educationally impaired when they are more than two grades behind in their performance in several areas of learning, and this has been the case for several years. A special problem is the fact that support measures are often effective only to a limited extent, or only for a short period. The study at hand focuses on the question of whether educationally impaired children with large deficits in mathematics can be supported successfully by means of a highly adaptive support measure (MARKO-T), and whether the effects of this support can be maintained over a certain period. For this, 32 educationally impaired third-graders with math deficits were supported individually with MARKO-T twice a week, over a period of ten weeks. As control group, 32 similarly impaired third-graders were paralleled according to the mathematical and cognitive achievements of the training group. Two further control groups, each with 32 unimpaired first-graders, were paralleled according to their mathematical and cognitive achievements, respectively. The results showed that the very poor mathematical performance of the educationally impaired children could be significantly improved with this support programme. Four months after the end of the training, significant support effects could still be established when compared to the educationally impaired control group. The comparison with the two control groups demonstrated that the developmental curve of the children with learning difficulties increased in a way that was comparable to that of the unimpaired first-graders. <![CDATA[<b>Forging a research community of practice to find out how South African children make their world mathematical</b>]]> In a search for ways to capture foundation phase children's competence in mathematics, a small research team was put together at a South African university four years ago. At first, working only in a single school where the objective was to model 80 learners' growth in competence over four years, the team transformed into a very different entity. This article narrates the founding and development of a community of research practice, which eventually included undergraduate- and postgraduate students, researchers from institutions in Germany, Switzerland and South Africa, teachers at local schools close to the university, and an educational research and survey company. Supported by funding from four different sources, the project is fairly close to reaching the goal of delivering a standardised mathematics competence test for 4-8 year-olds, which is a first of its kind for the country where educational measurement seems to be at a crossroads. In the story line of this community of practice, it is evident that progress can be assessed best by the learning that has been taking place in a community with a notable diversity of people and interests, but with the shared goal of investigating children's mathematical behaviour on a measure that can be trusted.