Strategic Learning in Primary Mathematics Education: Effects of an Experimental Program in Modelling

In most strategy research the focus is on ready-made models provided by the teacher or textbook. However, in this research project the effects are described of an experimental program in primary math education, concerning the construction and use of models by pupils in guided co-construction. This field experiment with an experimental group and a control group involved 238 grade-5 pupils. In a series of experimental lessons, pupils were taught to design models as a tool in the learning of percentages. The results of the experimental program were compared with the outcomes of a program in the control group, based on the teachers' strategy of “directly providing models” to the pupils. The conclusion, then, is that children in the experimental condition significantly outperform children in the control condition.     

Emergent mathematical thinking in the context of play

In the attempt to improve mathematical thinking for safeguarding our future societal needs, there is a worldwide tendency in schools to start training mathematical and arithmetical operations at an earlier age in children’s development. Recent theoretical developments and empirical research have pointed to alternative ways of approaching early mathematical thinking. In these latter approaches, mathematical development in the early developmental stages is seen as an emerging process in the context of children’s own activities that contributes to meaningful learning and stimulation of children’s cultural identity (Bildung approach). The discussion between the training approach versus the ‘Bildung’ approach is still intemperately going on. In this article, some outcomes of a research programme (based at the Free University Amsterdam) are discussed that present empirical studies and their theoretical background (cultural–historical theory, elaborated in an educational concept called ‘Developmental Education’) that demonstrates the promising potentials of promoting mathematical thinking through supporting young children’s appropriation of schematic representations and notations in the context of play.     

The development of informal statistical inference content knowledge of pre-service primary school teachers during a teacher college intervention

Teachers who engage primary school students in informal statistical inference (ISI) must themselves have good content knowledge of ISI (ISI-CK). However, little is known about how college education for pre-service teachers can contribute to the development of their ISI-CK. To address this shortcoming, we used a case study to investigate ISI-CK development in a class of 21 pre-service primary school teachers who participated in a short intervention (180 min). Based on qualitative and quantitative analyses of the pretest, posttest and intervention data, the results suggest that most participants acknowledged it is possible to make uncertain inferences. An assignment to search the media for inferential claims seemed to create awareness regarding inference and the need to distinguish between a sample and a population. A simulation involving random sampling and varied sample size probably increased the participants’ knowledge of sampling variability and random sampling. No development was seen in the participants’ knowledge about sufficient sample sizes. The statistical investigation conducted by the participants during a model lesson may have strengthened their awareness of ISI, but it also revealed that many participants continued to favour distributed sampling over random sampling. Further research on belief formation with regard to data as evidence, sampling methods and the expression of uncertainty in the context of ISI is needed.     

From context to contextualizing

Although context is rapidly becoming one of the core concepts in modern educational thinking, this notion still remains ill-defined in literature. This article aims at contributing to the definition of the notion of context and examining its value for research and development of educational praxes. The article starts out from a general conception of context, identifying its basic intentions as particularization of meaning and providing for coherence. In this article the activity approach to context is explored more particularly. It is argued here that one consequence from this approach is, that context should be conceived of dynamically, i.e. in terms of context-making (contextualizing). Reasoning from this activity approach, several new research questions arise.     

On the Narrative Nature of Young Children's Iconic Representations: Some evidence and implications

Reflection on the relationship between a sign and its meaning (i.e. semiotic activity) is a fundamental form of cognitive activity that already occurs at an early age. The improvement of this semiotic activity in young children prepares for their later learning activity. Iconic representations are one important category of signs for young children (3‐7 years old). Iconic representations (drawings, diagrams, schemes) are generally conceived of as means bridging the gap between early enactive, perception‐bound thinking and abstract‐symbolical thinking. From the Vygotskian perspective iconic representations are complex signs referring to some object (situation, action) in a special way. On the bases on the analysis of children's drawings it is argued that iconic representations are narrative in nature for young children. Children tend to supplement their drawings with verbal symbols in order to make sure that their intended meanings are maximally clear. In doing so, children learn to carry out semiotic activity and improve this activity with the help of more abstract symbols     

A Vygotskian perspective on teacher education

Contemporary teacher education demonstrates the continued use of competency‐based, personality‐based and inquiry‐based approaches. These approaches are commonly regarded as representing alternative paradigms for designing curriculum and pedagogy. From a Vygotskian perspective, characterized by the use of bridging concepts relating individual functioning and personal development to sociocultural process and setting, these approaches may serve to provide elements for a more comprehensive paradigm of professional development. Drawing on Vygotskian theory, a teacher‐education environment offers support to trainee teachers for developing a professional identity. A central element is that trainees explore the practice of teaching for its underlying public meanings and as these meaning relate to their own structures of personal meanings. Such an exploration involves the shaping and testing of personally‐meaningful action in professional practice. Commitment to meanings found to be valid and practicable constitutes the core of professional identity. The task students face in developing professional identity on the basis of an assignment of meaning to teaching needs an appropriate teacher‐education environment. These conditions are worked out from a Vygotskian perspective on professional development.