Schematising activities in early childhood education

The purpose of this study was to determine the importance of introducing schematising to children in early childhood and to determine whether schematising can be taught to children. This was done using a longitudinal, quantitative study with a quasi-experimental design (N = 133). In this study, the use of schematising was taught to an experimental group of children to determine if it is possible to realise significantly improved results in schematising tasks for an experimental group in comparison to a control group of children who were not taught schematising. Pupils in the experimental group demonstrated significantly better results on schematising, which cannot be explained by maturation. In our future research, we will investigate the mathematical performances of these experimental and control groups in the next grade of the primary school curriculum.     

Towards a knowledge‐rich learning environment in preparatory secondary education

In this case study a novel educational programme for students in preparatory vocational education was studied. The research questions were: (1) Which teaching/learning processes occur in a simulated workplace using the concept of a knowledge‐rich workplace? (2) What is the role of models and modelling in the teaching/learning processes? The curriculum project consisted of design and construction tasks. The students were collaboratively involved in the process of designing a tricycle for a real customer. This real‐life activity creates opportunities for students to develop and use models, which can be used in more than in one context. The case study explored how the teachers deal with the students’ explicit and implicit need for knowledge and skills. The main findings are that teachers more often provide this knowledge, rather than guide the students in reconstructing it, and towards the end of the project, knowledge tended to remain situated.     

Hans Freudenthal: A mathematician on didactics and curriculum theory

The main ideas in the work of Hans Freudenthal (1905-1990), the Dutch mathematician and mathematics educator, related to curriculum theory and didactics are described. Freudenthal's educational credo, 'mathematics as a human activity', is explored. From this pedagogical point of departure, Freudenthal's criticism of educational research and educational theories is sketched and fleshed out. Freudenthal's approaches to mathematics education, developmental research and curriculum development can be seen as alternatives to the mainstream 'Anglo-Saxon' approaches to curriculum theory.     

Curriculum differentiation: multiple perspectives and developments in education

This paper examines curriculum differentiation (i.e. streaming or ability‐grouping). After placing curriculum differentiation in an international perspective, it outlines the main conclusions from empirical research on differentiation over several decades. Against this empirical background, it describes and considers the three specific orientations towards curriculum differentiation: a genetic perspective, a cultural perspective, and a sociological perspective. The insights from the various perspectives are integrated and expanded in a framework of curriculum theory, research, and practice.     

Preferences for Various Learning Environments: Teachers' and Parents' Perceptions

In the last ten years, a number of innovations, mainly inspired by constructivist notions of learning, have been introduced at various levels of the Dutch educational system. However, constructivist learning environments are rarely implemented. Teachers tend to stick to expository and structured learning environments. This consistent finding requires research in order to gain insight into teachers' preferences for learning environments and to determine the factors that support and impede the realization of these learning environments. Regarding the influence of social backgrounds on student learning, is it also important to take stock of parental views on learning environments.This study is focused on teachers' preferences for learning environments, their reported teaching behavior, and how these match with parents' preferences. Three parallel questionnaires were developed for teachers (n = 285), students (n = 951), and parents (n = 636) to measure preferences and behavior at different levels of education, for three types of learning environments: direct instruction; discovery learning; and authentic pedagogy. The results show that teachers often prefer direct instruction, and seldom promote discovery learning. While teachers sometimes realize authentic pedagogy, constructive learning tasks are seldom used. Teachers' reported practice and parents' preferences for their children appear to correspond reasonably.Results of multiple regression analyses show that the use of the three types of learning environments yield different predictors. For the use of discovery learning and authentic pedagogy, confidence in students' regulative skills is an important predictor. In predicting the use of direct instruction, the teacher's own conception of learning turns out to be an important predictor.     

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.     

Effects of Training in the Use of Social and Cognitive Strategies: An Intervention Study in Secondary Mathematics in Co‐Operative Groups

ABSTRACT

This article reports on an intervention study into the effects of a training in the use of social and cognitive strategies on the learning outcomes of students in secondary mathematics education. Special attention is given to differential effects for high‐ and low‐achieving students. The focus on differential effects is derived from studies into learning in small co‐operative groups, and from the results of meta‐analyses into the effects of training in learning strategies. From these studies it can be concluded that in general such programs contribute to learning. However, it seems that low‐achieving students are unable to benefit from interventions of the kind investigated (i.e., co‐operative learning and training in learning strategies). The main question is whether it is possible to design an instructional program from which all students benefit, and from which the low‐achieving students profit more than their counterparts in the control‐program. In the present study three instructional programs for co‐operative learning were compared: (i) an experimental program with special instruction in the use of social strategies; (ii) an experimental program with special instruction in the use of cognitive strategies; and (iii) a control program without training in either cognitive or social strategies. The programs were identical with respect to mathematical content and general instructional settings (a combination of whole‐class instruction, working in co‐operative groups and individual work). The experiment addressed the following research question: what are the general and differential effects of a training in the use of social and cognitive strategies on the results of learning in secondary mathematics? The research was conducted in two schools for secondary education in a total of 21 classes, involving a total of 511 students. The design was a pretest‐posttest control group design, using two experimental groups and one control group. The data were analysed from a multi‐level perspective. The outcomes of the investigation clearly show the effects of the intervention. Teaching cognitive and social strategies has the expected, positive effects. In addition to this main effect, a compensatory effect for the low‐achieving students was found. The low‐achieving students in the experimental conditions outperformed their counterparts in the control group.

     

The effects of guided elaboration in a CSCL programme on the learning outcomes of primary school students from Dutch and immigrant families

This study examined the effects of guided elaboration on students' learning outcomes in a computer-supported collaborative learning (CSCL) environment. The programme provided students with feedback on their elaborations, and students reflected on this feedback. It was expected that students in the experimental (elaboration) programme would show better learning gains and that students from immigrant families would especially benefit. Two hundred primary school students of 9 different schools participated. The research can be characterized as a quasi-experimental study with a pre-test, post-test, control group design. In a multilevel regression analysis, no main effect of the intervention was found. However, there was a significant differential effect of the intervention; students from immigrant families in the experimental programme outperformed their counterparts in the control group. It can be concluded that guided elaboration in a CSCL programme through feedback and reflection is a promising approach.     

Audrey's acquisition of fractions: A case study into the learning of formal mathematics

National standards for teaching mathematics in primary schools in the Netherlands leave little room for formal fractions. However,a newly developed programme in fractions aims at learning formal fractions. The starting point in the development of this curriculum is the students’ acquisition of `numeracy infractions’. In this case study we describe the growth in reasoning ability with fractions of one student in this newly developed programme of 30 lessons during one whole school year. In the study we found indications that the programme and its teaching stimulated the progress of an average performer in mathematics. Moreover we found arguments as to what extent formal operations with fractions suits as an educational goal. This revised version was published online in July 2006 with corrections to the Cover Date.