Background: Creativity requires both divergent and convergent thinking. Previous research established that "divergent" thinking relates to mathematics performance, but generally ignored the role of "convergent" thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study…

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

Learning to solve subtraction problems that require borrowing (e.g., 83-57=) is challenging, and these problems often cause 'bridging' errors, such as the smaller-from-larger error. This study explores how bridging errors in subtraction are related to students' mathematical ability. The study involved 694 third-grade students and 35 teachers from…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

A first application of multilevel latent class analysis (MLCA) to educational large-scale assessment data is demonstrated. This statistical technique addresses several of the challenges that assessment data offers. Importantly, MLCA allows modeling of the often ignored teacher effects and of the joint influence of teacher and student variables.…

Ofsted was asked to provide evidence of effective practice in the teaching of early arithmetic, its report entitled; "Good practice in primary mathematics: evidence from 20 successful schools," was published in November 2011. Did this report pass you by? Unfortunately, as with many other reports not blessed with a "high…

The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…

Teachers in primary education experience difficulties in teaching word problem solving in their mathematics classes. However, during controlled experiments with a metacognitive computer programme, students' problem-solving skills improved. Also without the supervision of researchers, metacognitive computer programmes can be beneficial in a natural…

Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy.…

Solving word problems plays an important role in primary school mathematics education. However, many students have difficulty solving such tasks. In order to improve students' metacognitive and problem-solving skills, a computer program was developed consisting of word problems and metacognitive hints. The experimental group of Grade 5 (n = 23)…

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5…

This paper describes a limited longitudinal study of young children's early numeracy development within three testing cycles, at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-of-age), located within the broader context of progress through to Key Stage 1 SAT…

The aim of the Organization for Economic Cooperation and Development (OECD) project "Science, Mathematics, and Technology" is to formulate recommendations for educational policy. Preparations for the project were made in each of the various member countries. Reported here are the results of the Netherlands meeting. The conference and…

Small-group cooperative learning provides an alternative to both traditional whole-class expository instruction and individual instruction systems. The procedures described in this volume are realistic, practical strategies for using small groups in mathematics teaching and learning with methods applicable to all age levels, curriculum levels, and…