The goal of the current study was to investigate the role of executive functions in mathematical creativity. The sample included 278 primary school children (ages 8-13). Two models were compared: the starting model tested whether executive functions (shifting, updating, and inhibition), domain-general creativity, and mathematical ability directly…

Assessment is a crucial factor in the implementation of curriculum reform. Little is known, however, on how curriculum changes can be reflected adequately in assessment, particularly if the reform concerns process skills. This issue was investigated for the case of assessing mathematical thinking in a mathematics curriculum reform for…

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…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Cognitive interviewing (CI) provides a method of systematically collecting validity evidence of response processes for questionnaire items. CI involves a range of techniques for prompting individuals to verbalise their responses to items. One such technique is concurrent verbalisation, as developed in Think Aloud Protocol (TAP). This article…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

A recent discussion involves the elaboration on possible design principles for sequences of tasks. This paper builds on three principles, as described by Bokhove and Drijvers (2012a). A model with ingredients of crises, feedback and fading of sequences with near-similar tasks can be used to address both procedural fluency and conceptual…

The purpose of this study was to investigate the relation between early mathematical skills and cognitive processing abilities for two samples of children in Italy (N = 40) and the Netherlands (N = 59) who completed both a cognitive test that measures Planning, Attention, Simultaneous, and Successive (PASS) processing and an early mathematical…

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.…

In this study, the question was raised how basic cognitive processes are related to math abilities and how it can be best determined which children are at risk for developing those disabilities. The role of four distinct basic processes in the development of early mathematics was investigated: executive functions, fluid intelligence, subitizing,…

How can it be explained that early literacy and numeracy share variance? We specifically tested whether the correlation between four early literacy skills (rhyming, letter knowledge, emergent writing, and orthographic knowledge) and simple sums (non-symbolic and story condition) reduced after taking into account preschool attention control,…

People often have difficulties in understanding situations that involve non-linear processes. Also, the topic of non-linear functions is introduced relatively late in the curriculum. Previous research has nevertheless shown that already children aged 6 years and older are able to discriminate non-linear from linear processes. Within the present…

Self-regulated learners are expected to plan their own learning. Because planning is a complex task, it is not self-evident that all learners can perform this task successfully. In this study, we examined the effects of two planning support tools on the quality of created plans, planning behavior, task load, and acquired knowledge. Sixty-five…

Over the past 30 years, researchers at the Freudenthal Institute in The Netherlands have developed a mathematics curriculum and a theory of pedagogy known as Realistic Maths Education (RME). This curriculum uses "imaginable" contexts to help pupils to develop mathematically, with a strong emphasis on pupils "making sense" of…