Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

Logical reasoning as part of critical thinking is becoming more and more important to prepare students for their future life in society, work, and study. This article presents the results of a quasi-experimental study with a pre-test-post-test control group design focusing on the effective use of formalisations to support logical reasoning. The…

Studies in the field of learning analytics (LA) have shown students' demographics and learning management system (LMS) data to be effective identifiers of "at risk" performance. However, insights generated by these predictive models may not be suitable for pedagogically informed interventions due to the inability to explain why students…

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…

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…

Evaluated an experimental program in which students were taught to design models as a tool in the learning of percentages and compared results with outcomes from a control group in which teachers directly provided models. Results for 121 fifth graders in The Netherlands show significantly better performance in experimental condition than in the…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

This article addresses the issue of helping students who work collaboratively on mathematical problems with the aim of raising the level of their mathematical understanding and competence. We investigated two kinds of teacher interventions aimed at helping students. The rationale of these interventions was based on a process model for interaction…

Studies show that training students in the use of social and cognitive strategies contributes to learning; however, low-achieving students seem unable to benefit from such interventions. This intervention study addressed the following question: In secondary mathematics, what are the general and differential effects of training students in social…

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)

The Statistical Reasoning Assessment or SRA is one of the first objective instruments developed to assess students' statistical reasoning. Published in 1998 (Garfield, 1998a), it became widely available after the Garfield (2003) publication. Empirical studies applying the SRA by Garfield and co-authors brought forward two intriguing puzzles: the…

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…