Characterizing metacognitive processes and mathematical skills during problem solving by using a non-linear orientation base as a self-regulation tool

Abstract Over the past few decades, research has shown that metacognition plays a critical role in helping students in the solving of mathematical problems. Despite the existence of several tools for assessing the metacognitive processes in problem solving, there is a notable lack of tools designed to enhance these processes over time. The purpose of this study is to introduce an instrument called Non-Linear Orientation Base (N-LOB) and examine its impact on metacognitive self-regulation during pattern-based problem solving. In particular, the study aims to characterise the mathematical skills and metacognitive processes shown by three groups of sixth grade students as they construct and refine a N-LOB. Results suggest that metacognitive regulation processes have a general character when compared to the awareness and evaluation processes, which are more closely tied to specific skills required for pattern-based problem solving. Moreover, deeper engagement with the N-LOB correlates with the emergence of more advanced mathematical skills related to generalization. The study concludes by highlighting the potential of the N-LOB as a tool for promoting metacognitive self-regulation in the context of problem solving.