Metacognitive monitoring in educational contexts is typically measured by calibration indicators, which are based on the correspondence between cognitive performance and metacognitive confidence judgment. Despite this common rationale, a variety of alternative methods are used in the field of monitoring research to assess performance and judgment…

This study aims to investigate a mathematical-metacognitive discourse model with IMPROVE metacognitive self-question prompts (What, How/When, and Why) in order to promote a deeper level of discourse in mathematics classes. The study involved 32 math teachers and 824 fifth-grade students (from 32 public schools) from one district in Israel.…

Metacognition is a powerful predictor for learning performance, and for problem-solving. But how metacognition works for cognitive strategies and learning performance is not clear. The present study was designed to explore how metacognition affected the cognition (learning strategies and problem solving strategies) and different kinds of learning…

In this paper, we investigate the role of metacognitive postdiction skills, intrinsic motivation and prior proficiency in mathematics as Propensity factors within the opportunity-propensity (O-P) model of learning. We tested Belgian children from Grade 1 till 6 in January and June. The study revealed overlapping yet different predictors for…

An effective learning environment can be provided when teachers adopt metacognition-based teaching as a part of their course instructions. A well-developed metacognitive teaching approach can effectively develop students' problem-solving strategies. In addition to that contribution, it can provide opportunities for students to notice their own…

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been…

Metacognitive strategies are needed to solve complex problems such as mathematical modelling problems in groups in a goal-oriented and successful manner. In this paper, the results of an intervention study aiming at enhancing students metacognitive group strategies for modelling are presented. Students from 18 different classes (grade nine and…

The purpose of this study was to investigate whether primary school teachers' promotion of students' self-regulated learning (SRL) and metacognition changed during the course of a professional development (PD) program that focused on improving the quality of their implementation of mathematical tasks. The study involved three primary school…

The role of metacognitive postdiction accuracy and autonomous and controlled motivation in mathematics was explored in elementary school children (n = 208) within two perspectives, related to sample characteristics. A first study was set up in a population-based cohort. A second study was set up with children with and without a documented…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these…

Mathematical argumentation is generally thought to be the paradigm of cogent reasoning. The concept of mathematical proof thus seems to be associated with necessity and enforcement, but not with freedom; however, in various ways a reference to freedom is also needed to understand the phenomenon of mathematical proof, for example, to distinguish it…

The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

The cognitive relationship between intuition and proof is complex and often students struggle when they need to find mathematical justifications to explain what appears as self-evident. In this paper, we address this complexity in the specific case of open geometrical problems that ask for a conjecture and its proof. We analyze four meaningful…

For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they have examined how mathematicians assess and get to know a proof not just by reading it, but through active engagement with the proof. For example,…