Affect and mathematical thinking

The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers' diagnosis of 'negative attitude' is a causal attribution of students' failure, perceived as global and uncontrollable, rather than an accurate interpretation of students' behaviour, capable of steering future action. In order to make this diagnosis useful for dealing with students' difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated how students tell their own relationship with mathematics, proposing the essay "Me and maths" to more than 1,600 students (1st to 13th grade). A multidimensional characterisation of a student's attitude towards mathematics emerges from this study. This characterisation and the study of the evolution of attitude have many important consequences for teachers' practice and education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students: this result suggests that it is never too late to change students' attitude towards mathematics

A study of students’ conception of problem situations: Using conceptualization in scenario-based learning

Students’ appropriate conception of a problem situation can support improved problem solving in both self-regulated learning and STEM disciplines and can support the self-understanding which is the principal competency for self-regulated learning. The current study focused on students’ conceptualization of ten problem situations, half being Sequential (SEQ) and half being Non-Sequential (NonSEQ). Student participants conceptualized the problem situations using their own diagrammatic techniques. It was hypothesized that self-regulated learners can successfully conceptualize either problem situation. The results revealed that, while there was no significant difference between conceptualizations whether participants started with SEQ or NonSEQ situations, subsequent conceptualizations were significantly poorer for SEQ versus NonSEQ situations.</p

Attitudes, beliefs, motivation and identity in mathematics education:an overview of the field and future directions

Abstract Research on mathematics-related affect is varied in theories and concepts. In this survey we record the state of the art in this research through short sections from leading experts in different areas. We describe the historical development of the concept of attitude and different ways it is defined. Research on student self-efficacy beliefs in mathematics is summarized. There is reflection on the dialectic relationship between teacher beliefs and practice as well as on how their beliefs change. One section records the emerging research on student and teacher mathematical identities over the last two decades. Finally, mathematical motivation is explored from the perspectives of engagement structures, social behaviors, and the relationship between individual factors and social norms

Schematic representations in arithmetical problem solving: Analysis of their impact on grade 4 students

While the value of ‘schematic representations’ in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of ‘schematic representation’ (diagrams vs. schematic drawings) on the solving of arithmetical problems. The results show that the presence of schematic representations has a clear positive effect on overall student performance and that a non negligible proportion of students manage to reuse the representations encountered in order to solve new problems. While showing an effect slightly in favor of diagrams as opposed to schematic drawings, our results do not really permit us to draw any conclusions about the form that these representations should take, in particular since a differential effect was observed depending on the type of problem