Survey team on : conceptualisations of the role of competencies, knowing and knowledge in mathematics education research

This paper presents the outcomes of the work of the ICME 13 Survey Team on 'Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research'. It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as mathematical competence and competencies, mathematical proficiency, and mathematical practices, amongst others. The paper provides theoretical analyses of these notions-under the generic heading of mathematical competencies-and gives an overview of selected research on and by means of them. Furthermore, an account of the introduction and implementation of competency notions in the curricula in various countries and regions is given, and pertinent issues are reviewed. The paper is concluded with a set of reflections on current trends and challenges concerning mathematical competencie

Evolution of applications and modelling in a senior secondary curriculum

In Queensland Australia, mathematical modelling and applications have featured in senior secondary mathematics curricula for two decades. Part of a longitudinal study of the implementation of this initiative, as seen through the eyes of selected teachers and administrators who have been centrally involved in its development and on-going practice, is reported. The data consist of responses to structured and open interview questions, syllabus documents, and application and modelling tasks designed and implemented by teachers. Perceptions of why modelling and applications are valuable at this level of schooling, the distinction between applications and modelling, how established applications and modelling are in the curriculum, the sources of such tasks, and the sufficiency of support for the development of these tasks by teachers are presented

CAS-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Our research indicates that technologies that incorporate CAS capabilities have the potential to mediate collaborative approaches to mathematical enquiry within life-related mathematical tasks

Commentary on Part III:Connections to Theory and Practice

This chapter addresses the relationship between the promotion of mathematical modeling in the classroom – in particular linking mathematics and authentic real mathematics problem – and students’ attitude towards mathematics. This relationship has a twofold nature, based on two assumptions: on one hand mathematical modeling can help to construct or reinforce the belief concerning the utility and concreteness of mathematics, and therefore it can foster motivation in studying mathematics; on the other hand a positive attitude towards mathematics can strongly affect the way students approach real mathematics problems