Lucian Olteanu

Enhancing mathematics communication using critical aspects and dimensions of variation

This article deals with two prominent topics in the field of mathematics education: the communication in mathematics and its teaching and learning and the continuous professional development of mathematics teachers. In this article, a framework is proposed for analysing the effectiveness of communication in mathematics classrooms. The presentation is based on data collected, during a 3-year period, while different objects of learning is presented in nine classes, and it includes 22 teachers and 884 students. Among other things, the data consist of the students’ tests, the teachers’ lessons plan and reports of the lessons’ instructions. In the analysis, concepts relating to variation theory have been used as analytical tools. The results show that effective communication occurs in the classroom if it has the real critical aspects in student learning as its starting point. Also, the results show that teachers develop new strategies to present the contents by having the focus to open up dimensions of variation.

Construction of tasks in order to develop and promote classroom communication in mathematics

In this article, the focus is on task construction and the importance of this process to develop and promote classroom communication in mathematics. The students’ tests, examination of students’ mathematical work, the teachers’ lesson plans, and reports of the lessons’ instructions are the basic data for this article. The analysis indicated that teachers develop their professional decision-makers through developing the ability to construct relevant tasks for identifying the critical aspects in students’ learning. The findings suggest that construction of tasks can be a productive basis in helping teachers to make fundamental changes in their understanding of what they should focus on in a teaching situation to improve mathematical communication. In this process, the teachers integrate, in a natural way, the research results from mathematics education.

Effective communication, critical aspects and compositionality in algebra

This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the principle of compositionality should be considered as a methodological principle that describes how communication in the classroom should be designed. Here, I present the power of using variation theory whose main purpose is to generate an understanding of critical aspects and compositionality in practice.

Distributive law as object of learning through direct and inverse tasks

Purpose – Problem solving is a skill in mathematics which although always relevant has heightened priority due to the changes in the new mathematics GCSE (Department for Education, 2013). It has pr ...