Browsing by Author "Lourens, Ilze"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- ItemA systematic analysis of the generalisation concept in early algebra for young learners – some ideas for the classroom(Stellenbosch : Stellenbosch University, 2022-03) Lourens, Ilze; Wessels, Dirk; Stellenbosch University. Faculty of Education. Dept of Curriculum Studies.ENGLISH ABSTRACT: The importance of introducing algebra concepts and skills in the early years of mathematics education, has become increasingly acknowledged as imperative for algebra success in the secondary grades of mathematics teaching and learning. Research has shown that learners at a young age are able to reason algebraically. Generalisation is described as one of the core aspects of early algebra and should be embedded throughout the mathematics curriculum to form a deep understanding of the underlying structure of mathematics. In South Africa, the field of early algebra remains largely unexplored in the mathematics education research context. The content area, ‘Patterns, functions and algebra’ which aims to provide guidelines for the teaching of early algebra in South African early years classrooms, seems to be inadequate for the implementation of early algebra in early years classrooms. A lack of a relational approach in the sequencing of curriculum documents and learning and teaching materials, are provided for the teaching of patterns, functions, and algebra in the foundation phase. The purpose of this study was to determine how the generalisation concept can be implemented in early years classrooms to develop early algebra skills and concepts. A systematic literature review was conducted with the aim of extending on current research by designing a higher-order construct from existing literature. A thematic analysis of the literature led to the synthesis of an instructional sequence for the implementation of generalisation in early years classrooms. The instructional sequence was based on the principles of Realistic Mathematics Education from the Netherlands which included guided reinvention and emergent modelling as foundational principles. A historical overview of the development of algebra through the ages indicated three historical stages: the rhetorical stage, the syncopated stage, and the symbolic stage, as well as four conceptual stages: the geometric stage, the static-equation stage, the dynamic function stage, and the abstract stage. The emergence of the main components and big ideas of algebra from these stages provided a valuable insight as to how algebraic thinking developed naturally and informed an instructional sequence for the implementation of generalisation. An in-depth systematic review of the concepts which emerged from history was further conducted to understand the current state of algebra in schools, how algebraic thinking develops, the levels of algebraic thinking and what the main components of early algebra are, with a specific focus on generalisation. The study further explored an appropriate learning approach, namely the problem-centred approach, which ensures that mathematics is learned for understanding. The historical overview and the systematic review of early algebra, generalisation, and structure were used to construct the instructional sequence for the implementation of generalisation in early years classrooms.