Teachers’ Indications in Classroom and Pupils’ Construal and Knowledge
It seems uncontroversial that the nature of classroom discourse influences learning. The Malaysian primary mathematics curriculum advocates that teachers should guide the pupils’ towards a conceptual understanding of mathematics that compliments the skills developed through the manipulation of concrete objects and representations prior to the introduction of symbolism and algorithms, and also ensure that the construction of understanding in mathematical concepts plays an equal part to the development of skills. Against this background, this paper considers the way in which primary schools mathematics teachers’ actions within their classrooms may contribute towards their pupils’ achievement and understanding. Using lessons associated with determining fractions of whole numbers as an example, the paper considers the evidence to answer the question “What form of relationship exists between the teaching and learning of fractions?”. Episodes from lesson observations were associated with the knowledge and skill of the pupils through their personal constructions of the substance of the lessons. Whilst the pupils’ level of achievement may suggest broad understanding, in reality it is grounded within a limited frame of procedural competence construed from their teachers’ emphasis in the classrooms. Although there may be differences in achievement between pupils attending urban and rural schools, there are no qualitative differences in their understanding of fractions because there are no qualitative differences in the indications given by their teachers in the classrooms. The pupils’ perceptions of fraction are framed within a narrow procedural perspective derived from teacher indications which, whilst emphasizing the needs of an examination system, are at variance with the spirit and intention of the national curriculum designed to meet the nation’s aspiration of becoming an industrialized nation.
Keywords: Teaching, Learning, Understanding, Fractions, Knowledge
Dr. Ruzlan Md-Ali
Senior Lecturer, Department of Curriculum and Instruction