The role of concrete materials in developing children's understanding of the properties of quadrilaterals
Date of Award
Master of Education (M. Ed.)
Institute for Educational Development, Karachi
The purpose of the study was to try to understand how concrete materials can help to develop primary school children's understanding of quadrilaterals. Concrete materials for the purpose of the study refers to all materials and physical objects that can be seen, touched, felt and manipulated for mathematical learning. I worked with four boys (ages 9-11) of mixed ability from a private school that works in close collaboration with IED. I tutored them for one hour outside of their classroom situation. This teaching was done four times a week for seven weeks using at least nine different kinds of concrete material to teach about the sides, angles and diagonals of the parallelogram family of quadrilaterals (square, rhombus, rectangle and parallelogram). My role was dual in nature, that of a researcher as well as a teacher. After determining the needs of the students by an initial activity I designed materials to suit the learning needs of the children. Data was collected with methods suited to the qualitative paradigm of research, i.e., by field notes, audio taping the teaching/learning sessions and collection of samples of students' work and reflections. My own reflections guided the evolution of the research process. My biggest learning was that the role of the teacher is the key factor for effective teaching with concrete materials. The best of materials will not work unless the teacher takes the role of a facilitator, an assessor, a decision maker and a tailor. Concrete materials sometimes succeeded and sometimes did not succeed in developing an understanding of the concept in the children's minds, but in both cases played a key role in students' learning. The materials helped to develop students' mathematical language, encouraged discussion (both teacher-student and student-student), sharpened the ability of the students to question and probe their own and their peers understanding and also unveiled the alternate frameworks that the students harboured about the geometrical concepts under study. Important insights were gained into how children learn the different properties of the four quadrilaterals. For example, all students considered a rhombus to be a "tilted square”, the use of a flexiquad helped the students to learn to differentiate between the two. This study also discusses some of the possibilities and challenges of using concrete materials in the Math classroom and its implications for the teacher or a teacher educator.
Ahmed, A. (1998). The role of concrete materials in developing children's understanding of the properties of quadrilaterals (Unpublished master's dissertation). Aga Khan University, Karachi, Pakistan.