An investigation into learner understanding of the properties of selected quadrilaterals using manipulatives in a grade eight mathematics class.

Abstract

Benchara Blandford as quoted in Griffiths & Howson (1974) has provided the researcher with the inspiration to seek new methods of trying to improve the teaching and learning of geometry: "To me it appears a radically vicious method, certainly in geometry, if not in other subjects, to supply a child with ready-made definitions, to be subsequently memorized after being more or less carefully explained. To do this is surely to throwaway deliberately one of the most valuable agents of intellectual discipline. The evolving of a workable definition by the child's own activity stimulated by appropriate questions is both interesting and highly educational". Freudenthal (1973), who states that "the child should not be deprived of this privilege", further echoes this thinking. Recent literature on mathematics education, more especially on the teaching and learning of geometry, indicates a dire need for further investigations into the possibility of devising new strategies, or even improving present methods, in order to curb the problems that most learners have in geometry. It would seem that most educators and textbooks eschew the use of concrete manipulatives to teach important geometrical concepts, as they feel it is time-consuming and unnecessary since it creates noisier classrooms. In some cases, the educators have not been trained in the use of these manipulatives. This study intends highlighting the many uses that tangrams (a Chinese puzzle) have in enhancing learners' understanding of the properties of the square and rectangle, including the properties of their diagonals. The researcher also intends showing that the tangram pieces are an important cog in the wheel that keeps the geometry thinking and reasoning process ticking. The days of "kill and drill" are over because the tangram will soon become an interesting and stimulating manipulative that can effectively be used to teach important geometrical concepts and definitions. Not only will learners find it fun to work with, but it will also provide an alternate means of learning since it is not monotonous. It will create an environment which learners will find relaxing and enjoyable to work in, and consequently, promote collaborative learning. The tangram can be used as an important assessment tool; however, this investigation goes beyond the scope and intention of this study. Several useful implications have evolved from this study which may influence both the teaching and learning of geometry in school. Perhaps the suggestions made may be useful not only to educators, but to important stakeholders in policy-making as well. If these ideas can be incorporated in drafting the geometry curriculum, I am sure geometry will not be regarded as the stumbling block for many aspiring mathematics learners who are striving for an "A" symbol in the mathematics examination. The researcher has used action research and a task-based interview process with ten grade 8 learners to show that the use of manipulatives, namely tangrams, has been effective in enhancing learners understanding of the properties of the square and rectangle. In addition, tangrams can go a long way in helping learners achieve van Hiele level 3. The learners interviewed were able to develop a good understanding of the properties of the square and rectangle resulting in remarkable improved pre-test scores. Furthermore, the investigation reaffirmed the practice that learners can be effectively taught from the general to the more specific, enabling them to develop a better understanding of concepts being taught.