Teachers’ mathematical knowledge for teaching geometrical transformations in selected secondary schools in Lusaka, district.

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Mulenga, Justine
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The University of Zambia
The purpose of this study was to explore the mathematical knowledge that teachers had for teaching Geometrical transformations in selected secondary schools in Lusaka District. The study was guided by three (3) research questions namely; what iv knowledge of geometrical transformations do the teachers have? What instructional strategies do teachers use when teaching Geometrical Transformations? And what challenges do teachers face when teaching Geometrical Transformations? The descriptive survey design was used in conducting this research. Primary data was collected using a Mathematical Knowledge for Teaching (MKT) questionnaire; lesson observations and post lesson semi structured interviews were conducted. The sample for this study consisted of three (3) teachers who were purposively selected among teachers of mathematics in Lusaka District. Twenty four (24) lessons were observed and an interview on each lesson observed was conducted. Thematic analysis was used to analyse the data from the three sources. The study revealed that the teachers showed some incompetence’s in some of the six domains of the mathematical knowledge for teaching Geometrical Transformations. The findings showed that teachers were very competent in the first three types of transformations namely; translation, reflection and rotation. On the other hand, as teachers progressed to enlargement, stretch and shear they could not demonstrate all the domains of the mathematical knowledge for teaching Geometrical Transformations especially concerning identifying and describing each type of transformation. On the instructional strategies used by teachers, the study revealed that teachers restricted themselves to two methods when teaching Geometrical Transformations, namely the matrix and the formula methods. Finally, the study also revealed lack of teaching materials such as graphed chalk boards and board instruments, failure by learners to apply the pre requisite knowledge, and lack of mathematical instruments by some learners as some of the challenges teachers face when teaching Geometrical Transformations. Based on the findings of the study, some of the recommendations were that; the universities and colleges of education should integrate school mathematics (classroom mathematics) in their curriculum especially those topics that seem to be a challenge to most teachers, Mathematics Heads of Department should allocate enough time during lesson study meetings to enhance teachers’ mathematical knowledge for teaching Geometrical Transformations and teachers should ensure that the pre-requisite topics that are closely related to Geometrical Transformations such as matrices, vectors and construction are taught consecutively towards the teaching of Geometrical Transformations. Key words: Mathematical knowledge for teaching, pre-requisite topics
Mathematics--Study and teaching--Zambia