Challenges Pupils Face in Enlargement Transformation Geometry in Zambian Secondary Schools: A Case of Two Schools in Lusaka and Monze Districts

Abstract

Zambian Secondary Schools have experienced a low performance in Mathematics at School Certificate level in recent years (Examination Council of Zambia (ECZ), 2016). An analysis of results in terms of topics in the examinations showed that Transformation geometry is one of the topics in mathematics in which pupils have not been performing very well (ECZ, 2009; ECZ, 2008). For this reason, this study was set to establish the challenges pupils faced in learning transformation geometry in particular enlargement transformation geometry in two schools in Zambia. School A is located in Lusaka District and School B is in Monze district. The Van Hiele Model of levels of thought were used as the theoretical framework of the study. The study largely used a mixed method approach that included descriptive study design. The data was obtained through written test and interview schedules. One hundred Grade 12 pupils, all together from both schools wrote the test and six volunteered to undergo interview. Data was analysed through a process of coding, categorizing, clustering and performance indicators corresponding to the Van Hiele’s model were used in the analysis of data. The study findings revealed that pupils faced challenges in solving enlargement transformation geometry problems. The study demonstrated that most of the grade 12 pupils were reasoning at the lowest level (visualisation) of the Van Hiele’s model of geometric thought. Pupils had problems with the concept of the centre and scale factor of an enlargement. The findings revealed that pupils demonstrated ignorance of the basic relationships of figures under enlargement through identifying incorrect image of the triangular figure given. Pupils expressed challenges in explaining the steps they took to obtain the image after enlargement because they did not have enough pre-requisite knowledge on the topic. Zambian Secondary Schools have experienced a low performance in Mathematics at School Certificate level in recent years (Examination Council of Zambia (ECZ), 2016). An analysis of results in terms of topics in the examinations showed that Transformation geometry is one of the topics in mathematics in which pupils have not been performing very well (ECZ, 2009; ECZ, 2008). For this reason, this study was set to establish the challenges pupils faced in learning transformation geometry in particular enlargement transformation geometry in two schools in Zambia. School A is located in Lusaka District and School B is in Monze district. The Van Hiele Model of levels of thought were used as the theoretical framework of the study. The study largely used a mixed method approach that included descriptive study design. The data was obtained through written test and interview schedules. One hundred Grade 12 pupils, all together from both schools wrote the test and six volunteered to undergo interview. Data was analysed through a process of coding, categorizing, clustering and performance indicators corresponding to the Van Hiele’s model were used in the analysis of data. The study findings revealed that pupils faced challenges in solving enlargement transformation geometry problems. The study demonstrated that most of the grade 12 pupils were reasoning at the lowest level (visualisation) of the Van Hiele’s model of geometric thought. Pupils had problems with the concept of the centre and scale factor of an enlargement. The findings revealed that pupils demonstrated ignorance of the basic relationships of figures under enlargement through identifying incorrect image of the triangular figure given. Pupils expressed challenges in explaining the steps they took to obtain the image after enlargement because they did not have enough pre-requisite knowledge on the topic. The study concluded that pupils lacked relevant and enough pre-requisite knowledge to enlargement transformation, and they lacked exposure to more geometrical problem-solving situations. The study concluded that teachers should strive to motivate learners on the topic and equip them with necessary pre-requisite knowledge on enlargement transformation. This should include introducing pupils to more practical situational problem-solving tasks which should involve explanation as well.