Description

The emerging importance of statistical knowledge has led to statistics being introduced into the school internationally. South Africa, recognising this importance, has also introduced statistics in the secondary school system. The introduction of new and unfamiliar topics in a curriculum is often accompanied by a variety of challenges. The challenges that most schools face, in South Africa as well as internationally, is providing teachers who are able to effectively teach for the development of statistical understanding, rather than merely doing some calculations.
The purpose of this study was to identify the cognitive levels of statistical knowledge that students attain as they progress through the secondary school system and then develop a teaching framework to help teachers approach teaching statistics in a manner that would enhance statistical reasoning and thinking. Mixed methods methodology was used in this research. Data were collected in two stages. The first stage involved qualitative data collection. Three written assessment instruments (one for each of the Grades 10, 11 and 12) were developed, checked for reliability and administered to about 400 students. The objectives of these instruments were to establish concepts and skills that students had successfully achieved, concepts that students had been unsuccessful in and concepts that students had failed to apply successfully. Data analysis was done and 13 students were selected for interviews, the second stage of data collection. The interviews provided qualitative data for the study. Deeper insight into students’ understanding and misconceptions was revealed during the interviews.
The results of the study showed that most students only managed to achieve the lowest of the statistical cognitive levels, statistical literacy. This cognitive level does not equip students with tools to reason and think statistically. The results also revealed that students have learned statistics through the use of formulae, without understanding their foundation. Modern technology makes calculations instant and more accurate, minimising the importance of ability to perform manual calculations. This implies that the focus on statistical knowledge should be on reasoning and thinking. From these results it is recommended that statistics teaching that enhances development of reasoning and thinking needs to include the importance of context, computing, comparing, contrasting and connection between statistical concepts.