An investigation into some causes of cognitive deficiencies among high school pupils in the learning of differential calculus and implications for further study

Abstract

Little attention is usually given to the disadvantaged pupils' lack of problem solving skills and thinking skills needed for successful learning of differential calculus. Factors like what makes (disadvantaged) pupils not function (cognitively) very well are usually overlooked. The only factor considered by (some) teachers being only to comment on the impairments that already exists. That is for example labelling students as unintelliqent "foolish" or "dull". In some cases the blame is placed fully on the system (Government and its hidden agenda). While others blame the environment in which the pupils live without finding what impact the situations have on the learners' cognition. There is a need to know where and what causes cognitive impairment in general. This study looks at the domain of differential calculus. This research therefore sets out to find what the causes of cognitive deficiencies are in the learning of differential calculus. To find out some of the causes 67 High School pupils and 40 first year University students completed the questionnaires, 34 pupils wrote the differential calculus test, 10 final year matric teachers ,also contributed some information about some causes of cognitive deficiencies and how they could possibly be remedied. 4 first-year university mathematics students and 7 high school pupils were involved in the thinking - aloud interviews. The interviews were audio-taped and then subjected to a protocol analysis. Special references to this study were made to the works of Feuerstein, Perkins and Sternberg Thus in general the research set out to answer the following questions: 1. Which problems do pupils think they have with regard to learning differential calculus? 2. Which cognitive deficiencies or difficulties do pupils have in the learning of differential calculus? 3. What role do motivation and affective processes and other non-cognitive processes have in the learning of differential calculus? 4. Is there any relationship between the pupils' cognitive deficiencies, motivation and affective processes as well as the problems they think they have with regard to learning differential calculus? 5. What perception do practising teaching have on the above? 6. Is there any change or changes for first year university mathematics students? 7. Which instructional strategies can be used to rectify such deficiencies? 8. What are the implications and recommendations for further study? .... It was found that there are many cases of deficiencies among high' school pupils. These can briefly be summarised as follows: lack of effective institutional processes, poor socio-economic and political climate for blacks, inadequate research (thinking aloud) among the pupils. Finally the list of 28 recommendations and implementation for further study were suggested. These 28 recommendations were further divided into 5 general headings that teachers could experiment with in the classroom and school.