M.Ed. / Please refer to full text to view abstract

M.Ed. (Subject Didactics) / Research shows that "the aims of secondary school's teaching of mathematics are often not realized with many pupils leaving the school with passive knowledge of mathematics" (H.S.R.C. 1981:8). This means that knowledge of mathematical facts are reproduced on demand, instead of active mathematical knowledge " which is congruent with the aims of teaching secondary mathematics" (Crooks, 1988 : 6/7). Active knowledge of mathematics implies and characterised by the understanding of concepts, principles that underlie facts and ideas and principles and concepts that are connected to each other" (Entwistle & Entwistle, 1992 : 2). Active knowledge also enables pupils to act intellectually independently. One reason for the previously mentioned predicament is that "teaching often encourage passive knowledge because the teaching practice of mathematics teachers are often not in accordance with their educational aims" (Gravett, 1994 :6). Thus, a discrepancy exists between teacher's intentions of teaching mathematics and their conduct during teaching. It can be argued also that teachers teach mathematics in the classroom but that the pupils not always effectively learn. It is from the perception above that a constructivistic view of learning as a conceptual change underlies the idea that teaching "as the creation of a classroom context conducive to learning" (Strike & Posner, 1985:117). Biggs (1993 : 74) thus argues that "if knowledge is constructed, rather than recorded as received, it does not make sense to think of teaching as imparting knowledge, but rather as creating learning environments that enhance the process of mathematical knowledge construction". Russell (1969: 14) mentions that "mathematics is a subject in which we never know what we are talking about, nor whether what we are saying is true". The views, amongst others Oosthuizen, Swart and Gildenhuys (1992:2) see mathematics as "an essential language of a creative but deductive process which has its origins in the problems of the physical world", In the light of this, the origin of mathematics in the real world, it can be argued that from a "constructivistic perspective, mathematical learning is an active process by which pupils construct their own mathematical knowledge in the light of their existing knowledge and through interaction with the world around them" (Gravett, 1994 : 6/7). "Construction, not absorption or unfocused discovery, enables learning" (Leder, 1993 : 13). Mathematics is not something discovered by mankind, mathematics is a creation of mankind and is transmitted and changed from one generation to the next.

M.Ed. / The study examines the nature of English competence in both learners and teachers in black schools. It was conducted as a result of the investigator in this study being directly involved in teaching English as a second language in a black high school and being a beneficiary of English language teaching projects. As is shown in the study, these projects do not effectively serve their stated purpose, that is, to improve teacher and learner competency in English. The study was conducted by exploring existing literature on the topic and investigations already undertaken. An empirical component is included comprising an observation of an English lesson in progress. The conclusion reached in the study is that an unfortunate cycle still persists where learners taught by teachers who are incompetent in English go through the existing inadequate and inefficient milieu in education to become incompetent English language teachers themselves. The recommendations in this study are that there needs to be a re-evaluation of present English language teaching methods particularly in the light of the fact that the government is in the process of implementing a new educational system called Outcomes Based Education. Furthermore, this study draws attention to the inadequacies prevalent in teacher training and subsequent teacher practice in the classroom.