African Journal of Research in Mathematics, Science and Technology Education

This paper seeks to explore the nature of dialogue within calculus lecture rooms. This paper reports on part of a larger study, in which the participants were two lecturers lecturing to 198 third year pre-service teachers at a University in South Africa. This qualitative interpretive study was framed within the ambits of social constructivism and aspects of Mortimer and Scott’s framework were used to analyse dialogue in the lecture room. Data for this paper were generated through video-recorded lecture observations. Subsequently, a qualitative data analysis of the generated data revealed that dialogue within the calculus lecture rooms under study may be in the form of explanations and questioning. Questioning included questions that assess students’ prior knowledge, probing, follow-up and guiding questions. The findings of this study are of value to both lecturers and students within higher education with implications for teaching and learning mathematics within higher education are presented.

The Department of Basic Education in South Africa has identified factorisation as a problem area in Mathematics teaching. Learners in earlier grades are exposed to mathematical tasks, involving concepts, such as factors of integers, fractions, equivalent fractions and prime numbers, that are easier to solve when the divisibility rules are applied. An experiment was designed to investigate the effect of learners’ knowledge and their application of the divisibility rules on their gaze behaviour. Seventy-eight learners in Grades 4–7 participated in an eye-tracking study where questions on divisibility were presented on a computer screen. Learners were expected to indicate whether a five-digit dividend was divisible by a divisor and provide reasons for their answers. Gaze behaviour (expressed as the percentage of total fixation time that was spent on each digit), along with learners’ verbal responses were used to determine whether a given divisibility rule was applied correctly. The findings show that learners apply different strategies to inspect the dividend when they know the divisibility rules and apply them correctly as opposed to when they do not know the rules and/or apply them incorrectly. It is argued that, since knowledge of the divisibility rules is a reliable predictor for gaze behaviour, gaze behaviour can in turn be used to assist teachers to identify a lack of knowledge and/or the incorrect application of the divisibility rules. Teachers can then cautiously intervene with revision to assist learners whose gaze behaviour indicates that they need assistance.

The study aimed to determine the most effective of three pedagogies to improve Grade 12 learners’ understanding of the photoelectric effect when the teaching was done using chalk and talk, guided learning with computer simulations (CS) as a demonstration tool and semi-autonomous learning where the learners used the CS individually with limited support. A randomised pre-/post-test control group design was implemented. A paired-sample t-test on the post-test scores indicated that the guided learning experimental group (N=10) performed better than the semi-autonomous learning experimental group (N=10) [t-statistics, t(9) = −6.135, p < 0.05]. Even the control group (N=10) where the teacher used chalk and talk performed better than the semi-autonomous learning experimental group. An analysis of covariance on the post-test scores with learners’ pre-test scores showed a significant effect on the instructional group favouring the guided learning experimental group. It is, therefore, suggested that guided learning where the teacher manipulates the CS is a better method for the effective teaching of the photoelectric effect.