Attitudinal scale measures in Euclidean geometry: what do they measure?

The purpose of the study was to look at the two forms of validation, i.e. face validity and construct validity, of an attitudinal scale measuring learners' attitude towards Euclidean geometry. The article teases out elements involved in face and construct validation and then engages in a discourse to highlight and investigate those elements in validation that may be untenable in the light of existing practice. With the support of empirical data, the argument presented is that the use of face and construct validity should be a given in studies involving the measurement of attitude. South African Journal of Education Vol.24(1) 2004: 1-

Investigating the status of supplementary tuition in the teaching and learning of mathematics

The study seeks to investigate the status of supplementary tuition in the teaching and learning of mathematics and mathematical literacy. The study followed a descriptive survey design involving the use of learner and teacher questionnaires. A convenient sample of mathematics and mathematical literacy teachers together with a stratified sample of their Grade 11 learners were drawn from a purposive sample of highperforming high schools in the East London district of the Eastern Cape, South Africa. The results show that supplementary tuition is popular, especially among girls, and it is in three forms (i.e. private tuition, vacation school and problem-solving classes): Problemsolving classes dominated by working on past/model examination papers is the most preferred; in some instances supplementary tuition is offered for a fee; it is not only confined to poor performing learners; and participation in supplementary tuition is influenced by a variety of factors

The effect of a group approach on the performance of high school mathematics learners

In this study, we investigated the effects of a group approach versus a non-group approach on the mathematics performance of learners. A group approach refers to an arrangement in which learners sit together to discuss and solve mathematics tasks. We studied a convenience sample of low-performing Grade 10 mathematics learners using a quasi-experimental design with a non-equivalent control group. The experimental group was taught using a group approach and the control group using non-group approach instruction. To measure the effects of teaching approaches, we administered a Financial Mathematics Achievement Test (FMAT) before and after the experiment. Using a one-way analysis of covariance (ANCOVA) the study found that learners in a group approach learning environment performed significantly better than learners taught through a non-group teaching mode (p < 0.05). The theory of cognitive load was used to interpret the results. The results suggest that a group approach may be effective when teaching certain mathematics topics in Grade 10 classrooms

Students’ mathematics-related belief systems and their strategies for solving non-routine mathematical problems

This study explored students’ mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson’s 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students from five high schools in Tshwane North District, Gauteng province of South Africa. Data were collected using a mathematics beliefs questionnaire, a mathematics problem-solving test and interview. Quantitative and qualitative research techniques were used for data analysis. It was found that the students held all the three belief systems (utilitarian, systematic and exploratory) at different degrees of intensity and the belief systems and strategies for problem-solving had a weak positive linear relationship, and there were no statistically significant differences among mean scores of the students holding systematic, exploratory and utilitarian beliefs. They apply unsystematic guess, check and revise; systematic guess, check and revise; systematic listing; looking for patterns; consider a simple case; modelling; logical reasoning; no logical reasoning; trial-and-error and use a formula in solving non-routine mathematical problems. Furthermore, it was found that the systematic belief system could explain the students’ behaviour in problem-solving more than the exploratory and utilitarian belief systems

Lesotho’s students’ achievement in mathematics and their teachers’ background and professional development

The study sought to obtain information on the relationship, if any, between students’ achievement and teacher background as well as between students’ achievement and professional development. The respective correlation coefficient showed that there was a significant relationship between students’ achievement and teacher background and an insignificant relationship between students’ achievement and the extent of professional development. Of the three components of teacher background (viz., qualification, subject major and teaching experience), teacher qualification showed the strongest significant relationship with students’ achievement, followed by level of subject major. But teaching experience displayed a curvilinear significant relationship with students’ achievement. It was concluded that quality qualifications and deep subject content knowledge tend to make teachers more effective while teachers improve and develop when they are exposed to quality professional development programmes

Lesotho’s students’ achievement in mathematics and their teachers’ background and professional development

The study sought to obtain information on the relationship, if any, between students’ achievement and teacher background as well as between students’ achievement and professional development. The respective correlation coefficient showed that there was a significant relationship between students’ achievement and teacher background and an insignificant relationship between students’ achievement and the extent of professional development. Of the three components of teacher background (viz., qualification, subject major and teaching experience), teacher qualification showed the strongest significant relationship with students’ achievement, followed by level of subject major. But teaching experience displayed a curvilinear significant relationship with students’ achievement. It was concluded that quality qualifications and deep subject content knowledge tend to make teachers more effective while teachers improve and develop when they are exposed to quality professional development programmes