14 research outputs found
Connection between prior knowledge and student achievement in engineering mathematics
In the paper the author reports on connections between first-year engineering mathematics studentsâ prior mathematical knowledge and their achievement in an engineering mathematics (year) course in an extended curriculum programme. The importance of links between prior knowledge in learning and performance is widely supported in educational studies, also in learning mathematics. Furthermore, the transition from school to university is a substantial hurdle in the learning trajectory of many students, and particularly in science and engineering courses. The author exposed students to a carefully designed diagnostic entrance test that consists of different content and knowledge components, and correlated these results, by means of regression analysis, with studentsâ achievement scores at the end of term 1, term 2, and the first semester. The results show a moderate correlation. This research is meant as the beginning of exploring possibilities to predict study success in mathematics by means of an entrance test and of developing possibilities of remedying studentsâ entrance deficiencies and thus increasing study success. More broadly, this inquiry was conducted to explore adequate ways of assessing prior knowledge that could be useful in supporting studentsâ learning of engineering mathematics in a South African context.Institute for Science and Technology Education (ISTE
Strategic support to students' competency development in the mathematical modelling process: A qualitative study
This article reports on third-year mathematics studentsâ competency and sub-competency development through providing intentional support in the learning of mathematical modelling. Students oftenexperience modelling as difficult, and obstructions in the modelling process can lead to a dead end. Literature reports confirm that the modelling task is central in the modelling experience and a carefully planned task, aligned with a suitable activity sheet, can be used as a scaffold in learning mathematical modelling. Hence, this inquiry was conducted to provide a scaffold, as strategic support, for studentsâ mathematical modelling competency development in the early stages of a modelling cycle. Guided by the framework of the Zone of Proximal Development, key elements suggested by the metaphor scaffolding are considered in the learning experience. Based on an analysis of activity sheets collected through group work, an example of a realistic and an unrealistic solution is presented, and studentsâ development of mathematical modelling competencies is argued. Finally, suggestions for intentional support in the modelling process are discussed
Attitudes of pre-service mathematics teachers towards modelling : a South African inquiry
Abstract: This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in teaching modelling is widely recognized. Modelling was thus included for the first time in the mathematics education curriculum of a South African university. Based on their modelling exposure, the participants revealed their attitudes via an Attitudes towards Mathematics Modelling Inventory. The Mann Whitney U-test detected significant differences between gender and achievement groups. Most participants displayed positive attitudes towards modelling, even after this brief exposure. The main implications of the study are that the modelling competencies of mathematics pre-service-teachers could be strengthened during their formal education by lecturers that adopt an appropriate modelling pedagogy that takes cognizance of their attitudes, while gradually building their confidence
Uitdagings van uitkomsgebaseerde onderwys vir die bestuur van die wiskundeklaskamer
M.Ed.In South Africa outcomes-based education with Curriculum 2005 brought great changes to learners, educators and parents. The purpose of this investigation was in the first place to determine the influence of OBE on the classroom management of the Mathematics educator in the senior phase. Secondly this research was to determine effective classroom management guidelines. Data was collected before and after the implementation of OBE. The respondents were Grade 8 and 9 educators in four different schools, situated in four different urban communities, respresentative of the broader South African nation. Data was collected by means of focus group interviews, analyzed by means of content analysis and conducted by the researcher and an independent analyst. Teachers identified problems regarding classroom management, existing support factors and support factors that they would like to have. Many of the problems identified by the respondents were common before and after the implementation of OBE. Some of these problems were the learners lack of interest in their work, communication difficulties between the educator and learners from township communities, lack of a learning culture, a very low interest in school activities by parents, absence of resources and lack of support by the Department of Education. Educators mentioned some other problems that occurred after the implementation of OBE. A big issue to educators is overcrowding of classes and the amount of work that comes along with it. They find it impossible to teach Mathematics effectively in such big classes. Contributing to this problem are the negative attitudes of learners towards the learning situation. In OBE, the learners' input is important, and educators struggled to get them to work. Almost all the respondents require effective guidelines for teaching and the necessary resources. Educators as well as the learners struggle with the increased workload. In view of the findings, it is clear that teachers require the necessary skills for implementing OBE effectively. Enough resources, smaller classes and enough textbooks are important necessities. From this study it appeared that learners should be actively involved in the learning process, and educators have to be very well prepared for everyday's class. Well-prepared groupwork by educators provides for active involvement of the learners in the learning process and the opportunity for the learner to accept responsibility for his/her own learning success as well as that of his/her fellow-learners. Mathematics teachers need to spend more time on basic number skills, assessment of new work and should be very strict on homework. Educators in the Mathematics class have to motivate learners and this requires motivated educators. The enjoyment of learning should be a very important factor. The correct steps need to be taken by the Department of Education to ensure a positive learning experience by educator and learner
Assessment of tertiary studentsâ learning of statistical modelling
In this paper, we report on the learning of statistical modelling in a second-year statistics module through the assessment of a problem that required a Monte Carlo simulation. On the forefront of the 4th industrial revolution is science, technology, engineering and mathematics subjects, where mathematical statistics plays a key role in topics such as machine learning and predictive analysis. Students often find statistical modelling difficult, where obstructions in the modelling process could lead towards a dead-end. For this reason, assessment of learning, for learning and as learning in statistics education seems necessary. General pillars of good assessment practice is considered in this study, as well as guidelines for the development of studentsâ conceptual understanding of the content, such as, statistical reasoning, statistical thinking and statistical literacy. Therefore, this study was conducted to provide educators with information of student achievement of desired student learning outcomes. Based on an analysis of the reports collected individually and through voluntary group work, descriptive statistics are presented. These results are discussed in relation with assessment measures and provides a basis for teaching and learning statistics.Institute for Science and Technology Education (ISTE
Teaching and learning first-year engineering mathematics over a distance: A critical view over two consecutive years
This article reports on the empirical results and practical aspects concerning the teaching and learning of first-year engineering mathematics at a distance. The investigation over two consecutive years (2020 and 2021) is meant to yield prospects and contribute to the development of suitable pedagogies for online mathematics teaching and learning for engineering students in South Africa in the future. In 2020, lecturers were faced with a âsuddenâ shift from face-to-face to online teaching and the focus was to save the academic year and leave no student behind; in 2021 the situation was unchanged. Lecturers had to consider key aspects (such as the module structure, teaching theory and practice, and perspectives on âwhat can workâ) in the transition and continuation from face-toface to fully online and developing a suitable teaching and learning approach. Approximately 1000 first-year engineering students at the University of Johannesburg, South Africa, were exposed to the newly developed online teaching and learning approach in both years. The approach includes the following key elements: an evaluation of prior knowledge by a diagnostic test; an investigation of studentsâ attitudes towards mathematics by means of the SATM questionnaire; weekly virtual lecture and tutorial sessions; weekly homework tasks; additional online resources; discussion forums between all role players (students, tutors and lecturers); online tutor support; the use of e-textbooks and online assessments via the university learning management system and an external platform (such as WeBWorK). Both years followed a similar approach, although slight changes were implemented in 2021. Descriptive statistics from key elements were used to monitor the studentsâ involvement and progress in both years. Results show the teaching and learning approach is effective but has room for improvement. Particularly, the results encourage addressing the needs of the students and lecturers when implementing pedagogical aspects in learning mathematics at a distance
Investigating possibilities of predictive mathematical models to identify at-risk students in the South African higher education context
This article reports on the results of an investigation of the predictive accuracy of five different mathematical models to identify at-risk students in a Business Statistics course. Low levels of studentsâ success, especially in mathematics-related subjects such as statistics, are a salient problem in South Africa and other countries. Statistical knowledge is included in a variety of programmes offered by many faculties at tertiary level, and early prediction of at-risk students seems necessary to enhance academic success especially when dealing with large class groups. In this study, we used 395 Business Statistics studentsâ grades from an academic semester at an urban university in South Africa to build a predictive model to identify at-risk students. Grounded on Meyerâs model evaluation criteria and striving for a balance between accuracy and simplicity, two out of five models are identified as viable predictive models in identifying at-risk students by using a cross- validation test. The article shows the possibilities and limits in deriving information from a number of covariates. These results are interesting and have implications for educational practice in statistics courses
The Role of ICTs in Collaboration During the COVID-19 School Year
Abstract: The focus of this research was on the role of ICTs in collaboration amongst teachers in five secondary mathematics departments. Data was collected through an online form, which was largely defined from a previously utilized social network survey for educators from North Western University, and analyzed through a social network analysis method. Results indicate that ICTs played a significant role, largely via email, in providing a communication medium to secondary mathematics teachers that allowed collaboration to take place during the COVID-19 affected school year. The identified networks of collaborative interactions exhibited patterns of subgroupings, high status connected individuals, and a higher frequency of certain types of collaborations. There is also evidence that teachers rarely go outside their school departments for collaborations. Results could also be interesting for post-COVID school years
A strategy for the integration of mathematical modelling into the formal education of mathematics student teachers
Abstract: The inclusion of real-life examples and applications is regarded as an essential component in mathematics curricula worldwide, and likewise in South Africa. As a vehicle to investigate and solve real-life problems, mathematical modelling2 was first introduced in the Curriculum and Assessment Policy Statement (CAPS) in South Africa in 2011. Such authentic examples might enhance the mathematical modelling competencies of student teachers and school learners3 but it largely depended on in-service mathematics teachers who were well-prepared to teach mathematical modelling, meaning âquality teachingâ. However, local and international research reports confirmed the challenges faced by mathematics teachers in teaching mathematical modelling. The main purpose of this study was to identify a set of most desirable elements and underlying principles to contribute towards the effective integration of mathematical modelling into the formal education programme of mathematics student teachers. Three primary directives provided a stimulus for this study. Firstly, student teachers required adequate preparation in respect of their âknowledge-in-actionâ of mathematical modelling. This would include competencies for them as both modellers themselves and as facilitators of such activities. Secondly, mathematical modelling had a positive influence on the teaching and learning of mathematics and on its inclusion in (and desires of) the current South African mathematics curriculum (CAPS). Thirdly, the obligation rested with teacher education programmes to prepare student teachers adequately for their profession. As a result, the study exposed student teachers (both as mathematical modellers and facilitators of mathematical modelling) to a well-planned set of modelling activities, while also monitoring their development in mathematical modelling competencies and change in attitude towards such activities over time. Based on a pragmatic (real-world practice-orientated) world view, a design-based research (DBR) approach was chosen for the study. In order to answer the research questions, mixed data were collected, analysed and integrated according to the concurrent triangulation procedure. The DBR approach was carefully planned and based on an in-depth literature review, the researchersâ personal experience and ideas from other practitioners. The strategy...D.Phil.(Mathematics Education