Students’ performances in mathematics in an Open Distant Learning setting have not always been impressive. An exploratory study into the problem solving skills of the University of South Africa students in the Calculus module MAT112 is being conducted using past examinations scripts between 2006 and 2009. The study re-assesses the work done in the end-of-year Calculus examinations, by both looking at the distribution of marks awarded and assigning new scores based on an assessment rubric adapted for the problem at hand. Further assessment of qualitative dimensions that is important for problem solving in Calculus is developed from the data obtained from the assessment rubric. Using factor analysis, a hesitation factor, transfer-of-knowledge factor as well as ingenuity factor, are identified in successful Calculus problem solving. The study proposes two conceptual models; the first is to guide students in solving Calculus problems while the second one is meant to assist lecturers in the assessment of students of Calculus. / Science and Technology Education / M. Ed. (Technology Education)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho tem como objetivo auxiliar professores de Educação Básica a abordar alguns conceitos básicos de Cálculo Diferencial e Integral no terceiro ano do ensino médio, utilizando os softwares wxMaxima e Geogebra. Nossa proposta visa resgatar o ensino do Cálculo no âmbito escolar, mas de uma maneira diferente da tradicional, utilizando a tecnologia em nosso favor, como uma ferramenta facilitadora no processo ensino-aprendizagem de conceitos de limites, derivadas e integrais. A ideia é que toda a parte algébrica e gráfica, que exige conhecimentos matemáticos específicos, seja feita pelos softwares e que os estudantes aprendam a interpretar as soluções que as ferramentas nos fornecem e a conhecerem um pouco mais sobre a matemática e suas aplicações. / The present work aims to help Basic Education teachers to approach some basic concepts of Differential and Integral Calculus in the third year of high school using the software wxMaxima and Geogebra. Our purpose is to recover the teaching of Calculus in the school context, but in a different way from the traditional one, using the technology in our favor, as a facilitating tool in the teaching-learning process of boundary, derivative and integral concepts. The idea is that all the algebraic and graphic part, which requires specific mathematical knowledge, is done by software and that students learn to interpret the solutions that the tools provide us and to know a little more about mathematics and its applications.

The study attempted to determine the causes of poor performance among Grade 12 learners in tasks involving calculus, especially in cubic graphs and the application of differential calculus. The study was conducted in three schools of the Msukaligwa 1 Circuit in the Gert Sibande District, Mpumalanga Province in South Africa. Differential calculus is a branch of mathematics that is concerned mainly with the study of the rate of change of functions with respect to their variables especially through the use derivatives and differentials. Students have difficulties in learning and mastering this section of calculus as is revealed by examiners’ and moderators’ reports year after year. The purpose of this study was to investigate the possible reasons for the poor performance by Grade 12 learners in calculus-based tasks, especially in cubic graphs and the application in optimisation. The study sought to investigate the causes of the poor performance by Grade 12 learners in tasks based on these two subtopics of calculus. Three schools were selected by means of purposive sampling: one former model C, one Mathematics, Science and Technology Academy (MSTA) and one other school that does not fall in either of these two categories. This enabled the study to have participants from diverse backgrounds. A qualitative research design was used. Data was collected using learners’ scripts for the three formal tasks: May common test, June (midyear) and Trial (preparatory) examinations. Only the questions involving cubic graphs and the application of calculus were part of the study. Analysis was done in order to determine learners’ challenges, common mistakes, and misconceptions, but also of good responses given by learners. / Mathematics Education / M. Ed. (Mathematics Education)

Students’ performances in mathematics in an Open Distant Learning setting have not always been impressive. An exploratory study into the problem solving skills of the University of South Africa students in the Calculus module MAT112 is being conducted using past examinations scripts between 2006 and 2009. The study re-assesses the work done in the end-of-year Calculus examinations, by both looking at the distribution of marks awarded and assigning new scores based on an assessment rubric adapted for the problem at hand. Further assessment of qualitative dimensions that is important for problem solving in Calculus is developed from the data obtained from the assessment rubric. Using factor analysis, a hesitation factor, transfer-of-knowledge factor as well as ingenuity factor, are identified in successful Calculus problem solving. The study proposes two conceptual models; the first is to guide students in solving Calculus problems while the second one is meant to assist lecturers in the assessment of students of Calculus. / Science and Technology Education / M. Ed. (Technology Education)

With the realization that traditional instructional approach has not yielded satisfactory results, quasi-experimental and descriptive research designs were employed to investigate whether the application of constructivist instructional approach in the learning of stationary points in differential calculus by Grade 12 learners in South Africa would improve conceptual learning. Three Gauteng high schools of 204 Grade 12 learners constituted the research fields – one served as the control group while the other two represented the experimental group. Being a mixed-method research, quantitative data were gathered through pre-test and post-test while qualitative data were collected from classroom observations. Both inferential and descriptive statistical methods of data collection and analysis were used. The results obtained indicate that the experimental group demonstrated a better understanding of the concept of stationary points than the control group. / Mathematics Education / M. Sc. (Mathematics Education)

Intermediate calculus bridges secondary school and advanced university mathematics courses. Most mathematics education research literatures indicated that the conceptual knowledge in intermediate calculus has challenged first year undergraduate mathematics and science learners to a great extent through the lecture method. The content knowledge attained by them has been tremendously decreasing. Negative attitude exhibited by students toward calculus was highly influenced by the lecture method used. Generally, students have not looked at the learning of all mathematics courses offered in universities as normal as other courses. Due to this lack of background conceptual knowledge in learners, they have been highly frustrated by the learning of advanced mathematics courses. Taking the understanding of teaching and learning challenge of conceptual knowledge of calculus into consideration, Ethiopian public universities have been encouraging instructors to devise and implement active learning methods through any professional development training opportunity. The training was aimed to enhance learners’ content knowledge and attitude towards calculus. This is one of the main reasons for the motivation of this study that experimental group learners were allowed to be nurtured by the lecture method in their mainstream class, and then also the active learning intervention method integrated with GeoGebra in the mathematics laboratory class. Only conventional lecture method was used to teach the comparison group in both the mainstream and mathematics laboratory class. The purpose of the study was to explore the Gambari and Yusuf (2016) stimulus of the jigsaw co-operative learning method combined with GeoGebra (JCLGS) on statistics and chemistry learners’ content knowledge improvement and change of their attitude towards calculus. The post-positivism mixed methods tactic was used in a non-equivalent pre- and post-test comparison group quasi-experimental design. The population of the study was the whole freshman mathematics and science degree program learners of two public universities in Ethiopia in 2017. Samples of the size 150 in both the experimental and comparison groups were drawn utilizing two-stage random sampling technique. A questionnaire using a Likert-scale on attitudes and an achievement test were sources used for data collection. Data analysis employed descriptive statistics conducting an independent samples t-test and a Two Way ANOVA for repeated measures using SPSS23. Each of the findings on content knowledge, conceptual knowledge, and procedural knowledge development produced through the TWO-Way ANOVA, respectively as F(1,148)=80.917; 𝜂2=.353; p<.01, F(1,148)=106.913; 𝜂2=.419; p<.01, and F(1,148)=7.328; 𝜂2=.047; p<.01, revealed a statistically significant difference between the treatment and comparison groups from pre-test to post-test. These findings show that the experimental group participants were highly beneficial in developing their content knowledge and conceptual knowledge through the active learning approach and technology-based learning strategy using Vygotsky’s socio-cultural learning theory. The JCLGS learning environment representing Vygotsky’s socio-cultural learning theory modestly influenced the procedural knowledge learning of the experimental group learners’. Although the lecture method affected the comparison group students’ knowledge development in calculus during the academic semester, the impact was not comparable to that of the active learning approach and technology-based learning strategy. The major reason for this was the attention and care given to the active learning intervention integrated with GeoGebra by the researcher, data collectors, and research participants. Overall findings showed that the active learning intervention allowed the experimental group students to considerably enhance their conceptual knowledge and content knowledge in calculus. Learners also positively changed their opinion towards calculus and GeoGebra. The intervention was a group interactive environment that allowed students’ to be reflective, share prior experience and knowledge, and independent learners. As a matter of fact, educators are advised to model such a combination of active learning approach and technology-based learning strategy in their classroom instructional setting and practices. Consequently, their learners will adequately benefit to understand the subject matter and positively change their opinion towards university mathematics. / Mathematics Education / Ph. D. (Mathematics, Science and Technology Education)