This study investigates learning difficulties involving volumes of solids of revolution (VSOR) at two FET colleges in Gauteng province, in South Africa. The research question for this study was: Why do students have difficulty when learning about volumes of solids of revolution? In order to answer the research question five skill factors were identified as the conceptual framework, subdivided into 11 elements. The five skill factors are: I. Graphing skills and translating between visual graphs and algebraic equations/expressions, II. Three-dimensional thinking, III. Moving between discrete and continuous representations, IV. General manipulation skills and V. Consolidation and general level of cognitive development. Before collecting the main data for this study, a preliminary study and a pilot study were conducted. The data for the main study were then collected in six different investigations. The investigations consisted of two runs of a questionnaire, classroom observations, examination analysis; detailed examination responses and an interview with one student. The results from the questionnaire runs as well as the pilot study reveal that students performed poorly in tasks involving three-dimensional thinking (Skill factor II), moving between discrete and continuous representations (Skill factor III), and consolidation and general level of cognitive development (Skill factor V). Students' performance was satisfactory in tasks involving graphing skills and translating between visual graphs and algebraic equations/expressions (Skill factor I) and general manipulation skills (Skill factor IV). Students were also more competent in solving problems that involved procedural skills than those that required conceptual skills. The challenges that students were faced with in class, evident from the classroom observations allude to the fact that the topic of VSOR is difficult to teach and to learn. It is recommended that VSOR be taught and assessed more conceptually in line with the five skill factors; that curriculum developers must communicate with other stakeholders like industries and other institutions of higher learning and that the Department of Education must provide adequate training for these teachers and liaise with industry in this regard. It is also recommended that the suitability of this topic for the particular cohort of students be reconsidered as it appears to be of too high cognitive demand. / Thesis (PhD)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

Student Number : 0110601M - MSc research report - Faculty of Science / Based on the perceived need for improved graphing skills of students at first-year university level, two lecturers wanted to produce a web-based computer programme to improve first-year university biology students’ ability to construct and interpret graphs. Prior to designing and developing the package, however, it was important to establish whether there was a need for such a programme, and what might need to be included. The investigation to establish this provided the research described in this research report. A situation analysis was conducted to establish the nature and extent of the problems of graphing skills discussed anecdotally in the staff room of biology departments at a number of institutes. The ultimate intention (beyond this study) was to determine whether the problems were extensive and serious enough to warrant developing supplementary teaching materials to teach graphing skills. All lecturers (n = 5) and teaching assistants (n = 4) involved in using or teaching graphing skills to first-year biology students at one university were identified and interviewed. The purpose of the interviews was to establish the problems they believed are exhibited by their first-year students (with reference to graphing skills), and the nature and extent of current teaching of such skills in their first-year courses. In order to triangulate the information on student’s problems an item analysis was conducted of all questions incorporating graphs in two mid-year examination papers (n = 478 and n = 65), and students were observed during a practical session (n = 43). Results revealed that students experienced fewer problems with interpreting graphs than with graph construction. Of the four categories of graph interpretation problems identified by the teaching staff, the most popular category was students inability to describe quantitatively what the graph is showing (4 teaching staff). This was confirmed in the question paper analysis when 58% of the medics students (n=478) were unable to answer correctly one question involving several interpretation skills. No specific skills for graph interpretation were observed as being a problem in the College of Science question paper (n=65). Observations showed interrelating graphs as the biggest problem (5 students out of 43). Five categories for problems with graph construction were identified by the teaching staff. The most commonly mentioned problem (4 teaching staff) was identifying or plotting variables, whereas class observation revealed scaling axes as the most problematic skill shown by students (15 out of 43). In the exams, 80% of the medics students could not correctly answer one question requiring multiple skills including identifying variables, and 56% could not correctly answer another question that required skills that also involved identifying variables. The College of Science question paper revealed that 85% of the students could not supply the units of measurement for the y axis. A needs analysis was conducted to establish how the lecturers thought graphing skills should be taught and who should teach the skills. This information was needed to provide suggestions (from education “experts”) about what could be included in the computer programme to be developed subsequent to the research study, and how the teaching could best be done. Four members of the teaching staff said it was important to give students a lot of exercises to practice the skills and five members of the teaching staff said it was the responsibility of the university tutors or lab staff to teach graphing skills.

This study was designed to investigate the roles of gender and learning styles on tenth grade students&amp / #8217 / kinematics graphing skills. The study was conducted in 14 representative cities throughout seven different geographical regions over Turkey with a total of 989 tenth grade students in last four weeks of the spring semester of 2002-2003 school year. Findings of the kinematics graphing skills test indicated that general performances of the students were very low and many students have difficulties in interpreting kinematics graphs. When the data were analyzed using Analysis of Covariance (ANCOVA), while controlling the effects of students&amp / #8217 / age, previous physics course grades and previous mathematics course grades, the results indicate that there was no significant difference among the kinematics graphing skills test scores of students having different learning styles. Similarly, no significant difference was found between the kinematics graphing skills test scores of female and male students. However, a significant interaction was observed between gender and learning styles on students&amp / #8217 / kinematics graphing skills test scores. The most common learning style type was assimilator for the participants of this study. Accommodator female students&amp / #8217 / kinematics graphing skills test scores were higher than that of female students having other learning styles and converger male students&amp / #8217 / kinematics graphing skills test scores were higher than that of male students having other learning styles on kinematics graphing skills test. Bivariate correlations revealed significant positive correlations between students previous physics course grades, previous mathematics course grades, and age and their kinematics graphing skills test scores.