In this investigation an attempt was made to determine the misconceptions that engineering students have of the idea of a limit. A comprehensive literature study showed that there are a number of common misconceptions that students normally form. The empirical investigation was done in two phases. A questionnaire on the idea of a limit was given to the students during the first phase. During the second phase six interviews were conducted. The findings were grouped according to the nature of a limit and students' views on the relationship between the continuity of a function at a point and the limit at that point. An analysis of these findings led to the identification of the misconceptions that these students have of the idea of a limit. / In hierdie ondersoek is gepoog om die wanbegrippe wat ingenieursstudente van die limietbegrip vorm, bloot te stel. 'n Omvattende literatuurstudie het 'n aantal algemene wanbegrippe aan die lig gebring. Die empiriese ondersoek het in twee fases plaasgevind. Tydens die eerste fase is 'n vraelys aan die studente gegee in 'n poging om meer te wete te kom van hulle begrip van 'n limiet. Die vraelys is opgevolg deur ses onderhoude. Die responsies is gegroepeer in terme van die aard van 'n limiet en studente se sienings van die kontinuiteit van 'n funksie by 'n punt en die limiet by daardie punt. Die analisering van hierdie responsies het die identifisering van 'n aantal wanbegrippe by hierdie groep studente moontlik gemaak. / Educational Studies / M.Ed. (with specialisation in Mathematics Education)

This study involves an investigatioh into the nature and effectiveness of the pre-service training, where provided, of secondary school Mathematics teachers at the 11 colleges of education administered by the House of Representatives in the Republic of South Africa. The purpose of this study is to determine whether the HDE (Secondary) course offered at some of the aforementioned colleges of education is justified, In spite of the fact that it contravenes the requirements of the Education Act, No. 73 of 1969. Three different questionnaires were designed and during 1986 were sent to heads of Mathematics departments at the aforementioned colleges of education , to Mathematics teacher educators at these colleges and to beginning secondary school Mathematics teachers, teaching at schools administered by the House of Representatives in the Eastern Cape and Natal. The findings of this study show that the secondary course for Mathematics teachers is only offered at 5 of the 11 colleges of education and only a small percentage of students take this course. During 1986 most of the Mathematics teacher educators at the colleges of education were not suitably qualified. The study also shows that the Mathematics curriculum for the training of secondary school teachers is inadequate and a revision thereof is thus recommended. An obvious conclusion drawn from the findings is that the training of secondary school Mathematics teachers at these colleges of education is still in an early stage of development. One of the main recommendations of this study is that the training of secondary school Mathematics teachers at colleges of education administered by the House of Representatives should be terminated , in view of its ineffectiveness and In accordance with Education Act , No . 73 of 1969. On the other hand, in case this is not possible, suggestions are also made for the improvement of the pre-service training of secondary school mathematics teachers at these colleges of education.

The low grades that students score in some statistical units in Kenyan universities is of great concern and has evoked research interest in the teaching of some of the units and the students’ learning of the statistical content. The aim of the study was to investigate the difficulties undergraduate students experience in the learning of bivariate normal distribution in a Kenyan university. The research also aimed to answer the following research questions on the difficulties undergraduate students encounter in the learning of bivariate normal distribution. The first research question was based on the reasons why students find learning of bivariate normal distribution difficult and the second research question was to find the reasons why students experience such difficulties in learning bivariate normal distribution. The target population for this study included lecturers teaching statistics in the university, and second- and third- year students enrolled or who have previously completed the probability and statistics III unit, where the bivariate normal distribution content is covered. In selecting students for the study, the simple random sampling technique was employed while convenient sampling was used to select lecturers who participated in the study. A mixed methods design was adopted for this study where both quantitative and qualitative data was collected. A total of 175 students and six lecturers participated in this research study. All students who participated in the study did a bivariate normal distribution test (Appendix 1) designed by the researcher and then filled in a questionnaire (Appendix 2). The lecturers who participated in the study filled in an open-ended questionnaire (Appendix 3). The results showed that undergraduate students have difficulties in learning bivariate normal distribution. This is because most of them could neither state the bivariate normal distribution nor solve any of the application questions on the content. The students find it difficult to learn and comprehend the bivariate normal distribution equation with its many parameters and constants of the two random independent variables. The results also showed that students could not state the normal distribution equation nor could they solve questions on the normal distribution, which forms the foundational knowledge required for effective learning of the bivariate normal distribution content. ii Based on the results, the study recommended that emphasis should be placed on the basic and foundational knowledge of the normal distribution content and its applications before teaching bivariate normal distribution in probability and statistics III. In addition, it is recommended that all students should be involved in the learning of basic content to enable them to understand all parameters and constants in the equations and their applications. The study also recommends that lecturers revise the foundational knowledge and content related to the bivariate normal distribution before introducing and teaching the bivariate normal distribution content. This study also recommends that the university should consider a change of curriculum by teaching the bivariate normal distribution, as an introductory course to the unit under the multivariate distributions in statistics, in third year of the students’ studies. ; ; / Mathematics Education / M. Sc. (Mathematics Education)

One purpose of this study was to determine the relationships among community college students' mathematics, electronics, and electronics troubleshooting knowledge. A second purpose of the study was to determine the extent to which independent variables predicted troubleshooting knowledge. Students involved in the study were enrolled in electronics technician associate degree granting programs. More specifically the study was designed to examine the relationships among electronics troubleshooting knowledge and the following independent variables: 1. Number of mathematics courses taken at the community college level 2. Types of mathematics courses taken at community college level 3. Mathematics knowledge as measured by scores on a standardized mathematics test 4. Number of electronics courses taken at the high school level 5. Number of electronics courses taken at the community college level 6. Prior work experience in the electronics industry In addition to examining these variables, this study also sought to answer the question: Which combination of variables best tends to predict troubleshooting knowledge? Usable data were gathered from 100 North Carolina community college students who were enrolled in electronics technician degree granting programs at five randomly selected community colleges. The students participating in this study were administered three data gathering instruments. The instruments included a Student Information and Data Sheet designed to gather demographic information about each student, a standardized mathematics knowledge test designed to cover the mathematical concepts stressed in elementary, intermediate and college algebra, and finally, a paper and pencil electronics and troubleshooting test which consisted of troubleshooting an AM transceiver functional block diagram, a servicing block diagram, a power supply, and a summing circuit. It was determined that under the conditions imposed by this study only one of the independent variables, score on the Mathematics Knowledge Test, could be used with some accuracy to predict troubleshooting knowledge. The independent variable mathematics knowledge, as represented by scores on the standardized mathematics knowledge test, could only predict troubleshooting knowledge with 6.8% percent accuracy. / Ed. D.

Meaningful learning requires active teaching and learning approaches. Thus, with a specific focus on Mathematics teaching at university in Oramia, the study aimed to: • examine the extent to which active learning/student-centered approaches were implemented; • assess the attitudes of university lecturers towards active-learning; • investigate whether appropriate training and support have been provided for the implementation of an active learning approaches • assess the major challenges that hinder the implementation of active learning approaches and • recommend ways that could advance the use of active learning approaches in Mathematics teaching at university. A mixed-methods design was used. Among the six universities in the Oromia Regional State of Ethiopia, two of the newly established universities (younger than 5 years) and two of the old universities (15 years and older) were involved in the study. A total of 84 lecturers participated in the study and completed questionnaires. This was complemented by a qualitative approach that used observation checklists and interviews for data gathering: 16 lessons were observed while the lecturers taught their mathematics classes (two lecturers from each of the four sample universities were twice observed). In addition, semi-structured interviews were conducted with four mathematics department heads and eight of the observed lecturers. The study adhered to ethical principles and to applied several techniques to enhance the validity/trustworthiness of the findings. / Psychology of Education / D. Ed. (Psychology of Education)

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The purpose of the study was to investigate The effect of the Problem-Based Learning Problem Based Learning (PBL) approach in the teaching of composition and inverse functions in a foundation programme. PBL is a philosophical approach to teaching and learning where problems drive the learning. The study was important because it was trying to find out if PBL can improve students’ performance in compositions and inverses of functions at the bridging course for undergraduate mathematics at Oshakati Campus. The study intended to come up with a PBL model suitable for FP mathematics in the teaching of compositions and inverses of functions. The study was done on Science Foundation students who are registered for FP. Eighty students were randomly selected from the foundation students registered for the 2013 academic year. The students were randomly assigned into the experimental and the comparison groups of 40 each. In this study the comparison group of the Foundation students was predominantly taught through the traditional lecture approach while the experimental group was predominantly taught using a hybrid PBL approach. The study also attempted to establish the students’ perceptions with regard to the relevance of inverses and compositions of functions as a concept in a topic that determines their academic destination. It also attempted to ascertain how the PBL approach could best be implemented in order to improve FP students’ understanding of inverses and composition of functions; how Bridging course for undergraduate mathematics (FP) students experience the PBL approach in the teaching and learning of inverses and composition of functions compared to those who are taught using the lecture method and how FP students’ performance on inverses and composition of functions as a result of their PBL experience compare to those who are taught using the lecture method. This study used the concurrent nested mixed methods (qualitative and quantitative) research designs. A quasi experimental design was adopted through the administration of a pre-post-test on experimental and comparison groups. The other designs or methods included a questionnaire survey, focus group interviews, non-participant lesson observation and a group research project on compositions and inverses of functions. The experimental group was then mainly taught through a hybrid PBL approach while the comparison group mainly through the lecture approach for a period of three months. The findings of this research study showed that experimental group students performed significantly better in the overall results analysis but there were no significant differences in performance between the two groups for some Hypothetical Learning Trajectory (HLT) domains on compositions and inverses of functions. It is recommended that PBL should be implemented in the other foundation programme subjects. However, the role of the conventional teaching approaches cannot be undermined in the teaching and learning of compositions and inverses of functions since the students who were taught using this method also improved their performances, and as such these conventional teaching approaches should be used together with PBL in order to get the best results on FP students’ mathematics performance. This study recommends further research on how PBL can be implemented in other FP subjects. This study also recommended that PBL should be implemented right at the beginning of the year when the FP students start their classes in the foundation programme. / AFRIKAANSE OPSOMMING: Die doel van die studie was om die effek van die probleemgebaseerde leer (PBL) benadering in die onderrig van die samestelling en inverse funksies in 'n Stigting program te ondersoek. PBL is 'n filosofiese benadering tot onderrig en leer waar probleme ry die leer. Die studie is belangrik omdat dit probeer het om uit te vind of PBL kan studente se prestasie in komposisies en inverses van funksies te verbeter by die Stigting Program op Oshakati-kampus. Die studie bedoel om vorendag te kom met 'n PBL model wat geskik is vir fondament in die onderrig van komposisies en inverses van funksies. Die studie is gedoen op Science Foundation studente by Oshakati-kampus van die Universiteit van Namibië. Tagtig studente is lukraak gekies uit die fondament studente wat geregistreer is vir die 2013 akademiese jaar. Die studente is ewekansig toegewys in die eksperimentele en die vergelyking groepe van 40 elk. In hierdie studie is die vergelyking groep van die Stigting studente is hoofsaaklik geleer word deur die tradisionele lesing benadering terwyl die eksperimentele groep was hoofsaaklik geleer met behulp van 'n hibriede PBL benadering. Die studie het ook probeer om vas te stel uit wat die studente se persepsies met betrekking tot die toepaslikheid van inverses en komposisies van funksies is soos 'n konsep in 'n onderwerp wat bepaal hul akademiese bestemming. Dit het ook probeer om vas te stel hoe die PBL benadering kan die beste om FP studente se begrip van inverses en samestelling van funksies te verbeter geïmplementeer word; hoe FP studente die PBL benadering in die onderrig en leer van inverses en samestelling van funksies in vergelyking met diegene wat geleer is met behulp van die lesing metode en hoe FP studente se prestasie op inverses en samestelling van funksies as 'n gevolg van hul PBL ervaring vergelyk met dié wat geleer is met behulp van die lesing-metode. Hierdie studie gebruik om die konkurrente geneste gemengde metodes (kwalitatiewe en kwantitatiewe) navorsing ontwerpe. 'N quasi eksperimentele ontwerp is aangeneem deur die administrasie van 'n pre-na-toets op eksperimentele en vergelyking groepe. Die ander ontwerpe of metodes het 'n vraelys opname, fokusgroeponderhoude, nie-deelnemer leswaarneming, en 'n groep navorsingsprojek oor komposisies en inverses van funksies. Die eksperimentele groep is dan hoofsaaklik geleer deur middel van 'n kruising PBL benadering terwyl die vergelyking groep hoofsaaklik deur die lesing benadering vir 'n tydperk van drie maande. Die bevindinge van hierdie navorsing het getoon dat die eksperimentele groep studente uitgevoer aansienlik beter in die algehele resultate analise, maar daar was geen betekenisvolle verskille in prestasie tussen die twee groepe vir 'n paar MTT gebiede op komposisies en inverses van funksies. Die studie het ook bevind dat PBL aan die begin van die jaar reg geïmplementeer moet word wanneer die FP studente begin hul klasse in die fondament program. Dit word aanbeveel dat PBL in al die ander fondament program vakke moet geïmplementeer word. Tog kan die rol van die konvensionele onderrig benaderings nie ondermyn word in die onderrig en leer van komposisies en inverses van funksies, en as sodanig die konvensionele onderrig benaderings moet saam met PBL word gebruik om die beste resultate op FP studente se wiskunde prestasie te kry . Hierdie studie beveel aan verdere navorsing oor hoe PBL in 'n ander fondament program vakke geïmplementeer kan word.

Made available in DSpace on 2015-12-03T18:32:50Z (GMT). No. of bitstreams: 1 Alexandre_Silva_Rodrigues.pdf: 730519 bytes, checksum: 352a48ab1ef42b5b49d1e7a959719bda (MD5) Previous issue date: 2005-05-04 / This research focus in identifying and analysing the main factors that determine the difficulties in the learning process related process related to mathematical disciplines present in the business graduation programs 20 managers of different areas were interviewed and disclosed "what" is really important of mathematics for the administrator, and their answers based the construction of a questionnaire that, applied to 271 students of two privates education institutions in Sao Paulo, measured the agreement level for each one of the 26 questions. Results (data) were statistically analyzed using multivariate data techniques, specially factor analysis with a computacional tool, SPSS.The results showed six main factors that were named as follow: teaching process unconnected with reality generating monotony, didatics, exclusion by natural aptitude, level of effort needed, class methodology and enviroment. Each factor was analysed according to existent theorical approaches, clarifying that teaching process unconneted with reality is generated by an obsolete class methodology, found in the bulge of an inadequate didatics, as well the students effort in such disciplines is related to their natural aptitude didatics, as well the students effort in such disciplines is related to their natural aptitude to work with them. The enviroment, pointed as an important component for the learning process, is the scenary where all the mentioned factors are lived by the business programs actors. All the factors detected were confirmed as part of the three worse identified problems in the mathematical teach-learning process: teaching imperfections, cognitive disfunctions and enviroment. At the end, some suggestions were made in order to brighten up the mentioned problems. / O tema central desta pesquisa ?? a identifica????o e an??lise dos principais fatores que geram dificuldades de aprendizagem de disciplinas matem??ticas em alunos dos cursos de Administra????o de Empresas. Um grupo de 20 gestores das mais diversas ??reas revelou atrav??s de entrevistas estruturadas "o qu??" ?? importante de matem??tica para o administrador, sendo que suas respostas constitu??ram um importante subs??dio para a constru????o de um instrumento de pesquisa que, aplicado a 271 alunos de duas institui????es de ensino particular de S??o Paulo, apurou para 26 assertivas o grau de concord??ncia quanto ?? raz??o apresentada para as dificuldades aqui pesquisadas. Os dados foram submetidos a testes estat??sticos a analisados segundo o m??todo multivariado de an??lise fatorial, com o aux??lio da ferramenta computacional SPSS??. Seis fatores foram definidos, identificados como ensino "descontextualizado" gerando monotonia, did??tica, exclus??o por aptid??o natural, esfor??o, metodologia de aula e ambiente. Cada um dos fatores foi analisado segundo as teorias existentes trazendo a percep????o de que o ensino "descontextualizado" ?? gerado por uma metodologia de aula obsoleta, que por sua vez encontra-se no bojo de uma did??tica inedequada, assim como o esfor??o dispendido pelos alunos em tais mat??rias ?? decorrente da aptid??o natural dos mesmos em rela????o a tais assuntos. O ambiente, tamb??m apontado como determinante no processo de aprendizagem, ?? o palco sobre o qual os demais fatores s??o vivenciados pelos atores do curso de gest??o empresarial. A gama de fatores relevantes aqui detectada p??de ser confirmada como parte integrante dos tr??s principais focos geradores de problemas no ensino-aprendizagem de matem??tica, identificados pela academia como: falhas docentes, falhas cognitivas e problemas ambientais. Ao t??rmino, sugest??es relevantes s??o tecidas objetivando amenizar os problemas mencionados.

The pass rate of first-year university mathematics students at the University of KwaZulu-Natal (Pietermaritzburg Campus) has been low for many years. One cause may be weak algebra skills. At the time of this study, revision of high school algebra was not part of the major first year mathematics course. This study set out to investigate if it would be worthwhile to spend tutorial time on basic algebra when there is already an overcrowded calculus syllabus, or if students refresh their algebra skills sufficiently as they study first year mathematics. Since it was expected that remediation of algebra skills would be found to be worthwhile, two other questions were also investigated: Which remediation strategy is best? Which errors are the hardest to remediate? Five tutorial groups for Math 130 were randomly assigned one of four remediation strategies, or no remediation. Three variations of using cognitive conflict to change students’ misconceptions were used, as well as the strategy of practice. Pre- and post-tests in the form of multiple choice questionnaires with spaces for free responses were analysed. Comparisons between the remediated and non-remediated groups were made based on pre- and post-test results and Math 130 results. The most persistent errors were determined using an 8-category error classification developed for this purpose. The best improvement from pre- to post-test was 12.1% for the group remediated with cognitive conflict over 5 weeks with explanations from the tutor. Drill and practice gave the next-best improvement of 8.1%, followed by self-guided cognitive conflict over 5 weeks (7.8% improvement). A once-off intervention using cognitive conflict gave a 5.9% improvement. The group with no remediation improved by 2.3%. The results showed that the use of tutorintensive interventions more than doubled the improvement between pre-and post-tests but even after remediation, the highest group average was 80%, an unsatisfactory level for basic skills. The three most persistent errors were those involving technical or careless errors, errors from over-generalising and errors from applying a distorted algorithm, definition or theorem. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.

Meaningful learning requires active teaching and learning approaches. Thus, with a specific focus on Mathematics teaching at university in Oramia, the study aimed to: • examine the extent to which active learning/student-centered approaches were implemented; • assess the attitudes of university lecturers towards active-learning; • investigate whether appropriate training and support have been provided for the implementation of an active learning approaches • assess the major challenges that hinder the implementation of active learning approaches and • recommend ways that could advance the use of active learning approaches in Mathematics teaching at university. A mixed-methods design was used. Among the six universities in the Oromia Regional State of Ethiopia, two of the newly established universities (younger than 5 years) and two of the old universities (15 years and older) were involved in the study. A total of 84 lecturers participated in the study and completed questionnaires. This was complemented by a qualitative approach that used observation checklists and interviews for data gathering: 16 lessons were observed while the lecturers taught their mathematics classes (two lecturers from each of the four sample universities were twice observed). In addition, semi-structured interviews were conducted with four mathematics department heads and eight of the observed lecturers. The study adhered to ethical principles and to applied several techniques to enhance the validity/trustworthiness of the findings. / Psychology of Education / D. Ed. (Psychology of Education)

The aim of the study was to identify the factors that have an influence on the completion rates of undergraduate students in the fields of science, technology, engineering and mathematics (STEM). Using Tinto's retention rate theory as the theoretical foundation, data were collected from freshman who were enrolled in the years 2005 to 2008. Results showed gender and first-generation status were significant predictors of STEM completion and time taken to complete the degree. Institutional bias played a role in race/ethnicity not being a factor affecting completion rates, as this study was conducted at a Predominantly White Institution. SAT scores and first and second-year college GPA showed to have the most prominent influence on both STEM completion rate and time taken to complete the degree. Females with higher first-year college GPA and higher high school rank finished faster. Similar results were found with first-generation students as well. Students belonging to ethnic minority groups with higher SAT scores and college GPA had greater success in STEM fields as well. The study results can be used to increase completion rates of underrepresented students in the STEM fields, given what we know about the interactions between underrepresented student groups and the most important predictors.