This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

Entrepreneurial small businesses are significant to the U.S. economy, as they represent 99% of employer firms and employ 49% of the private sector. Nearly half of new businesses fail within the first 5 years of operation. While external factors beyond the control of business owners account for some failures, many occur because of managerial inadequacies. The purpose of this phenomenological study was to explore the lived experiences of successful entrepreneurs to understand the qualities needed to create and sustain new small and medium-sized enterprises (SMEs) beyond 5 years. The sample consisted of 21 entrepreneurs from Northeastern Indiana who created and operated SMEs successfully for at least 5 years. The conceptual framework for this study was human capital theory and entrepreneurial leadership theory. The data were collected from semistructured interviews. Participants completed transcript reviews and member checking was conducted to enhance data credibility and trustworthiness. The phenomenological reduction method was used for data analysis and included bracketing, horizontalizing, clustering, integrating invariant statements, and synthesizing composites. The following themes emerged in addressing the guiding question: entrepreneurial intention recognized at a young age, creative problem-solving skills, business and support systems, entrepreneurial passion, opportunity recognition and seizure, and task and managerial delegation. The study findings can help inform best practices to help future entrepreneurs, and those who educate, train, and mentor them, create and operate successful new ventures.

Text in Afrikaans, abstract in Afrikaans and English / Hierdie studie is daarop gemik om te bepaal tot welke mate wiskundeleerlinge op skool en onderwysstudente in wiskunde, onderrig in logika ontvang as agtergrond vir strenge bewysvoering. Die formele aspek van wiskunde op hoerskool en tersiere vlak is besonder belangrik. Leerlinge en studente kom onvermydelik met hipotetiese argumente in aanraking. Hulle leer ook om die kontrapositief te gebruik in bewysvoering. Hulle maak onder andere gebruik van bewyse uit die ongerymde. Verder word nodige en voldoende voorwaardes met stellings en hulle omgekeerdes in verband gebring. Dit is dus duidelik dat 'n studie van logika reeds op hoerskool nodig is om aanvaarbare wiskunde te beoefen. Om seker te maak dat aanvaarbare wiskunde beoefen word, is dit nodig om te let op die gebrek aan beheer in die ontwikkeling van 'n taal, waar woorde meer as een betekenis het. 'n Kunsmatige taal moet gebruik word om interpretasies van uitdrukkings eenduidig te maak. In so 'n kunsmatige taal word die moontlikheid van foutiewe redenering uitgeskakel. Die eersteordepredikaatlogika, is so 'n taal, wat ryk genoeg is om die wiskunde te akkommodeer. Binne die konteks van hierdie kunsmatige taal, kan wiskundige toeriee geformaliseer word. Verskillende bewystegnieke uit die eersteordepredikaatlogika word geidentifiseer, gekategoriseer en op 'n redelik eenvoudige wyse verduidelik. Uit 'n ontleding van die wiskundesillabusse van die Departement van Onderwys, en 'n onderwysersopleidingsinstansie, volg dit dat leerlinge en studente hierdie bewystegnieke moet gebruik. Volgens hierdie sillabusse moet die leerlinge en studente vertroud wees met logiese argumente. Uit die gevolgtrekkings waartoe gekom word, blyk dit dat die leerlinge en studente se agtergrond in logika geheel en al gebrekkig en ontoereikend is. Dit het tot gevolg dat hulle nie 'n volledige begrip oor bewysvoering het nie, en 'n gebrekkige insig ontwikkel oor wat wiskunde presies behels. Die aanbevelings om hierdie ernstige leemtes in die onderrig van wiskunde aan te spreek, asook verdere navorsingsprojekte word in die laaste hoofstuk verwoord. / The aim of this study is to determine to which extent pupils taking Mathematics at school level and student teachers of Mathematics receive instruction in logic as a grounding for rigorous proof. The formal aspect of Mathematics at secondary school and tertiary levels is extremely important. It is inevitable that pupils and students become involved with hypothetical arguments. They also learn to use the contrapositive in proof. They use, among others, proofs by contradiction. Futhermore, necessary and sufficient conditions are related to theorems and their converses. It is therefore apparent that the study of logic is necessary already at secondary school level in order to practice Mathematics satisfactorily. To ensure that acceptable Mathematics is practised, it is necessary to take cognizance of the lack of control over language development, where words can have more than one meaning. For this reason an artificial language must be used so that interpretations can have one meaning. Faulty interpretations are ruled out in such an artificial language. A language which is rich enough to accommodate Mathematics is the first-order predicate logic. Mathematical theories can be formalised within the context of this artificial language. Different techniques of proof from the first-order logic are identified, categorized and explained in fairly simple terms. An analysis of Mathematics syllabuses of the Department of Education and an institution for teacher training has indicated that pupils should use these techniques of proof. According to these syllabuses pupils should be familiar with logical arguments. The conclusion which is reached, gives evidence that pupils' and students' background in logic is completely lacking and inadequate. As a result they cannot cope adequately with argumentation and this causes a poor perception of what Mathematics exactly entails. Recommendations to bridge these serious problems in the instruction of Mathematics, as well as further research projects are discussed in the final chapter. / Curriculum and Institutional Studies / D. Phil. (Wiskundeonderwys)

This study focused on teaching strategies preferred and used by grade 8 mathematics teachers, what they thought was most effective for learning mathematics as well as students’ perspectives of their mathematics classroom. The aims of this study were to investigate the teaching strategies used in the South Korean mathematical classroom and to find out how they attain a high performance in mathematics, in comparison with other countries. The target population was chosen from within the Chungcheongbuk Province and ten schools were selected for the study. In order to determine what teaching strategies are used in the South Korean mathematics classroom, a case study using both quantitative and qualitative research methods was adopted. Data collection methods included questionnaires for the students while interviews were conducted with the teachers. The questionnaire contained fifty closed-ended questions divided into different sections to obtain data on teaching strategies used, on preferred learning styles from the students and on how they felt about mathematics and the mathematical classroom. The interview consisted of ten open-ended questions to get feedback from the mathematics teachers on what teaching strategies they used in the classroom and on what they thought were the best strategies with regard to teaching grade 8 mathematics. From the ten sampled schools there were two hundred and two students who participated in this research, and six teachers were interviewed. The results of the study showed that in the South Korean mathematics classroom a combination of direct instruction, practice and teacher guidance helps the students to learn problem-solving skills and to master mathematics. The students indicated that the teachers mostly used chalkboard instruction and that they practiced solving problems using worksheets, past exam paper questions and through homework or private study. The average student studied mathematics for about six hours a week and most attended afterschool academies for further studying mathematics. Although the South Korean students attained a high performance in mathematics it was evident that they indicated a low interest in the subject. The teachers stated in the interviews that they thought the students needed to see examples on the chalkboard, and then the students need to practice with guidance from the teacher. It was evident that the students focus a lot on guided practice, since they study for about six hours a week. The teachers also felt that the curriculum is overloaded and that there was a gap between the better and the poorer level of students in the mathematics classroom, this gap grew bigger as students lost motivation. The responses to the questionnaire showed that 65% of the students were not interested in mathematics; in spite of this South Korea is placed among the best performing countries in the world. The teachers also indicated that mathematics was very highly valued in South Korea and that parents and universities put a lot of pressure on students to perform well in this subject. This study provides better insight into what is happening in the South Korean mathematics classroom, what methods are used and how the students felt about the mathematics classroom and the strategies that are used. Apart from commenting on teaching strategies, there was also an indication of what teaching style the students preferred. The information in this research study can provide answers to questions regarding South Korean mathematics instructional practices and will be useful for future comparative studies regarding the teaching of mathematics in other countries. / Mathematics Education / M. Ed. (Mathematics Education)

This study investigated the effect of a blended-learning approach in the learning of problem-solving skills in a first-level distance education physics module. A problem-solving type of instruction with explicit teaching of a problem-solving strategy was implemented in the module, which was presented through correspondence, online using an in-house learning management system as well as two face-to- face discussion classes. The study used the ex post facto research design with stratified sampling to investigate the possible cause-effect relationship between the blended-learning approach and the problem-solving performance. The number of problems attempted, the mean frequency of using strategy in problem solving and the achievement marks of the three strata were compared using inferential statistics. The finding of the study indicated that the blended-learning approach had no statistically significant effect in the learning of problem-solving skills in a distance education module. / Educational Studies / M. Ed. (Open and Distance Learning)

Kreativitätsförderung im Studium der Informatik ist eine zentrale Herausforderung, um Studierende auf Anforderungen in ihren zukünftigen Tätigkeitsfeldern vorzubereiten. Um einen systematischen Einsatz von digitalen Medien in der Kreativitätsförderung zu ermöglichen, wird im vorliegenden Beitrag eine Systematik entworfen und begründet, die entlang der Phasen und Aktivitäten eines kreativen Problemlösungsprozesses Möglichkeiten des systematischen Einsatzes digitaler Medien identifiziert. Dabei wird deutlich, dass zum einen eine Verknüpfung von Medien notwendig ist, um den Anforderungen an einen kreativen Problemlösungsprozess gerecht zu werden. Zum anderen müssen Mechanismen entwickelt werden, die auf den Aufbau einer längerfristigen Beziehung zwischen System und Benutzer abzielen, damit Interaktion zu neuen Funktionen und schließlich zur Herausbildung neuer Kontexte führen kann.

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)

Text in Afrikaans / Summary in English and Afrikaans / This study analyses the adolescent's peer pressure and the handling thereofby the adolescent, the parents, teachers and educational psychologist. The literature confirms that peer pressure is a multidimensional phenomenon. Certain factors such as the parent's behavioural- and cognitive functioning, the adolescent's social competence and susceptibility to peer pressure influence his compliance to peer pressure. Processes such as identification, internalization, modelling and coercion are involved in this compliance. The implementation of a mentor system and suggested program at school and the teaching of social-, decisionmaking, problemsolving- and selfassertiveness skills will help the adolescent to use peer pressure positively. The educational psychologist can support the adolescent and parents through individual, family and group therapy. / Hierdie studie handel oor die ontleding van portuurgroepdruk by die adolessent en die hantering daarvan deur die adolessent self, die ouers, onderwysers en opvoedkundige sielkundige. Die literatuur bevestig dat portuurgroepdruk 'n komplekse fenomeen met verskeie dimensies is. Verskeie faktore soos die ouers se gedrags- en kognitiewe funksionering, die adolessent se sosiale bekwaamheid en sy vatbaarheid vir portuurgroepdruk bei:nvloed sy toegewing aan portuurgroepdruk. Prosesse soos identifikasie, internalisasie, modellering en dwang is by die toegewing aan portuurgroepdruk betrokke. 'n Voorgestelde program vir die skool, die implementering van 'n portuurmentorprogram en die onderrig van sosiale-, besluitnemings-, probleemoplossings- en selfgeldingsvaardighede kan die adolessent help om portuurgroepdruk te gebruik. Die opvoedkundige sielkundige kan die ouer en adolessent deur individuele-, gesins- en groepterapie bystaan. / Educational Studies / M. Education (Guidance)

This mixed methods research design, which was modelled on the constructivist view of schooling, sets out to investigate the effect of developing mathematical problem solving skills of grade 8 learners on their performance and achievement in mathematics. To develop the mathematical problem solving skills of the experimental group, a problem-centred teaching and learning environment was created in which problem posing and solving were the key didactic mathematical activity. The effect of the intervention programme on the experimental group was compared with the control group by assessing learners’ problem solving processes, mathematical problem solving skills, reasoning and cognitive processes, performance and achievement in mathematics. Data were obtained through questionnaires, a mathematical problem solving skills inventory, direct participant observation and questioning, semi-structured interviews, learner journals, mathematical tasks, written work, pre- and post- multiple-choice and word-problem tests. Data analysis was largely done through descriptive analysis and the findings assisted the researcher to make recommendations and suggest areas that could require possible further research. / Mathematics Education / M. Ed. (Mathematical Education)

The aim of this study was to investigate the effect of context-based problem solving instruction (CBPSI) on the problem solving performance of Grade 10 learners, who performed poorly in mathematics. A cognitive load theory (CLT) was used to frame the study. In addition, CLT was used to: 1) facilitate the interpretation and explanation of participants‟ problem solving performance; and, 2) influence the design of CBPSI to hone participants‟ problem solving skills. The study was conducted in the Gauteng province of South Africa and involved a two-week intervention program in each of the nine participating high schools. Participants consisted of 783 learners and four Grade 10 mathematics teachers. A non-equivalent control group design was employed, consisting of a pre- and post- measure. In addition, classroom observations and semi-structured interviews were conducted with teachers and learners. Teachers employed conventional problem solving instructions in four control schools while the researcher implemented CBPSI in five experimental schools. Instruction in experimental schools entailed several worked-out context-based problem solving examples given to participants in worksheets. The main aspects of CBPSI embraced elements of the effects of self-explanation and split-attention, as advocated by CLT. Due to the design of CBPSI participants in experimental schools became familiar with the basic context-based problem solving tasks that were presented to them through the worked-out example samples. In turn, the associated cognitive load of problem solving tasks was gradually reduced. The principal instrument for data collection was a standardized Functional Mathematics Achievement Test. The pre-test determined participants‟ initial problem solving status before intervention. A post-test was given at the end of intervention to benchmark change in the functionality of CBPSI over a two-week period. Using one-way analysis of covariance (ANCOVA), Analysis of Variance (ANOVA), and other statistical techniques the study found that participants in experimental schools performed significantly better than participants in control schools on certain aspects of problem solving performance. In addition, semi-structured interviews and classroom observations revealed that participants rated CBPSI highly. On the whole, the study showed that CBPSI is an effective instructional tool to enhance the problem solving performance of Grade 10 mathematics learners. / Mathematics Education / D. Phil. (Mathematics, Science and Technology Education)