D.Ed. (Didactics) / The main objective of this research is to develop a diagnostic model for the prediction of mathematics achievement for first year university students. In order to design this model of prediction, the following objectives were formulated: * to establish a profile of a typical successful and unsuccessful student in Mathematics; * to calculate the probable final mark achieved by a student in Mathematics; * to establish the probability of success by a student in Mathematics. In this research various factors determinating the academic performance of first year students at a university are discussed. Firstly the transition from school to university and its implications on the student, the teaching of a subject and its influence, and those factors inherent in the student are investigated. The factors inherent to the student are described as cognitive factors (intelligence, aptitude and previous performance) and non-cognititve factors (study methods and attitudes, interest, anxiety, personality and adjustment).

In the last decade, there has been an increase in the number of web-enabled mobile devices, offering a new platform that can be targeted for the development of learning applications. Worldwide, developers have taken initiatives in developing mobile learning (M-learning) systems to provide students with access to learning materials regardless of time and location. The purpose of this study was to investigate whether it is viable for first year students enrolled at the University of Namibia (UNAM) to use mobile phones for ad-hoc learning of mathematical concepts. A system, EnjoyMath, aiming to assist students in preparing for tests, examinations, review contents and reinforce knowledge acquired during traditional classroom interactions was designed and implemented. The EnjoyMath system was designed and implemented through the use of the Human Centred Design (HCD) methodology. Two revolutions of the four-step process of the HCD cycle were completed in this study. Due to the distance between UNAM and Rhodes University (where the researcher was based), the researcher could not always work in close relation with the UNAM students. Students from the Extended Study Unit (ESU) at Rhodes University were therefore selected in the first iteration of the project due to their proximity to the researcher and their similar demographics to the first year UNAM students, while the UNAM students were targeted in the second iteration of the study. This thesis presents the outcome of the two pre-intervention studies of the first-year students' perceptions about M-learning conducted at Rhodes University and UNAM. The results of the pre-intervention studies showed that the students are enthusiastic about using an M-learning system, because it would allow them to put in more time to practice their skills whenever and wherever they are. Moreover, the thesis presents the different stages undertaken to develop the EnjoyMath system using Open Source Software (PHP and MySQL). The results of a user study (post-intervention) conducted with participants at UNAM, ascertained the participants' perception of the usability of the EnjoyMath system and are also presented in this thesis. The EnjoyMath system was perceived by the participants to be "passable"; hence an M-learning system could be used to compliment an E-learning system at UNAM.

This dissertation consists of three related papers. The first paper, Rethinking mathematics bridge courses--An inquiry model for community colleges, introduces the activities of conventionalizing and axiomatizing from a practitioner perspective. In the paper, I offer a curricular model that includes both inquiry and traditional instruction for two-year college students interested in mathematics. In particular, I provide both examples and rationales of tasks from the research-based Teaching Abstract Algebra for Understanding (TAAFU) curriculum, which anchors the inquiry-oriented version of the mathematics bridge course. The second paper, the role of past experience in creating a shared representation system for a mathematical operation: A case of conventionalizing, adds to the existing literature on mathematizing (Freudenthal, 1973) by "zooming in" on the early stages of the classroom enactment of an inquiry-oriented curriculum for reinventing the concept of group (Larsen, 2013). In three case study episodes, I shed light onto "How might conventionalizing unfold in a mathematics classroom?" and offer an initial framework that relates students' establishment of conventions in light of their past mathematical experiences. The third paper, Collective axiomatizing as a classroom activity, is a detailed case study (Yin, 2009) that examines how students collectively engage in axiomatizing. In the paper, I offer a revision to De Villiers's (1986) model of descriptive axiomatizing. The results of this study emphasize the additions of pre-axiomatic activity and axiomatic creation to the model and elaborate the processes of axiomatic formulation and analysis within the classroom community.

This research investigated the career trajectories of mathematics professors of African heritage. The principal objective was to determine the factors that promoted self-efficacy, which made them complete a PhD in mathematics or an EdD in mathematics education regardless of the obstacles they encountered. I investigated 10 professors, males and females, of African heritage at the City University of the Northeast by using open-ended biographical questionnaires and individual interviews Several themes emerged from the data collected. The major themes that impacted the career trajectories of African American male and female mathematics professors were (a) family influence; (b) teacher influence; (c) peer influence; (d) problem solving approach; (e) perceptions of mathematics; (f) prior experience; (g) and individual perseverance (determination) and commitment (obligation). The findings of this research suggested that there are opportunities for young men and women of African heritage to develop into successful mathematicians (the term successful mathematicians is used to denote those men and women of African heritage who have completed their terminal degree, in mathematics or mathematics related subjects) provided that parents, teachers, and peers act their part.

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)

The purpose of this study was to investigate the relationship between individual student differences and academic success in three pedagogical methods (traditional classroom, computer-aided instruction (CAI) in an on-campus setting, and CAI in a distance education setting) for developmental mathematics classes at the community college level. Locus of control, math anxiety and learning style were the individual differences examined. Final grade, final exam score and persistence were the indicators of success. The literature review focused on developmental mathematics, pedagogical techniques and variables contributing to academic performance. Two parallel research populations consisted of 135 Beginning Algebra students and 113 Intermediate Algebra students. The Rotter I-E Locus of Control Scale, the Abbreviated Mathematics Anxiety Rating Scale, the 4MAT Learning Type Measure, and an instrument to gather demographic data were used. It was the conclusion of this study that the instructional methods were not equal with respect to achievement. In Beginning Algebra, the CAI students received significantly higher final grades than did the traditionally taught students. In Intermediate Algebra traditional students scored significantly higher on the final exam than did the CBI students. There were more students persisting than expected in traditionally taught Beginning Algebra and no significant difference in attrition in Intermediate Algebra. There was no significant prediction of achievement in Beginning Algebra. For Intermediate Algebra math anxiety was a significant predictor for final exam percentage and locus of control was a significant predictor for final grade percentage. Only the instructional method contributed significantly to the prediction of attrition. While these findings are statistically significant, they account for only a small part of student success. However, the results had implications for the future. In particular, further study should be given to the question of whether CAI, and its associated expenses, is prudent for developmental mathematics instruction.

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The United States are facing a critical workforce challenge, even though current unemployment is around 6.7%, employers find it difficult to find applicants that can satisfy all job requirements. This problem is especially pronounced in the manufacturing sector where a critical skills gap has developed, a problem that is exasperated by workforce demographics. A large number of employees across the various manufacturing sub-disciplines are eligible to retire now or in the near future. This gray tsunami requires swift action as well as long lasting change resulting in a workforce pipeline that can provide Science, Technology, Engineering, and Mathematics (STEM) majors in sufficient quantity and quality to satisfy not only the needs of STEM industries, but also of those companies outside of the STEM sector that hire STEM graduates. The research shown here will identify overt symptoms describing the capability gap, will identify specific skills describing the gap, educational causes why the gaps has not yet been addressed or is difficult to address, and lastly educational remedies that can contribute to closing the capability gap. A significant body of literature focusing on engineering in higher education has been evaluated and findings will be presented here. A multidisciplinary, collaborative capstone program will be described which implements some of the findings from this study in an active learning environment for students working on distributed teams across the US. Preliminary findings regarding the impact of these measures on the quantity of engineers to the US economy will be evaluated.

With the introduction in 2006 of the school subject Mathematical Literacy (ML) in the further Education and Training band, there have been expectations that such a subject might develop responsible citizens, contributing workers and self-managing people. The extent to which the subject can meet these aims is dependent on the ways in which the subject is taught and assessed, which influences the focus of ML in the classrooms. One of the differences between the respective subjects of Mathematics and Mathematical Literacy is that when it comes to the latter, there has been less emphasis on carrying out algebraic procedures, and a greater focus on working with contexts. However, algebraic skills can be advantageous even when solving problems set within contexts. One area, which surfaces the distinction between arithmetic and algebraic skills, is in the substitution and computation of a formula, as compared to the solution of equations. In this study, I focus on this distinction by examining Grade 11 ML learner skills in solving both result-unknown problems and start-unknown problems, where the former involves substituting and computing the result of a formula or equation for which the input is given. The latter involves re-arranging the equation or formula in order to solve for the input when the output is given. With this in mind, this study sets out to explore the strategies used by Grade 11 learners to solve result-unknown and start-unknown problems set in real life contexts. This is a qualitative study, carried out with three hundred and forty Grade 11 Mathematical Literacy learners from rural and urban school in North Durban. Data was gathered from a document analysis of 340 learners’ written responses to the research instrument, along with interviews with ten of these learners. There were four tasks in the research instrument, each of which had a result-unknown, a start-unknown and a reflection question. In the four tasks with the exception of Question 1.2.1 and 1.2.2 in tasks one, were set around a linear equation, while Question 1.2.1 and 1.2.2 involved a hyperbolic equation. Semi-structured interviews were conducted individually with ten learners and the audio recorded. The purpose of the interviews was to explore some of the factors that influenced their written responses. The findings revealed the solving of start-unknown questions to be a serious problem for learners. On average, the success rate at result-unknown questions was 75%, while it was 26% for start-unknown questions. For start-unknown questions based on linear equations only, the success rate was a mere 19 percent. Some strategies used by learners in responding to start-unknown questions included number grabbing, systematic guess and test, conjoining, symbol manipulation and working backwards. On average, over the four tasks based on linear equations, only nine percent of learners successfully used strategies based on algebraic skill. Most learners who obtained correct answers in the start-unknown questions used the guess and test strategy. Strategies identified in result-unknown questions included direct arithmetic strategy. The study recommends that for ML learners, teachers need to impress upon learners that the location of the formula in the question is not an indication that certain questions would be answered using the formula, because the formula is placed next to them. It also recommends that teachers create opportunities for learners to continue to practice the algebraic skills they learned in the GET band, particularly in the area of transforming and solving simple linear equations. / M. Ed. University of KwaZulu-Natal, Durban 2013.

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)