Academic literature on the topic 'Calculus, Study and teaching (Higher) - Lesotho'

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students’ achievement and the effects of the use of Microsoft Mathematics on students’ attitudes in relation to such experience. Two classes of the students from the first year student in Universitas Serang Raya were participated in the study. This study found that students who taught by using Microsoft Mathematics had higher achievement and has a positive effect on students’ confidence of mathematics.Keywords: Calculus, Educational Technology, Mathematics Education, Microsoft Mathematics, Technology Application DOI: dx.doi.org/10.22342/jme.61.63

The factors affecting job satisfaction of academic employees, with specific reference to the National University of Lesotho (NUL) were analysed. Understanding the factors that affect academic performance is pivotal for satisfactory levels of performance by higher education institutions. Satisfactory working conditions at universities like NUL can provide the impetus to attract well qualified academics. Six areas pertaining to working conditions, relationship with colleagues, access to resources, job security, recognition and advancement were focused on analyzing job satisfaction among academic employees at the National University of Lesotho. A concurrent approach of both quantitative and qualitative techniques was used. The target population of 156 respondents completed a 5-point Likert scale questionnaire. Quantitative data were analyzed using SPSS, version 22.0, while thematic analysis was used to analyse qualitative data. The findings of the study highlighted salaries as a factor influencing job satisfaction. Further, insufficient financial resources to support teaching, learning and research at the NUL impacted job satisfaction. Over and above dissatisfaction with benefits, allowances, lack of equipment, as well as poor institutional management, there was collegiality with heads of departments, working as a team. The findings are valuable to university administrators and academics to consider for improving job satisfaction among employees.

Many Higher Education Institutions use the Student Evaluation of Teaching (SET) scale to evaluate the quality of instructors’ teaching. It includes students’ evaluation of the teacher, the teaching process, teaching approaches and the learning outcomes. Due to its reported dubious reliability and validity, and inherent bias in measuring the quality of teaching, SET remains a hotly debated and controversial instrument. This study evaluated thereliability and validity of the SET scale adopted by the National University of Lesotho. Self-administered SET questionnaires were distributed to 104 third- and fourth-year Bachelor of Commerce students to evaluate ten lecturers, resulting in 751 assessment records. The data were analysed using the Statistical Package for the Social Sciences (SPSS) and Partial Least Squares Structural Equation Modelling (PLS-SEM). While the findings suggest that the SET instrument used at the university is reasonably reliable and valid, minor concerns were raised with regard to discriminant validity, and serious concerns in relation to content validity. Based on the existing literature and the psychometric properties of this SET instrument, it is recommended that university management exercise caution in using its results to make evaluative personnel decisions such as promotions, confirmations, and dismissals. It is also recommended that the SET instrument should be revised and validated and be primarily used for formative purposes such as obtaining feedback for the development of individual instructors. Key words: formative assessment, reliability, student evaluation of teaching, summative assessment, validity

The article deals with the psychoemotional state of students when studying the modules "Integral calculus" and "Differential equations" in the course of higher mathematics. The factors that affect the degree of assimilation of educational material by first-year students are described, and the causes of emotional (psychological) stress are noted. The study is confirmed by an empirical description, which was conducted using the "colour painting" technique, first used to assess the psychoemotional state of first-year students when studying sections of the higher mathematics course. The proposed method makes it possible to "see" the mood of students on each topic of the module, to track the dynamics of emotional states in the team on the topics of each module and the overall picture of the mood of each individual in the student group. Colour matrix allows recording the emotional response to events (for the authors of the article, these are modules of the course) and finding out how it was perceived by students, who of them is experiencing difficulties. The study of the psychoemotional state of respondents was conducted by means of a questionnaire, where the authors were interested in how the study materials on the topic "Integral calculus" and "Differential equations"affect the students' health/mood. Based on the analysis, the most difficult topics for learning modules were identified, and recommendations were given on their possible forms and methods of teaching.

One way in which the practice of inclusion can be actualised in classrooms is through the use of consistent, appropriate differentiated instruction. What remains elusive, however, is insight into what teachers in different contexts think and believe about differentiation, how consistently they differentiate instruction and what challenges they experience in doing so. In the study reported on here high school classrooms in a private and a government school in Lesotho were compared in order to determine teachers’ thoughts and beliefs about differentiation, the frequency of differentiated instruction, and the challenges faced by teachers who implement this inclusive practice. Sampled teachers offered their views on what they understood differentiated instruction to be, the frequency of differentiated instruction, and identified challenges via an administered questionnaire. Data analysis was based on frequency counts and bar charts for comparative purposes. Findings indicate that private school teachers have a higher frequency of differentiated teaching practice, with time constraints indicated as the main challenge. Government school teachers had a lower frequency of differentiation, and identified a lack of resources, and the learner-teacher ratio as challenges, among others. In the study we highlighted the critical role that private schools can play in the national call for the implementation of inclusive teaching in Lesotho, in terms of active collaboration with surrounding government schools. Private schools, with their resources and access to professional development opportunities, can become catalysts in the implementation of inclusive teaching practices.

Introduction: Urolithiasis is a common medical diagnosis that doctor encounters in the outpatients and emergency departments. The prevalence of renal stone disease has increased steadily over the past decades. There are different modalities of treatment of ureteric calculus. However, most of the distal ureteric calculus passes spontaneously thus the application of invasive procedure at the early stage can be considered overtreatment.Methods: The 68 patients of the surgical department, Manipal teaching hospital, Pokhara, with distal ureteric calculus of ≤ 8mm, who were under the treatment Tamsulosin Hydrochloride 0.4mg once daily for 2 weeks or till the expulsion of stone from 1st October 2017 to 30th September 2018 (one year period) were retrospectively evaluated for the spontaneous stone expulsion rate and its association with serum CRP level, WBC count and Neutrophil percentage. The patients were divided into 2 groups i.e. spontaneously ureteric stone expelled group and non expelled group. Furthermore, for statistical analysis, each group were subdivided according to normal and elevated serum CRP level, white blood cell count and neutrophil percentage. The associations between these factors and ureteral stone passage were then examined.Results: Most of the cases were in the age group of 21-40 years with the mean age of 40.09 ± 16.11, where 57.4% of patients were male. Among all mean duration of symptoms was 6 days. The ratio of left to right stone was 1.26:1. Out of 68 patients, 80.9% of the patient’s distal ureteric stone was passed out spontaneously with medical expulsion therapy. There were statistically significant (p<0.001) association between normal serum CRP level, White cell counts and neutrophil percentage with the expulsion of distal ureteric calculus with size ≤ 8mm.Conclusion: There is a higher expulsion rate of distal ureteric calculus of size ≤ 8mm with the patient of the normal level of serum CRP level, White cell counts and neutrophil percentage than that of abnormal level.

This study aimed to develop instructional design in teaching the Integration by Parts in Calculus. By engaging in a Lesson Study, the researchers underwent careful planning of the design, executed it through a research lesson, noted key observations during the delivery of the lesson, and conducted a post-lesson conference. From the observations and insights during the post-conference, two themes emerged from where recommendations were drawn. The first theme pivoted on the propensity of teaching Integration by Parts as highly procedural and mechanical despite attempts at activating students’ higher-order thinking. However, the extent to which the tabular method could be advantageous should be explained to the students to clarify misconceptions about using it as a shortcut in performing Integration by Parts. The second theme revolved around how supportive classroom environment and the use of Tabular Method made the students more engaged. Nevertheless, providing learning experiences where students can be work on higher-order thinking and where they can process results of their collaboration was recommended to be incorporated in the instructional design. Generally, both Tabular and Conventional Methods play a crucial role in developing students’ mastery of this integration technique and may eventually allow them to make connections to the real world

Abstract The mathematical concept of function is an essential underpinning for advanced study in mathematics, such as calculus, and influences success in higher mathematics. Teaching about functions is challenging as many students find it difficult to understand. Effective teaching strategies are reliant on a teacher’s knowledge of the current understandings of their students. The gestures of the twenty-three middle-secondary Australian students (14–15 years old) in this study clarified the meaning of their words as they were interviewed whilst viewing two different computer simulations. Five ways in which students used their hands when providing multiple representations of mathematical functions are presented, which provide insights into students’ thinking about functions not available in their words alone.

Background: Updated information on oral health status could be used to monitor oral disease patterns, as widespread variations in oral health outcomes within and between different countries are reported. Aim: The objective was to examine the status of oral and systemic health and their association with demographic characteristics of the population attending a public dental center. Methods: A cross-sectional secondary analysis of the patients’ record was conducted during June 2017 attending the dental center of Madina Teaching hospital Faisalabad, Pakistan. Study variables were analyzed using the t test and the c2 test with a significance level of P ≤ .050. Results: The mean age of the study sample was 31.9 ± 14.5 years; 56% were females; 48% had primary or higher education; 9% were hypertensive; 5% had hepatitis; and 5% diabetes mellitus; 52% were with poor oral hygiene, 68% had dental caries, 84% had no fillings, 27% had tooth loss, and 99% functional dentition; 74% patients had calculus, 67% had gingivitis, and 5% had periodontitis. Age was the strongest risk indicator. Dental caries, tooth loss, poor oral hygiene, gingivitis, periodontitis, and tooth mobility were significantly associated with diabetes mellitus; tooth loss and tooth mobility were associated with cardiac disease; tooth loss, periodontitis, and tooth mobility were associated with hypertension, whereas tooth loss and calculus were associated with hepatitis. Higher age and lower income were positively associated with poor oral hygiene. Conclusion: Age and gender remain to be the strongest predictors for both oral and systemic conditions. Poor oral health and tooth loss showed a strong relationship with chronic systemic conditions.

<p>Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students’ inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In order to overcome this learning deficit, it is necessary that the concept of “reflection” be implemented in the teaching of this subject. It is believed that the adoption of this teaching concept will allow students to learn mathematics by themselves. This article is aimed at presenting mathematical problem-solving of undergraduate students on Calculus I. Concrete problems were assigned to students to participate, to improve students’ way of mathematical thinking, and to encourage the students’ mathematical learning and advanced mathematical thinking. The study was a qualitative research project conducted with first-year undergraduate students of Rajamangala University of Technology Phra Nakhon who had enrolled for Calculus I. Data were collected from interviews and field notes, along with video recordings. Findings showed that students succeeded in solving mathematical problems from simple to complex levels and using the subject fundamentals to connect to several methods of higher levels of thinking. Students also created effective means of problem-solving and applied these concepts to solve new problems.</p>

The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated. A group of mathematics students at undergraduate level at the National University of Lesotho (NUL) was used as the sample for the study. Empirical data were collected by using interviews and questionnaires. These data were analysed using both the APOS framework and a semiotic perspective.

Within the APOS framework, the pieces of knowledge that have to be constructed in coming to understand the limit concept are actions, processes and objects. Actions are interiorised into processes and processes are encapsulated into objects. The conceptual structure is called a schema. In investigating the idea of limit within the context of a function some main epistemological obstacles that were encountered when actions were interiorised into processes are over-generalising and taking the limit value as the function value. For example, in finding the limit value L for f(x) as x tends to 0, 46 subjects out of 251 subjects said that they would calculate f(0) as the limit value. This method is appropriate for calculating the limit values for continuous functions. However, in this case, the method is generalised to all the functions. When these subjects encounter situations in which the functional value is equal to the limit value, they take the two to be the same. However, the two are different entities conceptually.

This study investigates the effects of implementing mathematical problem solving instruction in a regular calculus course taught at the college level. Principles associated with this research are: i) mathematics is developed as a response to finding solutions to mathematical problems, ii) attention to the processes involved in solving mathematical problems helps students understand and develop mathematics, and iii) mathematics is learned in an active environment which involves the use of guesses, conjectures, examples, counterexamples, and cognitive and metacognitive strategies. Classroom activities included use of nonroutine problems, small group discussions, and cognitive and metacognitive strategies during instruction. Prior to the main study, in an extensive pilot study the means for gathering data were developed, including a student questionnaire, several assignments, two written tests, student task-based interviews, an interview with the instructor, and class observations. The analysis in the study utilized ideas from Schoenfeld (1985) in which categories, such as mathematical resources, cognitive and metacognitive strategies, and belief systems, are considered useful in analyzing the students' processes for solving problems. A model proposed by Perkins and Simmons (1988) involving four frames of knowledge (content, problem solving, epistemic, and inquiry) is used to analyze students' difficulties in learning mathematics. Results show that the students recognized the importance of reflecting on the processes involved while solving mathematical problems. There are indications suggesting that the students showed a disposition to participate in discussions that involve nonroutine mathematical problems. The students' work in the assignments reflected increasing awareness of the use of problem solving strategies as the course developed. Analysis of the students' task-based interviews suggests that the students' first attempts to solve a problem involved identifying familiar terms in the problem and making some calculations often without having a clear understanding of the problem. The lack of success led the students to reexamine the statement of the problem more carefully and seek more organized approaches. The students often spent much time exploring only one strategy and experienced difficulties in using alternatives. However, hints from the interviewer (including metacognitive questions) helped the students to consider other possibilities. Although the students recognized that it was important to check the solution of a problem, they mainly focused on whether there was an error in their calculations rather than reflecting on the sense of the solution. These results lead to the conclusion that it takes time for students to conceptualize problem solving strategies and use them on their own when asked to solve mathematical problems. The instructor planned to implement various learning activities in which the content could be introduced via problem solving. These activities required the students to participate and to spend significant time working on problems. Some students were initially reluctant to spend extra time reflecting on the problems and were more interested in receiving rules that they could use in examinations. Furthermore, student expectations, evaluation policies, and curriculum rigidity limited the implementation. Therefore, it is necessary to overcome some of the students' conceptualizations of what learning mathematics entails and to propose alternatives for the evaluation of their work that are more consistent with problem solving instruction. It is recommended that problem solving instruction include the participation or coordinated involvement of all course instructors, as the selection of problems for class discussions and for assignments is a task requiring time and discussion with colleagues. Periodic discussions of course directions are necessary to make and evaluate decisions that best fit the development of the course.
Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate

The purpose of this study was to identify the nature of students' conceptual understanding of two concepts of calculus namely, derivative and function. As a way of collecting data two methods were employed: (a) modification of Piagetean clinical interview; and, (b) tutorial sessions. Whenever the students seemed to be confused about the issues being discussed, the researcher provided instructions through the tutorial sessions. The analysis of data was done by developing individual profiles and by response categories. It was found that the interview methodology was effective in revealing some aspects of students' concept images. The students were found to have little meaningful understanding of derivative. A number of students held proper concept images of function which should lead to the development of an appropriate concept definition. It was also evident from the study that students had adequate skill in using algorithm to solve problems. The results of the study would be useful to the instructors of calculus. It was suggested that introducing a concept by its formal definition would contribute to students' confusions and difficulties. Yet if a concept is presented by means of meaningful examples, students had better opportunity to develop their concept images. Thus leading them to form concept definitions. The researcher strongly recommended that more challenging exercises be posed to the students in problem-solving situations.
Education, Faculty of
Curriculum and Pedagogy (EDCP), Department of
Graduate

Making the transition from calculus to advanced calculus/real analysis can be challenging for undergraduate students. Part of this challenge lies in the shift in the focus of student activity, from a focus on algorithms and computational techniques to activities focused around definitions, theorems, and proofs. The goal of Realistic Mathematics Education (RME) is to support students in making this transition by building on and formalizing their informal knowledge. There are a growing number of projects in this vein at the undergraduate level, in the areas of abstract algebra (TAAFU: Larsen, 2013; Larsen & Lockwood, 2013), differential equations (IO-DE: Rasmussen & Kwon, 2007), geometry (Zandieh & Rasmussen, 2010), and linear algebra (IOLA: Wawro, et al., 2012). This project represents the first steps in a similar RME-based, inquiry-oriented instructional design project aimed at advanced calculus. The results of this project are presented as three journal articles. In the first article I describe the development of a local instructional theory (LIT) for supporting the reinvention of formal conceptions of sequence convergence, the completeness property of the real numbers, and continuity of real functions. This LIT was inspired by Cauchy's proof of the Intermediate Value Theorem, and has been developed and refined using the instructional design heuristics of RME through the course of two teaching experiments. I found that a proof of the Intermediate Value Theorem was a powerful context for supporting the reinvention of a number of the core concepts of advanced calculus. The second article reports on two students' reinventions of formal conceptions of sequence convergence and the completeness property of the real numbers in the context of developing a proof of the Intermediate Value Theorem (IVT). Over the course of ten, hour-long sessions I worked with two students in a clinical setting, as these students collaborated on a sequence of tasks designed to support them in producing a proof of the IVT. Along the way, these students conjectured and developed a proof of the Monotone Convergence Theorem. Through this development I found that student conceptions of completeness were based on the geometric representation of the real numbers as a number line, and that the development of formal conceptions of sequence convergence and completeness were inextricably intertwined and supported one another in powerful ways. The third and final article takes the findings from the two aforementioned papers and translates them for use in an advanced calculus classroom. Specifically, Cauchy's proof of the Intermediate Value Theorem is used as an inspiration and touchstone for developing some of the core concepts of advanced calculus/real analysis: namely, sequence convergence, the completeness property of the real numbers, and continuous functions. These are presented as a succession of student investigations, within the context of students developing their own formal proof of the Intermediate Value Theorem.

Thesis (MCur (Interdisciplinary Health Sciences. Nursing Science))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: HIV/AIDS is considered as a global problem with the number of people living with HIV infection continuing to increase. At the end of 2007 HIV/AIDS had already claimed 25 million lives. Of all new HIV infections 71% were diagnosed in the Sub-Saharan region in 2008, remaining the worst affected region globally. UNAIDS (2008:43) indicated that heterosexual intercourse remained the main origin for HIV infection in the Sub-Saharan region. Therefore the researcher is of the opinion that prevention strategies should focus mainly on sexual transmission of the disease. HIV/AIDS affects mainly people between the ages 15-24 years, notably the age group of most of the learners in Higher Education Institutions (HEIs). Lesotho, a country in the Sub- Saharan region, presents with the third highest HIV adult prevalence (23.2%) in the world and in the region. In an attempt to address the prevailing situation, Lesotho has a number of programmes geared towards addressing HIV/AIDS in the country. However, all these attempts exclude the learners in HEIs, yet the majority of learners are found within the most affected age group. It is also to be noted that Higher Education provides the bedrock for socio-economic and political development in Africa. Some studies have identified insufficient knowledge as being at the root of the increasing HIV infections among youth. However, other studies have shown that there is adequate knowledge among the young people, but still a challenge remains and that is to facilitate changes in behavioural patterns as a component to be linked to the knowledge. Studies conducted in other African countries have shown that there are anti-AIDS programmes and clubs for learners in HEIs where learners are involved in the fight against HIV/AIDS. No publication indicating the same for Lesotho’s HEIs could be found, except for the National University of Lesotho (NUL) that only launched its HIV/AIDS policy for learners in 2009. The researcher is of the opinion that HEIs in Lesotho are not doing enough to combat HIV/AIDS and hence intends to focus on HEIs in Lesotho. This study had two objectives namely:  To determine the knowledge of learners in a specific HEI in Lesotho regarding HIV/AIDS prevention and care.  To explore the needs of learners in a specific HEI in Lesotho regarding HIV/AIDS prevention and care. This mixed method study was conducted, comprising of both quantitative and qualitative designs. Quantitative phase used a questionnaire for determining the knowledge of learners. The questionnaire was adopted from a study that was performed to determine knowledge of South African educators in public schools with some modifications. The qualitative phase was used to explore the needs of the learners through the focus group discussions with the leaders of the learners. Sample was drawn from the entire population using stratified random sampling for the quantitative phase. The qualitative phase used the purposive sampling to obtain in-depth information concerning learners’ needs. Quantitative data was analysed through the use of statistical package for social sciences (SPSS) and qualitative data was analysed using the thematic analysis and open-coding. All ethical principles were adhered to especially the principle of respect for persons. The findings from the quantitative phase of the study showed that learners had adequate knowledge regarding HIV/AIDS prevention and care and the findings from the qualitative phase showed the various needs of the learners with regards to prevention and care of HIV/AIDS in a specific HEI in Lesotho. Recommendations have been proposed based on the findings from the two phases of the study. Limitations observed by the researcher have also been identified. In conclusion the objectives of the study were met and the research questions had been answered.
AFRIKAANSE OPSOMMING: MIV/Vigs word as ‘n internasionale probleem erken, siende dat daar ‘n verhoging in die toename van MIVgeïnfekteerde indiwidue tans is . Einde 2007 het MIV/Vigs het reeds 25 miljoen lewens ge-eis . In 2008 is 71% van al die nuwe MIV-infeksies in die Sub-Sahara streek gediagnoseer, wat aandui dat die streek die mees geaffekteerde streek tans is. UNAIDS (2008:43) het aangedui dat heteroseksuele omgang die hoofoorsaak van MIV-oordrag in die Sub-Sahara-streek is. Laasgenoemde het daartoe gelei dat die navorser van mening is dat voorkomende strategieë meestal op seksuele oordrag van die siekte moet fokus. MIV/Vigs affekteer meestal mense in die ouderdomsgroep 15-24, opmerklik is dit die ouderdomsgroep waarby meesste leerders in Hoëronderwysinstellings (HOI) is. Lesotho, ‘n land in die Sub-Sahara-streek, het tans die derde-hoogste MIV-voorkoms (23.2%) in die wêreld en in die streek. Lesotho het verskeie programme ontlont om MIV/Vigs te bekamp in ‘n poging om die huidige situasie te beredder . Nieteenstaande sluit al die programme leerders in HOI uit, alhoewel die leerders in die ouderdomsgroep van die mees-geaffekteerde groep val. Dit is ook duidelik dat Hoëronderwys die fondasie vir sosio-ekonomiese- en politieke ontwikkeling in Afrika verskaf. Sommige studies het onvoldoende kennis as die wortel van die verhoging van MIV-infeksies onder die jeug geïdentifiseer. Ander studies, daarenteen, wys dat kennis voldoende is onder jeug, alhoewel veranderinge in gedragspatrone om by die kennis aan te sluit ‘n uitdaging bly. Studies uit ander Afrikalande dui daarop dat daar anti-Vigs programme en klubs is waarby HO leerders betrokke is om teen die verspreiding van MIV/Vigs te veg. Geen publikasies in hierdie verband word in Lesotho aangetref nie, behalwe ‘n MIV/Vigs-beleid wat in 2009 deur “National University of Lesotho’ (NUL) gepubliseer is. Dus is die navorser van mening dat HOI nie genoeg doen om MIV/Vigs te beveg nie, daarom fokus sy op HOI in Lesotho. Hierdie studie het twee doelstellings ten doel gehad, naamlik om die leerders in ‘n sekere HOI in Lesotho se kennis aangaande MIV/Vigs voorkoming en sorg te bepaal en die behoeftes van die leerders aangaande MIV/Vigs voorkoming en sorg te verken. ‘n Studie met beide kwantitatiewe- en kwalitatiewe metodes is gebruik om die doelstellings te verwesenlik. In die kwantitatiewe fase is ‘n vraelys gebruik om leerders se kennis te bepaal. Die vraelys is verkry uit ‘n vorige studie wat in RSA gedoen is, maar aangepas om in die Lesotho-konteks te gebruik. Gedurende die kwalitatiewe fase is fokusgroep besprekings met die leiers van die leerders gehou om die behoeftes indiepte te verken. Die steekproef was uit die totale populasie getrek deur van gestratifiseerde streekproefneming gebruik te maak in die kwantitatiewe fase en ‘n doelgerigte steekproefneming is in die kwalitatiewe fase te gebruik. Die navorser het ‘n kwantitatiewe data-analise sagteware (SPSS)gebruik om kwantitatiewe data te ontleed en tematiese- oopkodering is gedurende die kwalitatiewe fase gebruik. Etiese kode is ten volle gerespekteer, veral die respek vir mense gedurende navorsing. Bevindinge van die kwantitatiewe fase het bewys dat leerders voldoende kennis aangaande die voorkoming en sorg van MIV/Vigs besit en die kwalitatiewe bevindinge het die behoeftes van leerders met betrekking tot die voorkoming en sorg van MIV/Vigs in ‘n spesifieke HOI in Lesotho geopenbaar. Die aanbevelings is gemaak, gebaseer op die bevindinge uit die twee fases. Beperkinge in die studie is uitgelig. Ter afsluiting is die doelstellings in die studie bereik en die navorsingsvrae beantwoord.

The purpose of this dissertation was to investigate the relationship between the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The review of literature shows that this possible relationship is based on Alexander Astin's longitudinal input-environment-outcome (I-E-O) model. The I-E-O model was used to analyze the relationship between the input and outcome of the two variables. In addition, this quantitative study determined the relationship between a score of 3 or lower on the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The sample population of this study contained 91 students from various high schools in Texas. Spearman's rank correlation revealed there was a statistically significant relationship between Advanced Placement Calculus AB exam scores and final grades in Math 1710-Calculus I.

The purposes of this study were (a) to develop, implement, and evaluate a computer-oriented instructional program for introductory calculus students, and (b) to explore the association between a computer-oriented calculus instructional program, a non-computer-oriented calculus instructional program, student achievement on three selected calculus topics, and student attitude toward mathematics. An experimental study was conducted with two groups of introductory calculus students during the Spring Semester, 1989. The computer-oriented group consisted of 32 students who were taught using microcomputer calculus software for in-class presentations and homework assignments. The noncomputer-oriented group consisted of 40 students who were taught in a traditional setting with no microcomputer intervention. Each of three experimenter-developed achievement examinations was administered in a pretest/posttest format with the pretest scores being used both as a covariate and in determining the two levels of student prior knowledge of the topic. For attitude toward mathematics, the Aiken-Dreger Revised Math Attitude Scale was administered in a pretest/ posttest format with the pretest scores being used as a covariate. Students were also administered the MAA Calculus Readiness Test to determine two levels of calculus prerequisite skill mastery. An ANCOVA for achievement and attitude toward mathematics was performed by treatment, level, and interaction of treatment and level. Using a .05 level of significance, there was no significant difference in treatments, levels of prior knowledge of topic, nor interaction when achievement was measured by each of the three achievement examination posttests. Furthermore, there was no significant difference between treatments, levels of student prerequisite skill mastery, and interaction when attitude toward mathematics was measured, at the .05 level of significance. It was concluded that the use of the microcomputer in introductory calculus instruction does not significantly effect either student achievement in calculus or student attitude toward mathematics.

The purposes of the study were: to determine the relationship between class size and academic achievement among university students in first-semester calculus classes, and to compare opinions about the instructor, course, and classroom learning environment of university students in small first-semester calculus classes with those in large classes. The sample consisted of 225 university students distributed among two large and two small sections of first-semester calculus classes taught at the University of Texas at Arlington during the fall of 1987. Each of two tenured faculty members taught a large and small section of approximately 85 and 27 students, respectively. During the first week of the semester, scores from the Calculus Readiness Test (CR) were obtained from the sample and used as the covariate in each analysis of covariance of four periodic tests, a comprehensive final examination, and final grade average. The CR scores were also used in a logistic regression analysis of attrition rates between each pair of large and small sections of first-semester calculus. Three semantic differentials were used to test the hypotheses relating to student opinion of the instructor, course, and classroom learning environment. It was found that for both pairs of large and small first-semester calculus classes there was no significant difference in the adjusted means for each of the four periodic tests, the final examination scores, the final grade averages, and the attrition rates. It was also found that the means of the student evaluation of the course by students in small and large classes were not significantly different, and the results of the student evaluations of the instructor and classroom learning environment by students in small and large first—semester calculus classes were mixed.

Acompanha: Manual didático para aplicação de testes estatísticos na análise do desempenho de alunos em disciplinas da graduação
Esta pesquisa teve como objetivo analisar variáveis a fim de entender se elas são significativas para a reprovação dos alunos ingressantes nos cursos de Engenharia na disciplina de Cálculo Diferencial e Integral I. Para tanto, adotou-se como hipótese básica que o comprometimento acadêmico é um dos fatores que interfere de forma expressiva neste contexto. O referencial teórico faz um breve apanhado sobre a origem e evolução dos cursos de Engenharia, sobre a importância do Cálculo, bem como sobre as reprovações e possíveis agravantes. Além disso, aborda as principais variáveis associadas à reprovação em Cálculo I apontadas na literatura existente. Trata-se de uma pesquisa com abordagem mista, sendo que as hipóteses secundárias buscavam confirmar ou descartar a influência de seis variáveis - nota obtida pelos estudantes na prova de Matemática do Exame Nacional do Ensino Médio (ENEM), pesos atribuídos às provas de Matemática do ENEM, período de ingresso no curso, carga horária semanal de aulas, conhecimento matemático prévio e metodologia de avaliação diferenciada - no desempenho obtido pelos calouros na disciplina em questão. Para tanto, estudou-se o desempenho de 3.010 alunos da UTFPR, pertencentes aos campi Pato Branco e Ponta Grossa, que ingressaram na instituição de 2010 a 2014. Os dados referentes às variáveis quantitativas foram coletados por meio de consultas ao sistema acadêmico institucional e aplicações de testes aos calouros. Em seguida, estes dados foram analisados com auxílio de ferramentas estatísticas. A coleta de dados referentes à variável qualitativa (comprometimento acadêmico) ocorreu por meio de entrevistas semiestruturadas realizadas junto a dezessete alunos, sendo que a análise se amparou na metodologia de Análise do Conteúdo, proposta por Bardin (1977). Os resultados sugerem a dependência entre cinco variáveis quantitativas analisadas e o desempenho obtido na disciplina de Cálculo I. Além disso, apontam que as posturas discentes adotadas frente a disciplina de Cálculo Diferencial e Integral I foram determinantes para o bom ou mau desempenho na disciplina. Como produto final foi confeccionado um aplicativo web que permitirá a reaplicação da metodologia de análise dos dados quantitativos nos outros câmpus da UTFPR e em outras instituições de ensino superior.
This research aims to analyse factors in order to understand their significance to the failure of Engineering freshmen students in Differential and Integral Calculus I. To this purpose, the basic hypothesis adopted is that academic commitment is a variable that expressively affects this setting. The theoretical framework summarizes the origin and evolution of Engineering courses, the relevance of the subject and respective failures, as well as potential aggravating circumstances. In addition, it approaches key factors related to failure in Calculus discussed in current literature. This is a mixed approach research and secondary hypotheses intended to either confirm or disregard the impact of certain variables, namely: grade achieved by students in Mathematics exam conducted in Brazilian High School National Exam (Exame Nacional do Ensino Médio, ENEM); weights assigned to ENEM Mathematics test; term of course admission (fall or spring); quantity of courses per week; previous knowledge on Mathematics; and distinct evaluation methodology. The research studies the performance of 3,010 students of UTFPR of both Pato Branco and Ponta Grossa campuses enrolled in the institution from 2010 to 2014. Data related to quantitative variables were collected through searches in the institution’s academic system and conduction of tests to first-year students. Subsequently, this data was analysed using statistics tools. The data accrual related to the qualitative variable (academic commitment) occurred through semi-structured interviews conducted along with some students and analysis was supported by Content Analysis methodology proposed by Bardin (1977). Results suggest the dependency among the five quantitative variables analysed and the performance achieved in the subject Calculus I. Furthermore, they indicate that students’ behaviour regarding the subject Differential and Integral Calculus I was definitive for either good or poor performance in the subject. The final product was the construction of a web applicative which allows the reutilization of quantitative data analysis methodology in other UTFPR campuses and college institutions.

It is common for students to make mistakes while solving mathematical problems. Some of these mistakes might be caused by the false ideas, or misconceptions, that students developed during their learning or from their practice. Calculus courses at the undergraduate level are mandatory for several majors. The introductory course of calculus—Calculus I—requires fundamental skills. Such skills can prepare a student for higher-level calculus courses, additional higher-division mathematics courses, and/or related disciplines that require comprehensive understanding of calculus concepts. Nevertheless, conceptual misunderstandings of undergraduate students exist universally in learning calculus. Understanding the nature of and reasons for how and why students developed their conceptual misunderstandings—misconceptions—can assist a calculus educator in implementing effective strategies to help students recognize or correct their misconceptions. For this purpose, the current study was designed to examine students’ misconceptions in order to explore the nature of and reasons for how and why they developed their misconceptions through their thought process. The study instrument—Calculus Problem-Solving Tasks (CPSTs)—was originally created for understanding the issues that students had in learning calculus concepts; it features a set of 17 open-ended, non-routine calculus problem-solving tasks that check students’ conceptual understanding. The content focus of these tasks was pertinent to the issues undergraduate students encounter in learning the function concept and the concepts of limit, tangent, and differentiation that scholars have subsequently addressed. Semi-structured interviews with 13 mathematics college faculty were conducted to verify content validity of CPSTs and to identify misconceptions a student might exhibit when solving these tasks. The interview results were analyzed using a standard qualitative coding methodology. The instrument was finalized and developed based on faculty’s perspectives about misconceptions for each problem presented in the CPSTs. The researcher used a qualitative methodology to design the research and a purposive sampling technique to select participants for the study. The qualitative means were helpful in collecting three sets of data: one from the semi-structured college faculty interviews; one from students’ explanations to their solutions; and the other one from semi-structured student interviews. In addition, the researcher administered two surveys (Faculty Demographic Survey for college faculty participants and Student Demographic Survey for student participants) to learn about participants’ background information and used that as evidence of the qualitative data’s reliability. The semantic analysis techniques allowed the researcher to analyze descriptions of faculty’s and students’ explanations for their solutions. Bar graphs and frequency distribution tables were presented to identify students who incorrectly solved each problem in the CPSTs. Seventeen undergraduate students from one northeastern university who had taken the first course of calculus at the undergraduate level solved the CPSTs. Students’ solutions were labeled according to three categories: CA (correct answer), ICA (incorrect answer), and NA (no answer); the researcher organized these categories using bar graphs and frequency distribution tables. The explanations students provided in their solutions were analyzed to isolate misconceptions from mistakes; then the analysis results were used to develop student interview questions and to justify selection of students for interviews. All participants exhibited some misconceptions and substantial mistakes other than misconceptions in their solutions and were invited to be interviewed. Five out of the 17 participants who majored in mathematics participated in individual semi-structured interviews. The analysis of the interview data served to confirm their misconceptions and identify their thought process in problem solving. Coding analysis was used to develop theories associated with the results from both college faculty and student interviews as well as the explanations students gave in solving problems. The coding was done in three stages: the first, or initial coding, identified the mistakes; the second, or focused coding, separated misconceptions from mistakes; and the third elucidated students’ thought processes to trace their cognitive obstacles in problem solving. Regarding analysis of student interviews, common patterns from students’ cognitive conflicts in problem solving were derived semantically from their thought process to explain how and why students developed the misconceptions that underlay their mistakes. The nature of how students solved problems and the reasons for their misconceptions were self-directed and controlled by their memories of concept images and algorithmic procedures. Students seemed to lack conceptual understanding of the calculus concepts discussed in the current study in that they solved conceptual problems as they would solve procedural problems by relying on fallacious memorization and familiarity. Meanwhile, students have not mastered the basic capacity to generalize and abstract; a majority of them failed to translate the semantics and transliterate mathematical notations within the problem context and were unable to synthesize the information appropriately to solve problems.

The challenge for African universities is to refocus their research and teaching missions to transform and revitalize the relationship between higher education and national development needs. Funded by British Academy African Partnerships (BAAP) programme, the University of Botswana, in partnership with The National University of Lesotho, University of Malawi and Calabar University in Nigeria, carried out 18 months of collaborative research project aimed at determining the implementation of Third Mission of Universities through rural community training and leadership. One of the two case studies, in D'Kar by Kellogg, in partnership with BA ISAGO University College yielded some very useful results. This included the necessity to build community leadership for sustainable development and the beginning of the poverty reduction process to take place.

This study aims to measure the impact of course coordination and part-time Precalculus instructor support on students academic performance. Our results show the Precalculus passing rate (71.53%) was slightly higher in the post-coordination cohorts. However, this difference was not statistically significant from the passing rate (70.70%) of the cohorts in pre-coordination. Also, there was no significant difference between the passing rates (66.90% vs 65.25%) of calculus in the pre- and post-coordination cohorts. However, when accounting for the two versions of calculus, we observed one passing rate was statistically significantly lower in post-coordination cohorts, while the other passing rate was statistically significantly higher after Precalculus coordination. This paper discusses how our results confirm that a careful curriculum design in addition to a dedicated course coordination can have a significant positive impact on students’ learning and their academic performance. We observed that the reflective teaching philosophy and opportunity to engage in critical conversations about teaching and learning promoted through course coordination influenced classroom practice and resulted in improved student outcomes. We recommend that departments should recognize the importance of course coordination and encourage faculty to work closely towards the common aim of delivering the best teaching practices.