The purposes of this study were (1) to compare the achievement levels of students enrolled in a beginning college mathematics course when taught by (a) closed-circuit television followed by student-assisted study periods, (b) closed circuit television followed by access to videotape replay with no supervised study periods, (c) closed-circuit television followed by unsupervised study and discussion, and (d) regular lecture-recitation methods conducted by the television instructor, and (2) to ascertain the students' attitudes toward their instructor, course, and method of instruction.

This quasi-experimental study examined the effects of participation in a Supplemental Instruction (SI) program on student test performance in a second-level developmental mathematics class in a four-year university setting. This research deviated from past research on Supplemental Instruction in that it examined effects of the program at the end of each test block rather than at the end of the course only. The quasi-experimental design was precipitated by an inability to control factors of participation and limited sample size. Test data were analyzed using analysis of variance; final course grades were analyzed using chi-square.

To obtain information regarding the effects of two divergent thought processes used in a college mathematics course for prospective elementary school teachers, this study compared the effectiveness of an adaptation of the traditional, deductive teaching method with that of an inductive method reflecting the recommendations of the Committee on the Undergraduate Program in Mathematics. In the spring semester of 1973, two sections of Mathematics for Elementary Teachers I, at Cameron College, Lawton, Oklahoma, served as experimental groups to test the two adaptations. The course followed the Committee on the Undergraduate Program in Mathematics recommendations for a first course in mathematics for prospective elementary teachers.

In view of the National Plan for Higher Education (Department of Education, 2001) that calls for an increased throughput of students at higher education institutions within South Africa, a quantitative study was undertaken at a particular higher education institution during 2005 to identify factors associated with achievement in mathematics at entry level to tertiary studies. Factors considered in this study pertained specifically to those that may facilitate the introduction of intervention aimed at assisting students enrolled for mathematics at tertiary level and who are at risk of failing. Students admitted to either a degree or extended degree programme in science, engineering and technology (SET) in 2005 at the higher education institution constituted the target population. A survey was conducted at the onset of the academic year among students in the target population providing written consent to participate in the study. Three pen-and-paper questionnaires were administered, i.e. a background questionnaire, a newly developed cognitive instrument for the measurement of basic mathematical skills, including mathematics language proficiency, and an adapted instrument, based on an existing standardised instrument, the Study Orientation in Mathematics (SOM) instrument (Maree, Prinsloo & Claassen, 1997), for the measurement of the affective and behavioural domains related to the studying of mathematics. Information regarding student achievement at the end of their first semester of study was obtained from student academic records. Background variables, in particular being an English second language (ESL) student and having received home language tuition at school were shown to be associated with the initial preparedness of students, i.e. their Grade 12 achievement. These variables did not, however, directly contribute towards the prediction of achievement at entry level to the institution. The extent to which students have acquired basic mathematical skills, particularly mathematical language proficiency (not necessarily reflected in their Grade 12 results) was shown to contribute significantly towards the prediction of achievement in mathematics at entry level. In addition, anxiety and attitude towards mathematics and the utilisation of effective study behaviour were also shown to be associated with achievement; the latter contributing significantly towards the prediction of achievement at entry level for both degree and extended degree programme students. The findings culminated in recommendations for tertiary institutions, educators and those embarking on future research relating to the theme in question. The issue of measuring basic mathematical skills, including mathematical language proficiency and study strategies of students studying towards careers in SET at the onset of their studies and providing support to improve these, is emphasised. / Prof. J. Strauss

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.

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A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 1997. / After Mozambique became independent from Portugal, the main aim of the government policy towards education was to create equity of opportunity to enter the formal education system for different social, gender and age groups. However, females are still under-represented in higher education particularly in courses which require an extensive mathematical background. Thus, the purpose of this study was, to explore possible gender differences in performance and attitudes toward mathematics among 1996 BUSCEP students at Universidade Eduardo Mondlane. Those students were tested on several affective and cognitive variables, using a questionnaire and tests. The results suggested that gender performance and attitudes towards mathematics tend to be similar, and the inequalities found, were more evident in the participation in mathematics related careers. These findings emphasise the need to further examine the interrelationships between gender and career choices which should be conducted with students from the secondary school. / AC2017

The in-class learning environments of a traditional and hybrid mathematics course were compared. The hybrid course had half the face-to-face meetings as the traditional course; outside of class, the students in the hybrid section completed asynchronous online assignments that involved watching content-delivery videos. Moving the content delivery outside of the classroom for the hybrid format had an impact on the interactions between the students and the professor inside the classroom. Quantitative and qualitative analysis of verbal discourse determined that the hybrid class format reduced the amount of in-class time devoted to direct instruction and increased the level of student discourse. Students assisted other students, had the freedom to make mistakes, and were able to receive personal guidance from the professor. The professor was able to address student misconceptions on formative assessments in class. Previous studies of the hybrid class model had focused on comparing differences in examination scores, GPAs, and pre- and post-test scores between the traditional and hybrid class model rather than comparing what is occurring inside the classroom. Quantifying what effect the shift from the traditional to the hybrid class model had on discourse inside the classroom is a first step towards confirming how the different methods of content delivery affects the in-class learning environment, and provides insight into certain pedagogic advantages the hybrid format may offer.

The purpose of this study was to evaluate whether supplemental instruction and online homework can improve student performance and understanding in a first-semester calculus course at a large urban four-year college. The study examined the metacognitive and study skills and posttest scores of students. The study also focused on students’ and instructor’s perception and experiences of supplemental instruction and online homework using WebAssign. The study used a modified version of the Motivated Strategies for Learning Questionnaire (MSLQ) to reveal any significant differences in metacognitive and study strategies between students in a class with supplemental instruction/online homework and students in a traditional class. Students’ scores on their final examination were analyzed to reveal the effect of mathematical achievement between the control and experimental groups. Surveys and interviews were utilized to provide anecdotal evidence as to the overall effectiveness of the online homework management system and supplemental instruction. Results of the study showed no substantial difference between the control group and the experimental group in seven out of eight sub-scales of metacognitive and study strategies: metacognitive self-regulation, time and study environment, effort regulation, help seeking, rehearsal, organization, and critical thinking. But, students with supplemental instruction/online homework showed a higher level of elaboration learning strategies. The interaction of pretest and type of class (traditional or treatment) did not have a significant effect on students’ posttest score. There was no substantial effect of pretest on posttest, but the treatment influenced students’ posttest score. Students’ gender, race, class level, or the number of courses they registered for were insignificant predictors of their posttest scores. The instructor and students agreed that time spent in supplemental instruction sessions and on WebAssign were worthwhile and beneficial. They believed supplemental instruction and online homework using WebAssign may have influenced students’ understanding and performance in the course.

This study examined the effect of problem-based instruction (PBI) on undergraduate students and prospective secondary mathematics teachers’ perceptions of mathematical proof and pedagogical views. Quantitatively, the Mathematical Proof Survey (MPS) was developed and used to assess the views of mathematical proof held by undergraduates in lecture-based and PBI mathematics courses. Qualitatively, research interviews examined the way teacher candidates’ experiences as mathematics learners in the courses affected their conceptions of mathematical proof and views of learning and teaching mathematics and proof. Findings from quantitative analysis of MPS data and qualitative analysis of interview data are presented, and results from the comparative analysis are discussed for implications. The results of the study suggest that experiences with proof and instruction in such PBI courses provide opportunities for undergraduates and prospective mathematics teachers to develop more humanistic perspectives of proof and process-oriented pedagogical views than do lecture-based courses. / text