The purpose of this study was to examine the relationship between certain pupil characteristics and performance on mathematics laboratories. The four classes of grade six students involved in the study were classified by sex, field-dependence-independence, reflective-impulsive tempo, past performance in mathematics, present performance in mathematics, and intelligence. Eight mathematics laboratories designed and used in the study were categorized topically into number theory or geometry laboratories. Each laboratory activity was designed to allow pupils to manipulate materials while exploring an idea and collecting data. In part two of a laboratory activity, which included a test section, pupils were required to analyze data, make a prediction, and verify the prediction using manipulative materials before extending a pattern or rule. Laboratories were randomly assigned to classes. Results showed that all the selected characteristics except sex had a significant relationship with performance on mathematics laboratories. Sex showed a significant relationship only to the geometry laboratories. An analysis of covariance was performed using past achievement as the covariate. The results indicated that there was a significant difference in performance only on the geometry laboratories between boys and girls and between field-dependent and field-independent students. The differences were found to be in favour of the girls and the field-independent students. The results of this study suggested that further research is necessary to determine the most effective means of using mathematics laboratories. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

It was the purpose of this study to investigate the effects of convergent/divergent teaching methods on student performance on two mathematical problem solving tasks (routine/non-routine problems). A concurrent purpose was to investigate the interaction between the convergent/ divergent teaching methods and the thinking style (either convergent or divergent) of the learner. Four grade ten classes were randomly selected from the eleven academic mathematics classes in the secondary school involved in the study. Due to subject absenteeism a total of sixty-six subjects were used for the analyses. Each subject was given the Watson-Glaser Test of Critical Thinking (Form YM) and the Torrance test of Thinking Creatively With Words (Booklet A) to determine their level on the independent measures of convergent and divergent thinking, respectively. Each subject was taught by one teacher using one method for approximately two hours. The content of these lessons involved the Fibonacci Sequence and Pascal's Triangle. At the end of treatment, each subject received a test on the dependent measures Croutine/non-routine problems). Trained observers were used to ensure consistency of teaching method. Analysis of covariance using the regression model was performed with convergent/divergent thinking styles as the covariates. There was no significant difference between convergent teaching methods and divergent teaching methods (p ≤ 0.05). Convergent thinkers scored significantly higher than did divergent thinkers on both dependent measures. However, as convergent thinking is far more highly correlated with intelligence than is divergent thinking, this result may have been confounded by intelligence. Therefore, in further studies in this area, the variance in problem solving due to intelligence should be partialled out. Only one of eight interaction effects was significant (p ≤ 0.05). This suggested that non-divergent thinkers did better with convergent (as opposed to divergent) teaching methods and that non-convergent thinkers did better with divergent (as opposed to convergent) teaching methods. The lack of other significant interactions indicated that intelligence may have been a confounding effect in this study. / Education, Faculty of / Graduate

M.Ed. (Mathematics in Education) / Primary school learners need to extend their knowledge of numbers to include common fractions. Common fraction concepts are important but learners find it more complicated and difficult to understand than whole numbers, they experience it as particularly challenging. Fraction consists of sub constructs which is adding to the complexity of fractions. The aim of this study was twofold, firstly, to identify the conceptual and procedural knowledge about common fractions that learners need to acquire from grade four to seven to enable them to be able to do calculations with fractions. The second aim was identifying effective teaching strategies to enhance learners’ conceptual and procedural knowledge about common fractions. Primary school learners are mainly in the concrete operational stage of development according to Piaget’s stages of cognitive development. Although the learner can reason, the ability to reason is based on tangible objects and direct experiences. The obstacles that learners encounter in developing deep understanding of fractions can be due to the nature of fractions or due to the instructional approaches employed by the teachers. Learners are able to understand at a concrete level, their reasoning is consistent with respect to real objects. To enable learners to develop meaning and understanding of fractions, learners should be provided with many experiences in partitioning quantities into equal parts. Teachers must ensure learners make the connections between the concrete models, manipulatives and pictures that are equally divided. Learners need to be able to represent numbers using words, models, diagrams and symbols and be able to make the connections between the representations. From a constructivist view learners construct their own knowledge and the learning of subject matter is the product of an interaction between what they are taught and the knowledge they bring to the learning situation.

Myra McIlvaine Marshall / Typescript / M.A. Florida State College for Women 1933 / Includes bibliographical references

A mass of raw data is available in the form of test scores of students who have completed "Basic mathematics for general education". These data have been only partially analyzed. This paper records some efforts to decide what statistical techniques might help one to see more in this mass of data-- to understand more fully the implications of these data. A better understanding of these data is of vital interest to the teaching staff of "Basic mathematics" in their efforts to improve the course. / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 39).

This single case study investigated the implementation of a modularized mathematics course designed to eliminate the usage of remedial mathematics courses from post-secondary mathematics curricula. The literature review revealed that introductory college level mathematics success and student retention rates in post-secondary schools was chronically problematic due in large part to the number of students unable to advance past remedial courses. According to the findings of this study, the modularized curriculum provided the necessary remediation tools embedded within course essential to student learning and development without the psychosocial pitfalls and financial burdens that follow remedial mathematics courses. The conclusion drawn from the findings is that enrolling post-secondary students in a modularized introductory college level mathematics course with embedded remedial support can be effective in increasing student confidence in successfully completing an introductory level mathematics course

Bibliography: pages 83-85. / This study examines children's developing mathematical abilities during the first three years of their schooling. More particularly, children in grades one, two and three of three different primary schools, in two different regions, had their performances on eleven mathematics tasks monitored over the course of 1996 to examine their developing mathematical abilities. These abilities were investigated in terms of task-particular performances and the assumed competencies (internal mental processes) underlying these performances. The data was generated through the use of a repeated measures design. The theory of the methods used to gather the data and to analyse the results is rooted in Vygotsky's (1978) experimental-developmental approach to the study of higher mental functions. This method of observation proved to be successful to the degree that it allowed for the study of changes in children's performances over a seven month period. The overall findings of the study revealed that the subjects in the sample population had the developmental readiness with which to improve their mathematical abilities. However, when this developmental readiness had to be taken further through formal instruction, their performances were inadequate. The investigation exposed the complexity and importance of language in the successful development of mathematical concepts. The data indicated that the subjects' learning was neither in advance of their development nor was it indicative of the constructivist approach to the task of teaching. Furthermore, there existed a conflict between spontaneous and formal knowledge in engaging with school mathematics tasks.

Includes Course Papers. / Includes bibliographies. / Very little is known about how young children think and behave when faced by computers and the broad array of mathematical software available. Much of the software has been developed by adults in the way adults see young children reasoning. A class of twenty English-speaking boys of approximately 12 years of age were exposed to carefully selected mathematical software without adult (teacher) interference, to clarify how these pupils would react to that software. Special focus was placed on the interactions of three children throughout the series of twenty lessons, using two video cameras to record their behaviour. The size of the groupings was changed to consider the effect of group size on the pupils' interactions. Various 'themes' evolved out of reviewing the video recordings. These 'themes' were then linked to Research data. It appears that these pupils had great trouble in reading and interpreting instructions accurately. Also, the software made assumptions of what the pupils could do. The interaction and collaboration by the boys seemed at its best when they were in a group of two as 'peer equals'. The class recognised and used the services of those boys they considered 'experts' in the use of computers. The video-recordings showed that the pupils preferred having pencil and paper available to record information and their estimations, rather than having to rely on memory. It seemed to give permanence to their thoughts and make these more explicit and organised. An analysis of the data also showed that the software and the boys' reaction to it was distinctly sexist. The names of the software (SNOOKER, PILOT, MATHS - CARS IN MOTION, etc.) can be seen as male. The boys gave the computer a 'personality' and referred to it as a 'he'. Also, a disturbing tendency among these pupils was the way they interpreted the software and reacted to it in a distinctive military fashion. This can be attributed to the boys having to battle, explode or bomb their way to victory; to shoot something or be shot in much of the software available. My role of being 'non-expert' was an extremely difficult one as the pupils had expectations of me, and the shortcomings in the software obliged some form of interference. My conclusions are that the mathematical software needs to be appropriate and relevant to what is being done in the class rather than to exist on its own outside of it, and that it could aid the pupil to think about his thinking.

My goal in this study was to investigate the role of primary source projects (PSPs) on instructor growth regarding the post-secondary mathematics teaching. A PSP is a curricular material that aims to guide students reading of primary historical sources through some tasks and secondary narrative by the author of the PSP (Barnett, Lodder, & Pengelley, 2014). This study was primarily motivated by university mathematics instructors’ growing interest in using PSPs for some part of their teaching through their participation in the National Science Foundation-funded Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) project. In this regard, an examination of instructor’s experiences with PSPs in a textbook-dominated field as undergraduate mathematics instruction has the potential to respond to the recent calls by major mathematical institutions’ for improving the quality of instruction at the undergraduate level (Saxe & Braddy, 2015). In this phenomenologically grounded study, I explored the interactions of two mathematics instructors who taught with the PSP, “Solving a System of Linear Equations Using Ancient Chinese Methods” (SSLE; Flagg, 2018) to investigate if, and how, such interactions contribute to the professional growth of instructors. One of the participants is the author of the PSP and the other one was a first-time user of the material. I used semi-structured interviews, instructors’ responses to the open-ended items in TRIUMPHS surveys, and their CVs as the data collection methods to understand their engagement with SSLE, and the role of such engagements on their professional growth. I used the Interconnected Model (Clarke & Hollingsworth, 2002) to document the changes that instructors reported as a result of using the PSP for their teaching, where I derived conclusions regarding instructors’ professional growth. PSP engagement had significant impact on Dr. Flagg’s and Dr. Edward’s classroom teaching, participation to scholarly activities, and hence contributing to their professional growth. In my detailed analysis of data, I observed that what both instructors considered prior to their PSP engagement as salient outcomes of mathematical learning experience had a pivotal role on the changes that they experienced as a result of their PSP engagement. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / 2019 / November 7, 2019. / Curriculum materials, Instructor growth, Primary historical sources, Professional development, Undergraduate mathematics education / Includes bibliographical references. / Kathleen M. Clark, Professor Directing Dissertation; Fengfeng Ke, University Representative; Christine Andrews-Larson, Committee Member; John P. Myers, Committee Member.

Dissertation submitted to the Faculty of Education in fulfillment of the requirements for the degree of Master of Education in the Department of Philosophy of Education at the UNIVERSITY OF ZULULAND, 1995. / This study examined the effects of second language in the learning of mathematics by the black pupils. The first aim was to investigate pupils' understanding of the meaning of words found in their text books. The second aim was to determine the level of difficulty experienced by pupils in learning the meaning of mathematical terms. The third aim was to find out whether mathematics performance is influenced by any particular respondents' characteristics. To this end, an achievement test with three subtests was administered to a representative sample of black pupils doing mathematics at standard nine and ten. The first subtest (TEST A) consisted of questions that require pupils to define concept found in their textbooks. The second subtest (TEST B) was designed to elicit dual conceptualisation from a pupil, i.e. a pupil responded by defining a concept or by means of a diagram. The third subtest (TEST C) consists of descriptions of concepts. The pupil had to respond by a word to each description. A large percentage of black pupils did not perform very well in all mathematics tasks. They made best responses by means of diagrams, but did poorly in language expression. This is an indication that culturally different pupils * poor performance in mathematics tasks, is due to language limitations. Further on there is no relationship between language and spatial tasks. The present study revealed that standard nine and ten pupils have problems in defining concepts that are found in their mathematics text books. They also fail to associate a concept with a description. The causes for these problems are varied. It may be due to language that it is restricted to the classroom situation or the methods used in teaching new concepts are to culturally different pupils. Results also indicated that performance of pupils is less influenced by variables like sex and age than by class, stream and mathematics grade. It has been found that age has no influence on the performance of mathematics tasks. The performance of all age groups is the same. It was found that the performance of boys and girls does not differ. On the other hand, standard ten pupils' achievement was better than that of standard nine pupils. In the same vein, the science group pupils did better than the general and commerce pupils. Pupils doing higher grade mathematics also showed better performance than pupils taking standard grade mathematics. / University of Zululand