The Govan Mbeki Mathematics Development Unit (GMMDU) provides additional mathematics content to learners via mathematics workshops and DVDs. Mathematics is presented in PPT format. The prominence of feature phone usage has been confirmed amongst learners in socio-economic disadvantaged schools, specifically those learners participating in the GMMDU mathematics workshops. Feature phones typically contain limited device resources such as memory, battery power, and network resources. Distributed computing provides the potential to facilitate a new class of mobile applications with the provision of off-device resources. The objective of this research was the design of an architecture using Cloud Computing for the provision of mathematics in the form of PPT slides to feature phones. The capabilities of typical feature phones were reviewed as well as various distributed computing architectures that demonstrate potential benefit to the mobile environment. An Architecture using Cloud Computing for Content Provision (AC3P) was subsequently designed and applied as a proof of concept to facilitate the provision of mathematics in the form of PPT slides to feature phones. The application of AC3P was evaluated for efficiency and effectiveness. It was demonstrated that the application of AC3P provided efficient and effective provision of PPT to feature phones. The successful application of AC3P provided evidence that Cloud Computing may be used to facilitate the provision of mathematics content to feature phones. It is evident that AC3P may be applied in domains other than the provision of mathematics.

Staff developers are facing new challenges in the 1990's in British Columbia as secondary education is criticized not only for what it teaches, but also, for how it is being taught. This project addresses the very complex nature of improving the learning situation of students by focusing on staff development. This study documents the inservice, implementation and teacher responses to a model for staff development at a secondary school which included: 1. the introduction of new teaching strategies which supported learner-focused classroom practice 2. teacher collaboration and peer support 3. the theory of constructivism and its incorporation into classroom practice. To gain some insight into teachers' perceptions of new teaching strategies and skills, collaboration, and a constructivist approach to classroom practice was one major research strand. Another strand of the research investigated the process of change as facilitated through staff development. Specifically, the intent of the study was to identify and elaborate on those factors which are liberating and prone to influence in a process known as staff development and to recognize those factors which are resistant and tend to act as barriers to change. Data for this study was gained by following a study group of six secondary teachers from three curricular disciplines over a time period of three months. Group interviews during the study and individual interviews at the end of the study were collected and transcribed. The responses of the participants to the research questions are reported in detail in an effort to preserve the contextual influences. Through these responses the reader can enter into the individuals' thought processes as participants reflect upon their personal experiences with the challenge of change. The findings of this study support and extend the literature on important components and influences to staff development. In particular, this study gained further insight into: 1. how a constructivist approach can be translated into a model of staff development 2. how influences, such as peer collaboration and peer support enhanced a change in classroom practice. 3. how a change incorporating a constructivist approach to teaching is more likely to be assimilated by an individual who has a transactional or transformational orientation to curriculum. A transmissive orientation to teaching acts as somewhat of a barrier to the conceptual change of a constructivist approach. 4. how the motivation and teacher satisfaction for participating in change is determined to a degree by perceived improvements in learning by students. 5. how all participants experienced change but the nature of that change was very individual, gradual, and incremental in nature along the continuum from teacher to learner-focused education. The study concludes with recommendations for individuals planning staff development which incorporates the research findings. / Science, Faculty of / Mathematics, Department of / Graduate

It was the purpose of this study (1) to review the literature in regards to the predictive validity of the available mathematical counselling tests; (2) to analyze the sequences of mathematics courses that have and would be undertaken by students; (3) to analyze the content of these mathematics courses for skills and concepts; and (h) to determine the content of the new mathematical counselling test. All versions of this counselling test consisted of two distinct sections. Part one contained problems whose solutions were dependent upon the student's comprehension of mathematical concepts and procedures to which he had been exposed. The second section was based on new material presented in a teach-test format. The test was administered, evaluated, revised and administered again several times. On a small sample of students the test scores from both sections had a correlation coefficient of just less than 0.70. The correlation coefficient between the two sections has been close to 0.50. Each section of this test is a good predictor of a student's grade in mathematics and measures different aspects needed for mathematical competence. / Education, Faculty of / Graduate

This study was motivated by the writer's belief that youngsters do have a tendency to group, and that this propensity, no matter how emphemeral and vacillating it may be at times, should be taken into account in the design of teacher strategies. Grade four students were assigned to two groups at random, and then, in one group, subgroups of four students were randomly made up. All students were instructed by film loops for three days on writing an equation for a division problem. On the fourth day of the experiment, the students wrote a criterion test of twenty-five division problems. The investigation of student-student interaction was done by comparing the effects of instruction to groups of four students with those of instruction to the individually taught students. A two-tailed t-test was used to test the significance between the means of the two groups and a F-test was employed to test the difference in the variances of the two groups. There was no significant difference between the individual-taught group and the group-taught group in terms of either mean or variance. The conclusion was drawn that the use of small groups to teach students to write equations for division problems did not improve the instruction. But it was felt that further research using different dependent variables is both warranted and desirable. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

An analysis of the literature showed that there is very little agreement on when and how a computer program should branch a student through a CAI program. This, together with the fact that research in the field of arithmetic has shown that drill should follow effective teaching of concepts, led the author to investigate whether students working on arithmetic drill-and-practice would do better on a COMPUTER-PACED program or a SELF-PACED program. COMPUTER-PACED was defined to be where the computer program determined when the students should be branched to more or lass difficult questions. SELF-PACED was defined to be where the students determined when they were presented more or less difficult questions by pushing one of the two marked keys on the computer terminal. The evaluation was done by comparing the achievement of the COMPUTER-PACED and the SELF-PACED groups. For the length of the study the two groups of grade six students had a daily arithmetic lesson followed by a session at a computer terminal to work on arithmetic drill-and-practice programs. The results of the post-test (adjusted by using a pre-test as a covariate) showed that there was no significant difference between the two selection mechanisms. Further analysis showed that there was no significant difference between the males and females performance and that there was no significant interaction (sex X groups) effect. The results of the study indicate that when working with arithmetic drill-and-practice, students will do as well if the computer program controls when to branch as they would if the students control when to branch to a different level of difficulty. / Education, Faculty of / Graduate

The general goal of the present study was to assess mathematics achievement at the end of Grade 12 in the Dominican Republic, with particular attention to school and regional differences, as well as gender differences. Also, gains in achievement were examined by comparing the achievement of students in Grade 12 to that of students finishing Grade 11. In addition, the performance of Grade 12 students was compared to that of Grade 8 students as assessed in the Teaching and Learning of Mathematics in the Dominican Republic (TLMDR) study and to that of students from other countries in the Second International Mathematics Study (SIMS). The sample included 1271 students in Grade 12 and 1413 in Grade 11, distributed over 49 schools. Three types of schools were sampled, public schools, and two kinds of private schools. They were urban schools located in the twelve largest cities of the country. These cities were grouped into three regions of similar size. The mathematics test consisted of 70 multiple-choice items distributed over two test forms. Students' scores were analyzed to assess how much mathematics students in Grade 12 know. Grade 11 data were used as a surrogate for pre-test scores to estimate gains in achievement. School means were used in an analysis of variance designed to examine the effect of school type and region on mathematics achievement. Males' and females' scores were used to analyze gender differences in achievement at the item level, and within each of the school types and regions in the sample. Grade 12 students' responses to 14 items were compared to those of Grade 8 students. Finally, Grade 12 students' responses to 10 items were compared to those of students from other countries in SIMS. Among the findings of this study were: 1. Students in Grade 12 scored poorly on the mathematics test. Grade 11 and Grade 12 students obtained similar achievement levels which indicated that the achievement gains between the two grades were very small. 2. School type and region were found to significantly affect mathematics achievement, but no interaction effect was found. 3. The comparison of school type means showed that only one type of private school significantly outperformed public schools. This type of school also outperformed the other type of private school. 4. The comparison of region means did not produce the predicted outcome. The pairwise comparisons showed that none of the regions was significantly different from the other, despite the fact that the region factor was significant. 5. The analysis of gender differences in mathematics achievement showed that males performed significantly better than females. At the item level, males outperformed females on only 19 items. Most of these items dealt with geometry, or were at the application level. 6. Gender differences favoring males were found to be independent of school type and region. 7. Comparison between Dominican Grade 12 and Grade 8 students revealed that mathematics achievement improved between the grades for most items. 8. Dominican performance was very poor on the SIMS items and it was far behind that of other countries. / Education, Faculty of / Graduate

The purpose of this study was to investigate, with or without prompts, students’ small group discussions of their solutions to mathematical problems and to determine the extent to which the students demonstrate mathematical power. Mathematical power was defined in terms of student assessment standards (SAS) and their integration. SAS, each of which has associated with it categories of mathematical activities, comprise communication, problem solving, mathematical concepts, mathematical procedures, and mathematical disposition. Other insights perceived to be important from the discussions were also documented. Grade 9 students of the regular school program were used for the study. There were 18 students in the class but only one group of students comprising 2 females and 2 males was the focus of the study. They responded to mathematical problems individually for 20 minutes and then used 40 minutes to discuss, in groups, their solutions to the problems. Also, they responded to questionnaire items. The group discussions were video recorded and analyzed. Data were collected on 7 different occasions using 7 different problems over a period of 3 months. - Results of the study indicate that students demonstrated mathematical power to the extent that at least one category of the mathematical activities associated with each SAS was reflected by the small group discussions of students’ solutions to mathematical problems. Other results indicate that combining students written scripts with students’ talk provides a better insight into the things about which students are talking. Also, monitoring students and providing them with prompts while they work in groups is useful in helping them accomplish tasks in which they are engaged. Finally, when students work in groups, they can shift their viewpoints consensually or conceptually to align their viewpoints with majority viewpoints. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

This study explored the teaching processes in mathematics education for adults and how they are shaped by certain social and institutional forces. Teaching processes included the selection and ordering of content to be taught; the choice of such techniques as lectures or groupwork; the expectations, procedures and norms of the classroom; and the complex web of interactions between teachers and learners, and between learners themselves. The study addressed three broad questions: (1) What happens in adult mathematics classrooms? (2) What do these phenomena mean for those involved as teachers or learners? and (3) In what ways do certain factors beyond the teachers’ control affect teaching processes? The theoretical framework linked macro and micro approaches to the study of teaching, and offered an analytical perspective that showed how teachers’ thoughts and actions can be influenced and circumscribed by external factors. Further, it provided a framework for an analysis of the ways in which teaching processes were viewed, described, chosen, developed, and constrained by certain “frame” factors. The study was based in a typical setting for adult mathematics education: a community college providing a range of ABE-level mathematics courses for adults. Three introductory-level courses were selected and data collected from teachers and students in these courses, as well as material that related to the teaching and learning of mathematics within the college. The study used a variety of data collection methods in addition to document collection: surveys of teachers’ and adult learners’ attitudes, repeated semi-structured interviews with teachers and learners, and extensive ethnographic observations in several mathematics classes. The teaching of mathematics was dominated by the transmission of facts and procedures, and largely consisted of repetitious activities and tests. Teachers were pivotal in the classroom, making all the decisions that related in any way to mathematics education. They rigidly followed the set textbooks, allowing them to determine both the content and the process of mathematics education. Teachers claimed that they wished to develop motivation and responsibility for learning in their adult students, yet provided few practical opportunities for such development to occur. Few attempts were made to encourage students, or to check whether they understood what they were being asked to do. Mathematical problems were often repetitious and largely irrelevant to adult students’ daily lives. Finally, teachers “piloted” students through problem-solving situations, via a series of simple questions, designed to elicit a specific “correct” method of solution, and a single correct calculation. One major consequence of these predominant patterns was that the overall approach to mathematics education was seen as appropriate, valid, and successful. The notion of success, however, can be questioned. In sum, mathematics teaching can best be understood as situationally- constrained choice. Within their classrooms, teachers have some autonomy to act yet their actions are influenced by certain external factors. These influences act as frames, bounding and constraining classroom teaching processes and forcing teachers to adopt a conservative approach towards education. As a result, the cumulative effects of all of frame factors reproduced the status quo and ensured that the form and provision of mathematics education remained essentially unchanged. / Education, Faculty of / Graduate

This study sought to determine, by means of a questionnaire, the answers to the following research questions. 1. To what extent are secondary mathematics teachers in British Columbia currently participating in local curriculum development? 2. What are the attitudes of secondary mathematics teachers toward curriculum development at the local level? 3. What are the characteristics of teachers with respect to involvement in local curriculum development and attitudes toward local curriculum development? A special three-part questionnaire was constructed to answer these questions. The first part asked fifteen factual Yes/No type guestions about the current participation of mathematics teachers in local curriculum development activities. The second part of the questionnaire determined teacher attitudes toward local curriculum development through a 20-item Likert scale. The third part gathered descriptive data from the respondents. After a pilot study, the final questionnaire was sent to 200 secondary mathematics teachers randomly selected from the membership list of the British Columbia Association of Mathematics Teachers. The return rate for the questionnaire was 57%, and the Hoyt reliability estimate of the Likert scale was .86. Face validity of the Likert scale was determined by a panel of judges. Analysis on the first part of the questionnaire revealed that in general, there was a lack of support for curriculum development at the district, school and individual levels. In answer to question two, the attitudes of secondary mathematics teachers generally were favourable to local curriculum development activities as measured by the Likert scale. An examination of specific items revealed that teachers generally supported the provincial core program but were undecided as to whether districts should develop their own core. Furthermore, most teachers expressed a desire to be more involved in curriculum planning and indicated their willingness to serve on district and school curriculum committees. In answer to question three, the only characteristic of teachers that seemed to have some relationship to their attitudes was teaching level. Junior secondary teachers had significantly higher scores on the attitude scale than senior secondary teachers. The study found no significant differences between male and female mathematics teachers, between those with graduate education and those without, between teachers in small schools and large schools, and between teachers who were or were not department heads. Also, age, years of teaching experience and educational diversity did not have any significant relationship to attitudes. Recommendations were that more support be given for local curriculum development activities at the district, school and individual levels, that some form of provincial learning assessment program be used, and that teachers be allowed to choose their textbooks from an approved list. Final recommendations were that support of secondary mathematics teachers in local curriculum development activities should be directed to mathematics teachers as school groups at the junior secondary school level and that the attitudes of mathematics teachers toward local curriculum development should be further studied since only a small portion of the variance in their attitudes was explained. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

The purpose of the study was to determine whether item format significantly affected scores on a mathematics achievement test. A forty-two item test was constructed and cast in both multiple-choice and constructed-response formats. The items were chosen in such a way that in each of three content domains, Computation, Application, and Algebra, there were seven items at each of two difficulty levels. The two tests were then administered on separate occasions to a sample of 213 Grade 7 students from a suburban/ rural community in British Columbia, Canada. The data gathered was analysed according to a repeated measures analysis of variance procedure using item format and item difficulty as trial factors and using student ability and gender as grouping factors. Item format did have a significant (p < 0.05) effect on test score. In all domains multiple-choice scores were higher than constructed-response scores. The multiple-choice scores were also transformed using the traditional correction for guessing procedure and analysed. Multiple-choice scores were still significantly higher in two of the three domains, Application and Algebra. There were significant omnibus F-statistics obtained for a number of interactions for both corrected and uncorrected data but there were significant Tetrad differences (p < 0.10) only for interactions involving format and difficulty. The results indicate that students score higher on a multiple-choice form of a mathematics achievement test than on a constructed-response form, and therefore the two scores cannot be considered equal or interchangeable. However, because of the lack of interactions involving format, the two scores may be considered equivalent in the sense that they rank students in the same manner and that the intervals between scores may be interpretable in the same manner under both formats. Therefore, although the traditional correction for chance formula is not sufficient to remove differences between multiple-choice and constructed-response scores, it may be possible to derive an empirical scoring formula which would equate the two types of scores on a particular test. / Education, Faculty of / Graduate