Theses abstracts (4)
No abstract
Transactional Analysis, or TA, has been used for more than four decades to enhance interpersonal relationships and promote personal growth through counselling and psychotherapy. It has been used to advantage in organisations, principally in the business world. It was thought at the outset of this study that TA could also be of benefit to schools. The aim of this study was to find out whether TA methods could be used in schools to improve student outcomes in science and mathematics, to enhance interpersonal relationships and to promote positive behaviour. The study trialled TA by using it with a group of at-risk students to discover whether its use would bring about positive change. A group of ten at-risk students became part of a mentoring program, using TA. This program focused on the behaviour and academic progress of the students, and sought to empower them to make positive changes. This group referred to as the sample group, was compared with a control group. The Adult ego-state (thinking) was promoted in the students in order to shift their 'locus of control' from their Negative Adapted Child ego-state, the source of much non-productive, inappropriate and rebellious behaviour. The study upheld the reliability and validity of the questionnaires used, namely the Questionnaire on Teacher Interaction, the Coopersmith Self-Esteem Inventory (School Form) and the Mooney Problem Checklist. The study prompted the construction of an informal test, the Ego-State Questionnaire, which proved to be informative. Poor attendance and school behaviour records were good indicators of a student's 'at-risk' status. At-risk students were found to be already achieving below their potential in science and mathematics at entry to secondary school. The mentoring program ran for six months, and at the end of this the sample group had improved behavioural records and increased self esteem. Their number of perceived problems had dropped dramatically, and their academic results were improved. Interpersonal relationships between the sample group and their science teachers were better than the interpersonal relationships with their mathematics teachers, indicating a continued difficulty with abstract ideas at the end of the program and a need to run such programs over a longer time span. Interpersonal relationships did improve out of school with parents and peers. Clear preferences were indicated for what students preferred in the behaviours of their ideal teacher: understanding, helping/friendly, leadership and strict behaviours. Encouragement of Adult ego-state was shown to be an appropriate and productive approach to the improvement of academic and behavioural outcomes for at-risk students in science and mathematics. The study also showed that at-risk young people had a lower than average Nurturing Parent ego-state available to them. Teachers rated their TA101 course highly, and found that it gave them a fresh perspective on classroom difficulties. Both teachers and students benefited from the use of TA in this study.
Proponents of socially and culturally oriented mathematics education have argued that teaching approaches which value and connect with the learner's prior knowledge and everyday experience are more likely to promote active, meaningful, relevant and liberatory learning than approaches which rely on transmission and abstract presentation of mathematical content. In Malawi proposals to reform the outdated secondary mathematics curriculum have been made with the aim of aligning mathematics instruction with the social and political changes in the current Malawian society. Using a case study approach, this study investigated the extent to which everyday experiences could be used as a vehicle for changing the learning and teaching of secondary mathematics in Malawi. The study was collaborative, taking place over a period of five months in severely overcrowded and poorly-resourced classes in two schools. It involved three mathematics teachers in a cycle of planning and teaching mathematics lessons based on the use of everyday experiences, and observation of and reflection on these lessons, in order to document the effects of using everyday experiences on student learning and teachers' teaching practices. The data was collected through student questionnaires; classroom observations and field notes; interviews and reflective meetings with teachers; and informal meetings with key education officials in Malawi. Mathematics examination results from students involved in this study and a corresponding group from the previous year were collected. A reflective and critical approach was adopted in the interpretation and discussion of the data. Teachers' participation in this study resulted in heightened awareness of their teaching roles and the value of linking school mathematics with everyday experience. The study also shows that students found mathematics interesting and important to learn despite their lack of success in it. In addition, the study documented a number of constraints to change in mathematics instruction such as teachers' focus on mathematics content and examination requirements, and students' resistance to inquiry learning. It also recorded possibilities and barriers to collaboration both between teachers and researchers, and teachers themselves. The findings of this study are timely since they could serve to inform the reform of the Malawian secondary mathematics curriculum currently being undertaken, which began without a critical examination of the classroom conditions necessary to accommodate a socio-politically relevant mathematics education.
In this study, the author and his Year 8 mathematics students set out to develop a functional and effective collaborative peer interactive classroom learning environment. This research was informed by the multiple theoretical perspectives of collaborative learning in mathematics education, Vygotskian learning and teaching approaches, and the Constructivist referent for pedagogic practices. Working in groups of three or four, the students developed their social norms and utilised a collaborative approach to their learning of mathematics. Groups engaged in discussion, explanation, negotiation, peer teaching, giving and receiving help, and consensus building as part of their daily routine in the classroom. The author kept qualitative and quantitative records of progress during the first six months of the school year. He collected daily field notes, audio and video recordings, observations taken by researcher colleagues, learning environment surveys and a variety of other artefacts. All of this data was analysed daily, weekly and monthly, so producing the monthly narratives. By adopting a Vygotskian perspective they utilised their peer interactive environment to develop and enhance 'scientific' and 'everyday' concepts through individual and group dynamic, overlapping (multiple) 'zones of proximal development' as well as their class-wide 'zone of proximal development'. The constructivist perspective aided them in focusing on prior knowledge and experiences, which in turn enhanced the effectiveness of their collaborative classroom learning environment. Detailed analyses of the data from Months 1, 2 and 3 of this implementation, coupled with highlight analyses of the data from Months 4, 5 and 6, led the author to conclude that teachers and their students can develop a functional and effective collaborative peer interactive classroom learning environment based on the multiple theoretical perspectives utilised in this study.
This thesis reports the findings of a study of the influence of the classroom learning environment on students' cognitive and affective outcomes among 2,498 third-year computing students in 50 university-level classes in Indonesia. Students' perceptions of the classroom environment were measured using a modified Indonesian version of the What Is Happening In This Class? (WIHIC) questionnaire. To assess students' affective outcomes, a scale derived from the Test of Science Related Attitudes was adapted for use in higher education computing classes and translated into Indonesian. Students' final scores in their mathematics course (either linear algebra or statistics) were used as a measure of cognitive achievement. Secondary aims of the present study were to examine whether differences exist between (a) students' perceptions of the actual and preferred classroom learning environment, (b) the perceptions of male and female of the actual and preferred classroom environment and (c) students' perceptions of the actual learning environment in linear algebra and statistics courses. The results of this study make important contributions towards explaining why Indonesian students are achieving at less than desirable levels in their computing courses.
This study investigates the beliefs of Aboriginal children, their parents, Aboriginal educators and non-Aboriginal teachers towards the learning and teaching of mathematics in years 5 and 6 in a rural community in New South Wales. Areas explored include the beliefs expressed by the students, their parents and educators about mathematics education, how these sets of beliefs compare and contrast, and what the pedagogical consequences are for mathematics education based on these beliefs. The study was conducted in a rural school following trials in other sites. Conversational interviews were conducted and from the transcript sixteen core categories of beliefs across all participant groups were identified. The belief statements demonstrate the complex nature of the social, cultural, economic, historical and political contexts in which the learning of mathematics takes place. A number of actions intended to enhance Aboriginal children's learning of mathematics are proposed. Non-Aboriginal teachers need to share their beliefs with the Aboriginal community, and conversations need to occur between Aboriginal and non-Aboriginal people about mathematics education. Teachers require pedagogical strategies that address Aboriginal children's learning of mathematics, and educational systems need to include an Aboriginal perspective in mathematics curricula. Future collaborative research in mathematics education has to be based on the premise of researchers working in close co-operation with Aboriginal people.
By 1955 Australia had accepted its first million post war immigrants. This first wave of mainly Anglo-Celtic immigrants was succeeded by a wave of Europeans from non-English speaking countries. By the 1970s a third wave of mainly Asian, African and South American immigrants was arriving. In fifty years Australia's small and relatively homogenous population had become one of the most diverse populations in the world. Assimilation characterised the main thrust of early immigration policy but, by the late 1970s, acknowledgement of the impact made on the Australian way of life by diverse immigration, resulted in a policy of multiculturalism, which recognised the place of different ethnic cultures in Australia's society. In education, multiculturalism meant the establishment of English language resources in schools and government funding directed towards appropriate curriculum resources. Mathematics education in this interval had retained its important constituency in the curriculum of Australian schools. Despite difficulties created by post-war shortages of accommodation and teachers, a curriculum was evolving in which pedagogy was directed to each student as an individual learner. New mathematics curriculum had been devised and in the ensuing years the trend towards individualistic pedagogy, now placed largely in the domain of the classroom teacher, continued. This educational direction, on the surface appeared to relate well, to the spirit of multiculturalism. Support for culturally related mathematics education came also in the 1980s and 1990s, from research findings in mathematics teaching and learning which negated the view of mathematics education as a remote and purist discipline, and identified cultural connection as a key factor in its teaching and learning. How then did mathematics educators respond to the diverse cultural backgrounds of ethnic minority students? Two sets of mathematics educators governed events within the mathematics classroom. Government and sector authorities, called macro educators in this thesis, were responsible for intentional policy and its dissemination to schools and practicing classroom teachers were responsible for the implementation of mathematics education within the classroom. How complementary were any policy responses of the macro educators to the practical responses implemented by a group of Victorian mathematics teachers? It was found that while some responses in the policy and practice of the mathematics educators were complementary, others were contradictory. Responses made by one set of mathematics educators were not made by the other. In an example of this latter circumstance, teachers had recognised the role of culture in the mathematics education of their ethnic minority students, before the findings of research which related to culture and mathematics education had emerged, and had devised strategies to address what most of them perceived as disadvantage. The macro educators, for all the multicultural rhetoric they used in education papers and documents relating to policies of multiculturalism in education, applied these policies to various subjects but not to mathematics. They did however, unlike teachers, recognize, explore and value attributes of the experiences ethnic minority students brought with them to Australian mathematics classrooms. In the 1990s, macro educators became concerned with mathematical standards in Australian schools and imposed programs of compulsory curriculum and testing. Globalisation has accelerated population movement patterns and immigration around the world. New types of international mobility are assuming major significance, especially clandestine movement and asylum seeking. In 2001 Australia is treading a confused path through an onslaught of illegal immigration. Communication and shared endeavour between the mathematics educators, between research and practice in mathematics and between mathematics education and immigration policy would seem to be priorities in the future years.
Continuing to learn is universally accepted and expected by professionals and other stakeholders in professional practice. However, despite changes in undergraduate professional education in response to research findings, most continuing professional development (CPD) practices focus on delivery of content rather than on learning. Professional development still largely consists of brief, didactic episodes, often separated from practice or ongoing support. In exploring reasons for the lack of significant change in support for continuing learning, scant research was found about how professionals experience learning through their working lives. This study explores how allied health professionals learn in the current changing work context. The aim of the study is to enhance understanding about continuing learning so that support for professionals can improve. The findings have implications for learning in health and other professions. Using a phenomenological framework, continuing professional learning (CPL) is conceptualised in this study as part of the professionals’ lived experience of everyday practice. This conceptualisation challenges the problematic way in which much previous research views professional knowledge as a commodity that can be transferred and accumulated, separate from the professionals’ working context. Rich and diverse descriptions of learning were gained from interviews with sixteen therapists, contextualised through worksite visits, network meetings and relevant policy documents. These data were analysed using Giorgi’s empirical phenomenological methodology. A key finding of this study is the identification of significant dissonance between the reality of the professionals’ experiences of learning and the rhetoric of stakeholders’ expectations about professional development. The main focus of previous research, on the implementation and outcomes of CPD activities, fails to acknowledge the complex, diverse, multifaceted and idiosyncratic nature of professional learning experiences. Professional responsibilities with respect to CPD are linked to supervision of standards, monitoring of accountability and promotion of evidence based practice. As this study clearly reveals, the participants are enthusiastic learners who take these professional responsibilities seriously, but consider that their continuing learning is richer than this narrow CPD interpretation. The findings are reported in two phases. The first describes commonalities across diverse experiences of CPL, in terms of four inter-related constituents: understanding, engagement, interconnection and openness. Within the complexity of descriptions of CPL, tensions are revealed, particularly between the openness and uncertainty of learning, and the constraints and regulation of context. How tensions are resolved depends on each person’s way of being a professional, so that each professional’s learning has a unique quality permeating what is essentially a shared experience. The second phase of the findings draws on phenomenological philosophy to interpret the shared experience of CPL. The key argument of this phase is that the dissonance between rhetoric and reality in CPL is largely hidden from public discourse, being mainly voiced between professionals in supportive environments. It is argued that the hidden nature of this dissonance is one reason for the lack of significant change in CPD practices, in that few professionals publicly question CPD practices or the current context for learning. Within the usual CPD discourse, learning is viewed in epistemological terms as change in professional practice knowledge, with the professional viewed as deficient and in need of developing. In this study, the ontological dimension of CPL is highlighted, in that who the professional is shapes and directs what and how the professional learns. The ontological dimension of learning and the impact of context on learning are overlooked in most CPD practices. It is important that learning providers are cognisant of the complex, diverse nature of CPL so that innovative ways of supporting professionals to learn can be encouraged. Although CPL can’t be controlled, it can be supported, so that professionals can continue to learn in their own authentic way, whilst taking into account the expectations of their working contexts. In seeking a balance between responsibility and agency in CPL, a framework of 'Authentic Professional Learning' is proposed as congruent with, and supportive of, professionals’ experiences of learning, yet cognisant of the realities of the workplace with respect to accountability. Constructive strategies are developed from this framework to enable change from the current practice of CPD to that of authenticity in CPL. This study integrates, empirically confirms and extends research in higher education, workplace learning and adult education. The contribution made to understanding and supporting CPL is both theoretical and practical. Furthermore, demonstration of the value of a phenomenological framework as an alternative approach to researching continuing learning makes a methodological contribution to research in this area.
This study explored connections between primary teachers' attitudes to a list of research-based features of effective professional development and their beliefs and classroom practices. The investigation arose from concerns as to why some teachers benefited and made changes in their classroom practice as a result of professional development, while other teachers continued with their usual classroom practice. The professional development context for the study was a short course entitled 3Cs: Chance, Constructivism & Collaboration (3Cs) and was undertaken by eighteen primary teachers over a period of two school terms. Data was collected through classroom observations, interviews, and transcripts of the 3Cs workshops. Analysis was made of one transcript of classroom interactions for each teacher prior to the beginning of the short course. This analysis enabled a two-way classification to be made of the teachers based on aspects of handling classroom discussion, with teachers being grouped as 'instrumental' or 'relational'. Instrumental teachers generally saw themselves as the holders of mathematical knowledge and believed that it was their role to impart this knowledge to their pupils. Relational teachers created a 'discourse community', where knowledge was constructed and shared between pupils and teacher. This two-way classification was combined with a distinction based upon whether the teachers were beginning or experienced, yielding four distinct categories. One teacher was selected from each category and an in-depth case study made. The first part of each case study included reporting and analysis of the teacher's classroom practice and their beliefs about the nature of mathematics, the role of the teacher in the classroom and how children learn mathematics. From this, a prediction was made for each case study teacher on their possible reaction to the 3Cs program and on their attitudes to the features of effective professional development. The second part of each case study included reporting and analysis of the teacher's reaction to the 3Cs content and to the features underlying its organisational structure. Comparison was then made between the predictions and the findings from this second part of the case study. A number of insights were generated from the comparisons made and used as a basis for discussion on data from the whole cohort of 3Cs participants. Several findings resulted. Each teacher's beliefs, classroom practices and attitudes towards features of professional development was unique; many of the organisational features identified in the literature as effective were more suited to the relational teachers because of their use of reflective practice both in the classroom and as a preferred learning style; the value of classroom trialling was diminished for those teachers whose beliefs and practice did not match the agenda of the professional development; and attending professional development with close colleagues provided a valuable shared experience as follow-up to workshop sessions. These four main findings led to recommendations being made for consideration by professional development planners and researchers in the field.
The purpose of this study was to evaluate the effectiveness of cooperative learning in a liberal arts mathematics course and to examine any gender-related differences in the effects of cooperative learning in terms of achievement, composition of the cooperative groups, mathematics anxiety, attitudes toward mathematics, attendance, and retention. The quasi-experimental design compared a control section using individualized learning methods with three treatment sections using cooperative learning methods based on the Learning Together model of Johnson and Johnson (1991). The compositions of the three treatment groups varied: heterogeneous ability/heterogeneous gender, heterogeneous ability/homogeneous gender, and self-selected. The Academic Skills Assessment Program (ASAP) was used as a pre-test to show that the groups were equal. The Revised Math Attitude Scale and the Mathematics Anxiety Rating Scale (MARS) were used as pre- and post-tests to measure changes in attitudes and anxiety. Achievement was measured by individual and group course grades. Group grades were determined by taking 67 percent of a student's individual exam score plus 33 percent of the group's average on the exam. Cooperative learning and composition of groups had no significant effect on achievement. The differences between individual and group grades were insignificant, and the group grading method benefited the grades of only five students. Attendance had a large effect on achievement, and the ASAP score and the Math Attitude Post-test were significant predictors of achievement. The MARS post-test was negatively correlated with individual course grade. While no significant gender-related differences surfaced, some trends appeared. The ASAP, MARS, and Math Attitude pre-test scores were equal, however, females achieved slightly higher course grades than males. In each of the four research groups the individual course grades were higher for females than for males. Also, females had a larger decrease in mathematics anxiety with a drop of 22 points compared to the males' drop of 10 points. Males and females each improved their attitudes toward mathematics by only one point, however, in three of the four research groups, females had smaller attitude changes than males, and two of the cooperative learning groups had decreases in their attitude scores.
The aim of this study was to provide teachers with a practical means to obtain timely indications of their students' reactions to individual activities. Teachers could then modify their presentations of activities cognisant of those students' perceptions. The study set out to establish a suitable instrument, and then to evaluate its use by classroom teachers. Five experienced science and mathematics teachers identified five characteristics of interest when considering students' perceptions of classroom activities: Understand Content, Communication, Relevancy, Work Output, and Enjoyment. A fifteen-item instrument based upon these characteristics was developed for this study. The viability of the survey for use by busy classroom teachers was increased by the short and succinct format, as well as the provision of a computer graphing template to process and display responses. The combination of the survey and computer template is called the Students' Perceptions of an Activity Instrument and Display (SPAID). Teachers appreciated the provision of a structure to assist their reviewing the use of activities, and the rapidity with which the information was available. Students' responses provided timely support for teachers' decisions to engage classes in the activities and increased teachers' confidence in the worth of the activities. Alterations to activities were small in scale and idiosyncratic to the student cohorts. Teachers' use of the SPAID package was also noted to enhance cooperation with colleagues within the government secondary schools of Brunei Darussalam.
This study investigates the teaching and learning of mathematics in four rural schools in the Eastern Cape Province of South Africa. The study is set against the backdrop of Curriculum 2005 (C2005) - an outcome based curriculum reform initiative that has been introduced to all South African schools. The objective of the study is to investigate the teaching and learning practices of four rural teachers of mathematics in this complex reform milieu. The following broad research question guides this study: 'How do teachers interpret and implement the new mathematics curriculum in terms of a political perspective (how teachers and learners are connected to the curriculum); a socio cultural perspective (what adjustments the teacher makes to accommodate the learners' circumstances); and a practical perspective (how the teacher implements the goals of C2001?' The South African situation provides a unique and particularly challenging context for teaching and learning and curriculum reform. It is understood that schools differ - and therefore curriculum issues cannot be solved through general pronouncements but rather viewed from a multiplicity of perspectives. In this thesis, the author examines the teaching and learning of mathematics in four rural classrooms in the Eastern Cape. By way of honouring the contextual complexity of the situation, a multiple perspectives approach to analysing what goes on in these four classrooms has been adopted. A political perspective is used to help understand how power operates in the curriculum process. A socio-cultural perspective is employed to examine how the curriculum process attends to the local circumstances of teachers and learners. A practical perspective is used to examine how the curriculum is implemented in a technical sense. This constructivist interpretive study employs the techniques of case study and narrative inquiry to study the curriculum practices of four teachers. Multiple methods - including interviews, participant observation and video recording - were used to gather data. Narrative accounts of the teaching and learning of mathematics were constructed and then analysed using the three perspectives. The study concludes that the curriculum can be interpreted at different levels formal, perceived, operational and experiential - and each level can be analysed in terms of the political, socio cultural and practical. Bringing these three perspectives together is a challenging, but necessary task in order to understand and act upon the complexities of educational reform in rural South African classrooms.
This thesis describes a one-year study of 120 fifth grade students whose teachers participated in a program entitled Project SMILE (Science and Mathematics Integrated with Literary Experiences). The purpose of the study was to investigate the extent to which the classroom implementation of Project SMILE positively influenced the classroom environment and student attitudes toward reading, writing and mathematics. This was accomplished by, first, facilitating a series of five professional development workshops with the teachers and, subsequently, asking these teachers to use the strategies with their students. Because Project CRISS (CReating Independence through Student-owned Strategies), the foundation of SMILE, had already proven to be successful nationwide for secondary students, this study focused on elementary (K-5) school students and their teachers. The author's evaluation of this unique program, that integrates children's literature and mathematics, focused on student attitudes and the nature of the classroom learning environment. Her research represents one of the relatively few studies that have employed learning environment dimensions with students in the elementary school mathematics classroom as criteria of effectiveness in the evaluation of educational innovations. The My Class Inventory (MCI) and an adaptation of the 1988 NAEP (National Assessment of Educational Progress) Attitude Survey were administered to a sample of 120 Grade 5 students as measures of students' perceptions of the classroom learning environment and their attitudes. Qualitative data were composed of student and teacher interviews, classroom observations and work samples. Methodologically, this study supports previous research that successfully combined qualitative and quantitative methods of data collection. The learning environment and attitude scales exhibited satisfactory internal consistency reliability and discriminant validity; additionally, the actual form of most learning environment scales was capable of differentiating between the perceptions of students in different classrooms. The implementation of SMILE was found to have a positive impact on the students and classes of the teachers who participated in the inservice program. In particular, students' attitudes to mathematics and reading improved, and there was congruence between students' actual and preferred classroom environment on the scales of satisfaction and difficulty. Therefore, others can implement SMILE with confidence. As well, prior research was replicated in that students' satisfaction was greater in classrooms with a more positive learning environment, especially in terms of student cohesiveness.
This is a report of an investigation of children's beliefs about the nature of mathematics, the nature of learning and helping factors for learning mathematics. The study aimed to investigate whether beliefs held by eight learners of eight to nine years of age could be articulated and portrayed. It aimed also to develop procedures to facilitate this process, to portray children's beliefs from their responses to the research procedures, to provide insights into possible complexities and subtleties of young learners' beliefs, to reflect upon the significance for the mathematics classroom of the insights gained, and to reflect upon the value of the procedures developed for the study. The research took the form of individual case studies of four girls and four boys of eight to nine years of age from two schools in suburban Melbourne. Four children were teacher-perceived low achievers in mathematics and four were teacher-perceived high achievers in mathematics. The children were each interviewed on ten occasions over a five-month period using thirty semi-structured, creative interviewing procedures that were developed or adapted for the study that included drawing, writing, discussing scenarios presented through photographs, video snippets and other children's drawings, ordering of descriptors, and responding to questionnaires presented verbally. The interview data consisted of transcripts and artefacts. Some class administered tasks, lesson observations and interviews with the mathematics teachers provided background information. Analysis of interview responses was undertaken through a criss-cross examination in which themes were drawn from each child's data. Responses were not judged for correctness or for a match to any predetermined categories and the researcher sought to take a stance of neutrality to the phenomena under study. The research suggests that teachers and others involved in the education of young learners of mathematics should know the following. It is possible to gain insights into children's beliefs about maths (the term used most commonly by the children), learning, and helping factors for learning maths. To gain insights into young children's beliefs, it is important to have dialogue with the children to avoid making assumptions about their interpretations or meanings. The creative interviewing procedures developed for the present research are helpful as they can stimulate reflection and prompt conversation. Young children's beliefs can be complex, subtle, broad and deep. Young children's beliefs are individually constructed and differ from child to child. Children may not see mathematics concepts in the same ways as their teachers and other adults. Beliefs are sufficiently diverse and significant to affect the way children see the mathematics learning situation. Although the beliefs of children of eight to nine years of age may, on the surface, appear simplistic and naive, they are not necessarily so. Young learners are able to reflect on their own and others' experiences and often construct complex beliefs. There is a lot happening in the minds of these children. The research suggests also that it is important that educators do not to make assumptions about what children see as maths (or mathematics); what children see as learning; and what children see as helping factors for learning maths. A key factor facilitating children's reflection and expression was the range of visual, verbal, and text-based creative interviewing strategies developed for the present study. The individual procedures provided suitable prompts to allow young children to articulate or represent their beliefs. The semi-structured procedures, through which ideas were explored on multiple occasions, followed by theme-based, criss-cross analysis of interview transcripts and artefacts, resulted in rich and trustworthy portrayals of beliefs, increasing the validity of the findings. The research provides the education community with insights into young children's beliefs that are unlikely to emerge within the day-to-day activity of the classroom and, through the availability of the research procedures, facilitates further gaining of insights into beliefs either by classroom teachers or other researchers.
This thesis makes an attempt to assess the part played by man to control and direct the development of civilisation. The course of that development is examined to discern any regularity of trend. The rise and the decline of powers within Western European civilisation are noted, and some common features are considered as appearing in each of the large phases of its development. From an examination of the part played by the great thinkers, in relation to the trends of their time, to give guidance to society, an attempt is made to indicate the course that should be followed in the formulation of theories of social dynamics.
This action research study was conducted to investigate the efficacy of a constructivist approach to the training of first-year Chinese student mathematics teachers in the Hong Kong Institute of Education where the author is employed. A four-stage teaching model was designed, based on the learning theory of constructivism and taking into particular consideration the characteristics of Chinese learners: the maintenance of hierarchical and group harmony and high achievement motivation. In order to determine whether the application of this model in a methodology could alter the teaching beliefs of newly enrolled students, a two-phase procedure was employed. First-year students in each phase of the study were involved in solving a teaching problem. Through self-articulation, group- and class-discussions and self-reflection, the students were examined to determine any change in their beliefs about teaching mathematics. Prior beliefs about mathematics teaching, and beliefs held at the end of the methodology module were determined and compared in order to determine if new learning was in evidence. The creation of an authentic interactive learning environment to foster the kind of learning desired - a potentially safe, trusting and non-judgemental environment for free disclosure of students' opinions and feelings about mathematics teaching - was investigated. Data was generated by different quantitative and qualitative methods. Findings were cross-checked by a critical colleague and through the author's observation and reflections, and these were recorded as clearly and accurately as possible. The first phase results were employed to inform and to improve the teaching of the same methodology module in the second phase. Findings in the two phases were indicative of the creation of a genuine social constructivist learning environment in which student teachers enjoyed their learning. Student teachers in the second phase implementation of the study indicated an understanding of their role in a constructivist classroom - to construct their own theories of teaching mathematics, to assist their peers in knowledge construction and to learn to learn. Student teachers in the two cohorts were found to hold entrenched constructivist beliefs about teaching mathematics. They agreed that the teacher's role was a facilitator of learning and that persistent questioning could alter knowledge about mathematics. However, at the conclusion of the module, the Phase I students seemed to re-adopt traditional approaches to teaching, whereas the Phase II students exhibited two different perspectives - an indication of the instability of their teaching beliefs. The Phase II student teachers, nevertheless, showed that they became more aware of sequencing the various interactive activities for their pupils in secondary schools. In the actual teaching, they professed their inability to realise their teaching ideals because of their inexperience in teaching and of the unexpected situations in the school settings. The present research study adds to the paucity of literature in two areas: the employment of a constructivist approach in the preparation of teachers of junior secondary mathematics, especially in the training of Chinese student mathematics teachers; and also the study of a higher education lecturer conducting research to improve his/her own practice. Undeniably, further research on models to change student teachers' prior knowledge (about mathematics, about the nature of mathematics, and about the teaching and learning of mathematics), on factors affecting the instability of beliefs, and on models to facilitate continuous development of the teaching professionals are necessary if not exigent.
Computer-based teaching and learning systems have become ubiquitous to many facets of life in the modern world including education in recent years. Its association with distance education in particular is powerful and is the subject of much discussion amongst distance education practitioners. The powerful link to distance education is due to its potential to bridge the 'time' and 'distance' gap between the instructor and the student that is inherent to distance education. Many developing countries in particular see distance education as the only viable option left to solving the problem of access to education particularly at the tertiary level. Faced with a booming population and the consequential shortage of tertiary spaces, Papua New Guinea (PNG) has also strongly advocated a distance-based, computer technology-mediated expansion of educational opportunities. The present study, in rising to the challenge, investigates the teaching of a distance education mathematics course using computer-assisted instruction (CAI) at the Institute of Distance and Continuing Education in the University of Papua New Guinea. The study sought to explore the viability and the applicability of a computer-assisted instruction mode of teaching and learning in a mathematics course in comparison to the traditional text and face-to-face modes. The findings in the study suggest that a computer-assisted instruction mode of teaching and learning mathematics in PNG is viable and can be effective. Students in a CAI tutorial group performed as well as students who did the course through the traditional methods in a mathematics achievement test. The study has important implications for the adoption and implementation of computer-based learning systems in PNG especially in distance education.
This study set out to determine the relationship between assessment practices and teaching methods. The author wanted to investigate whether making mathematical investigation assessment tasks available to elementary-school mathematics teachers would have a positive effect on their teaching. Research tells us that standardised tests influence instruction. This research explored whether a national Assessment Task Bank of mathematical investigative tasks could influence teachers. With these aims in mind, the following research questions were formulated: Will the teachers' use of mathematical investigation tasks for assessment purposes influence their view of mathematics? Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they teach, and if so, in what ways? Will the teachers' use of mathematical investigation tasks for assessment purposes influence the way they assess their students, and if so, in what ways? The research was divided into two parts: a national study involving teachers-leaders throughout the country, and an intensive study in a small Israeli community, called Sharon. The first part examined how the national courses on assessment that the author conducted affected the participating teacher-leaders in terms of their concept of mathematics, their teaching methods and their assessment practices. The second part examined the same issues with regard to the mathematics coordinators in the Sharon community. In each case, the author has detailed her experiences so that the reader can gain a view of all facets of the study. The research methodology adopted was based on a constructivist paradigm, sometimes referred to as a 'naturalistic inquiry', utilising ethnographic principles wherein the data collection and analysis procedures were eclectic. In the course of the five years of research, the author used many strategies of data collection - for example, unstructured participant-observations, interviews, questionnaires and content analysis of artefacts (tests and tasks written by teachers). The ideas of reform mathematics are based on a broadened vision of mathematics with emphasis on higher-order thinking. The research indicated that the use of mathematical investigation tasks helped the teachers in this study reach the awareness that mathematics, even on the elementary school level, involves generalisations, justifications and even creativity. Prior to this research, and because of her position, the author was aware that Israeli teachers were concerned primarily with teaching routine procedures and that their work sheets for the most part involved single-answer exercises. Her research indicated that the use of mathematical investigation tasks indeed influenced the way teachers teach. Verbalisation has become integral to the teaching practices of the participants in this study. Nowadays, the Israeli teachers the author worked with use 'authentic tasks' in their classrooms: real-life situations that involve some mathematics. Unfortunately, these tasks are not always planned properly. The research demonstrated that teachers attending the author's professional courses found the mathematical investigation tasks to be useful for assessment purposes, providing them with additional information about their pupils, not obtainable through conventional assessment methods. The additional criteria for evaluating the pupils' work aided in defining these additional areas. The author found that while teachers were quite willing to use the mathematical investigation tasks to supplement the conventional tests, they were reluctant to use them as replacements. Exposure to the Assessment Task Bank influenced to a certain degree, the way the teachers in this study assessed their students. The tests of the teachers who were participants in the study now regularly include elements that were previously absent: questions requiring explanations and questions with more than one possible answer. Although the teachers of this study were increasingly using questions that required higher-order thinking, the tendency was to use the tests in a summative manner, rather than formatively. In other words, many teachers found it difficult to use test results for planning their subsequent lessons. While they were able to analyse their students' work and could report in some detail on each student's performance, they failed to understand how this should affect their teaching. Before they were exposed to the tasks they had administered tests merely in order to provide grades, whereas now the teachers were often trying to understand the students' thinking. While long-term change is still elusive, this research has demonstrated that exposure to reform mathematics through the mathematical investigative tasks of the Assessment Task Bank did have some influence on the teachers' view of mathematics, as well as their teaching and assessment practices.
This study examined the different types of mathematical errors exhibited by primary level pupils in Brunei when working with fractions. In addition, the study examined pupils' attitudes towards the learning of fractions and investigated if there were gender differences among Brunei pupils' performances with fractions and with their attitudes towards fractions. The study was longitudinal in nature and its two phases involved a single cohort of Primary 5 pupils followed through a full year period in four government-funded primary schools in Brunei Darussalam. Pupils' mathematical errors were assessed by means of researcher-developed paper-and-pencil tests, while pupils' attitudes towards the learning of fractions were measured by means of an adapted version of attitude questionnaire that has been used previously with Brunei pupils. Guided by six research questions, a number of statistical analyses were carried out to ensure the validity and reliability of the instruments used. These included piloting and revising the instruments, the use of Cronbach's alpha with the items in the attitude questionnaire, and the calculation of the Pearson Product Correlation Coefficient between scales of the questionnaire. The data was analysed by calculating the percentages and means of occurrences of each type of error. Paired and independent sample t-tests were carried out in order to investigate gender differences in pupils' errors and the impact of further instruction on fraction at the P6 level, while the GLM test was administered in order to investigate if there were significant change in pupils' attitudes towards fractions from the pre- to the posttests. Qualitative information obtained through pupils' interviews, field notes and lesson observations was used to support the quantitative data. The study revealed that though pupils' achievement in the post-test improved, their performances on fraction work remained generally unsatisfactory. Many pupils in the study continued to have difficulty with the basic operations on fractions and resorted to the use of keyword strategies in dealing with word problems. Despite the pupils' unsatisfactory performance in the diagnostic tests, they generally held very positive attitudes towards the learning of fractions. No significant gender differences were observed either in pupils' performance in working with fractions tasks nor with their attitudes towards the learning of fractions. The findings of this study also highlight a number of issues for mathematics teachers to consider when dealing with fractions, and the findings also have implications for the quality of the instructional activities provided by the teachers, for the impact of language transfer in the medium of instruction - that is, from Bahasa Melayu to English at the pupils' Primary 4 level- and for the quality of the teacher training program in Brunei.
The general goal of this study was to investigate the feasibility of creating a constructivist learning environment in a university mathematics course as an alternative to the dominant transmissionist learning environments currently in place in most such courses. In order to accomplish this goal the researcher, a university professor, attempted to create this environment and document it in a case study. The study sought to ascertain which dimensions of a constructivist learning environment - autonomy, prior knowledge, negotiation, student-centeredness - university students preferred and how these preferences changed after being in such an environment. It also sought to find out how students' preferred environments matched the environment they perceived to be in place. In addition, the study sought to determine what changes the instructor had to make in his teaching practice to implement each of the dimensions. The results of the study suggest most students very strongly preferred the prior-knowledge and negotiation dimensions, strongly preferred the autonomy dimension, and weakly to moderately preferred the student-centeredness dimension. The data indicate that during the study student preferences for prior knowledge and negotiation increased slightly, preferences for student centeredness increased moderately, and preferences for autonomy increased significantly. In addition, the researcher found that the four dimensions were not implemented equally. While the first three dimensions were strongly implemented, the student-centeredness dimension was only moderately implemented. Interestingly, the learning environment the students perceived to be in place closely matched their preferences.
There are three distinct but interrelated parts to this research. The first part measures language learning strategies (LLS) and other individual differences (IDs), as well as the relationship between LLS and the other IDs of year 9 students of Indonesian as a foreign language (L2). The second part measures differences in use of LLS between the control and experimental groups, and then over time. The third part measures the effects of training in LLS on listening comprehension. The study had three main aims. One was to determine the relationship between participants? LLS use and their language learning background, affective factors, learning styles and aptitude. A second was to determine changes to strategy use following training in certain LLS. The third was to find what changes occurred to strategy use following the training.
In any standard school class there will be a wide range of learning style preferences. To develop a writing curriculum that meets the needs of each style is a pursuit that has been only superficially explored. This study has addressed some of the issues involved in understanding the writing needs of a wide range of styles. It has accomplished this by the researcher studying one class of ten-year-olds through becoming their full-time teacher for one year. A program of text production was planned and implemented that took the students from monomodal, handwritten texts, via wordprocessed monomodal and partially multimodal texts, to fully multimodal computer-mediated texts. A weak pedagogical framing was deliberately established as the learning environment, and computer technology was constantly available. By observing the changes over a ten-month period and analysing in detail the learning environment that was the same for all 26 students, it has been possible to see strong patterns emerging from the data. This patterning has been matched with the cognitive styles of the students as assessed by a cognitive styles analysis. Some students, mainly those with a strong imager cognitive style and who were struggling or failing with literacy in the monomodal sense, have been shown to require multimodal scaffolding to successfully communicate with texts. Others, mainly those with a strong verbaliser cognitive style and adept at expressing themselves fluently and successfully with words, found multimodal contexts not only distasteful but a hindrance to their production of texts. Intermediate to the two extremes of style was a group, some of whom showed characteristics close to those of either extreme group, whereas others demonstrated that they were adept at switching from monomodal to multimodal, and seemed equally at ease with either. By invoking the theory of transmediation or transduction it has been possible to deduce that a student's style affects the way that material is transferred across the semiotic modes, and thus the method of handling both verbal monomodal texts and multimodal texts. The study thus indicates that of the factors influencing the changes in students' text production as they move from monomodal to multimodal text production, cognitive style is very powerful in a weakly framed pedagogical environment, and that there is an issue of equity. If, as is being suggested, some students require the scaffolding of multimodal environments before they can adequately transmediate and realise their text-production potential, then the literacy pedagogies may need to be adapted to provide access to multimodal elements in the curricula.
The purpose of this study was to investigate the beliefs and related classroom practices of a selected group of in-service teachers within the context of a mathematics professional development intervention for primary school teachers in the Eastern Cape of South Africa. A cohort of 34 teachers drawn from urban and rural schools in the Eastern Cape engaged in an accredited professional development intervention offered by the Rhodes University Mathematics Education Project (RUMEP). The 34 teachers were referred to as key teachers as they were expected to stimulate mathematics activities with fellow teachers in their school and in a cluster of nearby schools. The professional development intervention took place in a context of transition and transformation in education in South Africa. Curriculum transformation has been inspired by the production of a national policy document known as Curriculum 2005. This document rests on the theoretical assumptions of a learner-centred, outcomes-based approach within a constructivist framework. The professional development experiences of the RUMEP intervention were based on a strongly constructivist rationale recognising the need for key teachers to implement learner-centred, outcomes-based approaches in their classrooms. Although the study included both qualitative and quantitative data gathering techniques the research paradigm was mainly interpretive. From the group of 34 key teachers, a purposive sample of three cases was selected for classroom observation. Two observation periods of six months each made up the First Phase and Second Phase classroom visits, interspersed with intensive professional development contact sessions. During the First Phase observations, 1 as the participant observer, visited the classrooms of Lulama, Makana and Ruth (pseudonyms), the three case study teachers. In the Second Phase period, a colleague and 1 video recorded the classroom practices of all three teachers. The videotapes were analysed by a consultant panel of observers to identify emergent themes using Yager's (1991) Constructivist Learning Model to guide the analysis process. The panel identified a number of dominant themes and these meta-themes have possible implications for a teaching and learning approach that is based on learner-centred, constructivist strategies as advocated in the Curriculum 2005 document. The meta-themes included such challenging issues as a constructivist learning environment, learner-centredness, learner participation, collaboration, reflection, teacher content knowledge, topic progression, and power relations. The findings of the study also suggested that the case study teachers' beliefs did influence their classroom practices. A significant outcome was that teachers in the field were unlikely to sustain outcomes- based, constructivist approaches without regular on-site support. Arising out of this study, 1 was able to isolate ten features that should usefully be incorporated into other professional development interventions in the Eastern Cape, and one of these features was the support provided to teachers in the classroom. Of further significance was the realisation that future interventions need to focus on the conceptual development of teachers' mathematics content knowledge and the systematic planning of related activities when preparing the pace and a particular mathematics topic using the National Curriculum Statement (2001) as a guide. Quantitative data from the full cohort of 34 key teachers was collected via mathematics Beliefs Scale, authentic assessment tests (Insight Tasks), and a School Level Environment Questionnaire (SLEQ). The results on the Belief Scale indicated significant differences teachers' beliefs on two out of the' c subscales. These differences were in the teaching and learning of mathematics. There was no significant difference on the sequencing topic subscale. The key teachers completed the Insight Tasks pre an intervention to measure gains in their content and pedagogic (professional) knowledge. The Insight Task results indicated that the key teachers made clear progress in their professional development. Quantitative data was also gathered from six mathematics teachers in a selected urban school. The School Level Environment Questionnaire instrument was administered to the six teachers. The aim was to profile the teachers' pedagogic needs within a context of curriculum transformation. The profile raised two items for discussion: Staff Freedom and Resource Adequacy. It would appear that the teachers in this particular school wanted more guidance in planning outcomes-based mathematics topics, and they highlighted the need for classroom- based resources if they were to adequately implement such a curriculum.
The present research examined whether teachers in South Africa could use feedback from a learning environment instrument to help them to increase the degree to which they emphasised constructivist-oriented teaching strategies in their classroom. The study also investigated the validity of a widely-applicable classroom environment questionnaire, as well as associations between attitudes and classroom environment. The study involved a combination of quantitative and qualitative research methods and was carried out in two phases. In the first phase of the study, data were collected using the Constructivist Learning Environment Survey (CLES), to assess learners' perceptions of the constructivist learning environment, and an attitude scale to assess learners' attitudes towards their mathematics classroom. The instruments were administered to 1864 learners in 34 intermediate (Grades 4 - 6) phase and senior phase (Grades 7 - 9) classes. Data were analysed to determine whether (a) the CLES is valid and reliable for use in South Africa and (b) relationships exist between learners' perceptions of the learning environment and their attitude toward their mathematics classes. Descriptive analysis was used to generate feedback information for teachers based on graphical profiles of learners' perceptions of the actual and preferred learning environment for each class. Analyses of data collected from 1864 learners in 34 classes supported the factor structure, internal consistency reliability (Cronbach alpha coefficient), and discriminant validity of the CLES, as well as its ability to differentiate between classes. The results suggest that researchers and teachers can be confident about using the modified version of the CLES in mathematics classes in South Africa in the future. Simple correlation and multiple regression analyses were conducted to examine whether associations exist between learners' attitudes towards their mathematics class and their perceptions of the learning environment. The results indicated that student attitudes were associated with more emphasis on all four CLES scales used. Two scales, Uncertainty and Student Negotiation, were found to contribute most to variance in student attitudes in mathematics classes in South Africa when the other CLES scales were mutually controlled. Descriptive analysis was used to provide information about the constructivist nature of mathematics classes in the Limpopo Province of South Africa. The results indicate that students would prefer a learning environment that is more positive than the one that they perceive as being present in terms of emphasis on all four CLES scales used. The second phase involved a 12-week intervention period during which two teachers used the pretest profiles of actual and preferred classroom environment means to assist them to develop strategies aimed at improving the constructivist orientation of their classroom learning environments. The teachers implemented the strategies and maintained daily journals as a means of reflecting on their teaching practices. Throughout the 12-week period, the researcher made regular support visits that included classroom observations, reviews of daily journals, discussions with teachers and interviews with learners. As well, the researcher had the opportunity of giving support to the teachers in the implementation of their strategies. At the end of the 12 weeks, the CLES was re-administered to learners to determine whether their perceptions of the constructivist emphasis in their classroom learning environments had changed. The posttest graphical profiles indicated that there was a sizeable improvement in teachers' emphasis on CLES dimensions in their classrooms. Apparently, teachers using action research are able to use learners' responses to the CLES to develop and implement strategies for improving their learning environment. The study suggests that journal writing, as a tool used by teachers on a daily basis, can improve their professional expertise as reflective practitioners.
In this thesis the level of participation in Physics and the allied discipline of rigorous Mathematics at Tertiary and upper Secondary level is examined. Various possible supply side constraints are considered, in particular the condition of Maths and Physics in lower Secondary schools in Queensland. Some of the effects of weak Maths and Physics in that part of the education chain are examined indicating that there is a commonality of interest between many school students, especially males, and the disciplines per se. Participation in Physics at Tertiary level is in decline in USA, Canada and Germany as well as in Australia. There are indications from both Germany and USA that those declines are not entirely explicable by a consideration of demand side influences, supply side factors must have some influence. Because it may be possible to manipulate supply side influences, the work reported here concentrates on those issues, in particular in Queensland. Participation in Physics and especially rigorous Mathematics in the last two years of Secondary schooling has been in medium to long term decline across Australia. In Queensland that decline is mainly a decline in male participation. The student decisions not to study those subjects are made at the end of Year 10. Hence their educational experiences prior to that time are important. Clear evidence is presented from a large sample of school Principals in Queensland that there is a high degree of concern in the schools about the condition of both Mathematics and Science in Years 8,9 and 10. An inappropriate structure of relevant Statutory Authorities in Queensland has led to there having been no collection for 15 years of data vis-à-vis student outcomes up to the end of year 10. The only exception being a single but excellent study for Mathematics that showed that outcomes are highly variable and frequently weak, particularly for algebra. For physical Science there is no data but indications from textbooks are that very little numerical Science is studied. Hence there is a discontinuity at the Year10/11 interface. It is known that participation in the physical Sciences is highly dependent on previous educational experiences. The discontinuity referred to will affect participation in Physics and Maths C, the most rigorous Mathematics in Queensland at the Year11/12 levels. An analysis of effects on student Overall Position (the equivalent of ENTER) consequent to the concurrent study of Maths B, Maths C and Physics shows that students are advantaged in OP terms by that concurrent study. Hence the decision by an increasing number of capable students not to take those subjects may have a deleterious effect on their final outcomes. A survey of students from five North Queensland schools confirms that students who are taking Maths B/Maths C/Physics are comfortable with it and recognise that it has been to their advantage. Another part of that survey demonstrates a degree of ignorance about both Physics and Maths C amongst the Year 10 students at the time that they are making their subject selections. It is noteworthy that the advantage gained by taking the combination Maths B, Maths C and Physics is at least as noticeable for males as for females. Consequently it is an area of comparative advantage for males. An examination of male/female performance in rigorous Mathematics and numerical Science across the whole state demonstrates that, contrary to received wisdom, females are not performing better than males of similar general ability or have relatively improved their performance over the last decade at least. It is suggested that a major overhaul of both Mathematics and physical Sciences in lower Secondary schools in Queensland is required. Such an improvement would tend to raise participation levels in both Physics and rigorous Mathematics to the advantage of many students, particularly males and provide a larger pool of qualified students from which Tertiary physical Science and Engineering Departments could draw. The condition of both Mathematics and physical Sciences in Years 8/9/10 is at best highly variable, at worst poor, to the detriment of many thousands of students and the related disciplines Mathematics and Physics. It is suggested that Parliament, the Statutory bodies, schools and Tertiary Education Faculties need to accept that a problem exists, accept a part of the responsibility for that problem and act decisively to rectify the situation.
While there have been enormous changes in the South African system of education since 1994, the legacy of apartheid and the different education of Black teachers is still evident in township schools. This study examined the practices of mathematics teaching in three township secondary schools by conducting a detailed investigation of eight teachers in three schools. Classroom observations and video recordings of teachers of Grades 10 to 12 served as the main data collection method. A sample of 12 lessons was analysed using the Secondary Teaching Analysis Matrix-Mathematics (STAM-Mathematics) instrument. The researcher used STAM to categorise teachers' classroom practices along a three pronged continuum, namely didactic, transitional and conceptual teaching for the purpose of answering research questions about the content, the teaching, the assessment practices, the interactions between the teacher and the student, and the resource availability. Analysis of the data collected using the 22 STAM descriptors showed that the practices of teaching mathematics in township secondary schools was primarily didactic, with only minimal characteristics of transitional teaching and fewer attributes of conceptual teaching. Identifying the gaps between the teachers' practice and the descriptors for transitional and conceptual teaching with respect to the content, the teaching, the approaches to assessment, interactions between teacher and students, and resources availability has provided insight and a baseline for teacher inservice. Consequently, this study has provided research-based evidence for appropriate intervention to improve mathematics teaching and learning as prioritised by the Department of Education since the creation of the democratic government in 1994.It is recommended that mathematics teachers in township schools use the STAM instrument in pairs or groups to observe and analyse each other's lessons with particular focus on the 22 descriptors and to use this framework as a guideline for daily lesson preparations and to help guide the teachers from teacher-centred instruction to conceptual instruction. Further, the STAM could be incorporated into teacher education and professional development programs and thereby lead to more conceptual forms of teaching that could contribute towards a greater understanding of mathematics and ultimately raise the pass rate of learners in external examinations at Grade 12.
The new South African national curriculum for the twenty first century adopted an outcomes-based education approach. The new curriculum represents a crucial shift in emphasis from learners concentrating on formal and procedural mathematics (with an absence of meaning) to learners making meaning of mathematics and becoming flexible mathematical thinkers, with problem solving and mathematics investigations as central focus. This study reports on an action research collaboration between two teachers and the author, a university mathematics educator. It was conducted over a period of three years. The main purpose of their collaboration, and this thesis, was to explore mathematics teacher learning in the context of the OBE-based reforms. The data were gathered through questioning, journal keeping by the two teachers and the author's participant observations. Using the two teachers' reflective writings and field notes the author analysed the data in two stages - narrative analysis and analysis of narratives. What emerged from the study were several issues clustered around three characteristics of teacher learning - teacher teaming as situated, teacher learning as social and teacher learning as distributed. These three overlapping characteristics of teacher learning were used as heuristic devices or convenient organisers for the description, analysis and discussion of the issues that emerged. This study revealed several overarching propositions that may have applicability beyond its boundaries. The first proposition is that teachers reflect on and revise their personal practical knowledge if exposed to learning experiences that encourage them to attach meaning to and make sense of the underlying concepts of new curriculum reforms. The second proposition is that interactions with literature improve the quality of teacher learning. The third proposition is that teachers are motivated to experiment with new ideas if they observe these ideas being modelled in practice. The fourth proposition is that teachers develop positive perceptions about learning if the expectations of multiple stakeholders (both in their classrooms and beyond the classrooms) are not contradictory. The fifth proposition is that teachers' listening to learners' thinking opens opportunities for explorations. The sixth proposition is that teachers respond to learners' learning by being more curious about classroom discussions. The seventh proposition is that teachers who play an active role in collaborative working relationships are more likely to revise their pedagogy. The eighth proposition is that true collaborative relationships take time. The last proposition is teachers who are supported are more likely to distribute their knowledge and learning. Some implications of this study are also highlighted in the last chapter.
Mathematics plays a key role in many of today's most secure and financially rewarding careers. In almost every sector of the economy, a substantial core of mathematics is needed to prepare students both for work and for higher education. The impact of computers and information technology in areas as diverse as manufacturing and advertising means that understanding mathematics becomes more important because it provides students with basic prerequisites in other useful areas such as problem-solving. Technical students in Brunei are trained with the skills needed in the world of industry and commerce to become competent workers and many of them continue to pursue higher education. They need the right balance of mathematics that can prepare them for both purposes. Considered to be academically weak, and coming from the system (high schools) whose teaching approaches benefit abstract learners, these students need to be motivated and have their interest in mathematics nurtured. This study is an attempt to improve the mathematical skills of technical students in Brunei by developing a teaching and learning package that can be used by mathematics instructors with their students. The package was designed to provide student-centred instruction and focuses on the learning environment aspects of 'Teacher Support', 'Innovation', 'Cooperation', 'Task Orientation' and 'Relevance'. These learning environment aspects were incorporated into each category of the ARCS motivational model for the purpose of enhancing motivation. It was anticipated that students' mathematical understanding and attitude would be improved when their learning environment and thus their motivation was enhanced. When the package was implemented among a group of technical students, they experienced an approach to the teaching of mathematics that shifted from instruction fostering the procedures of practice and memorisation toward instruction that emphasised mathematical inquiry and conceptual understanding. Integrated curricula and cooperative learning techniques were used to link both the mathematics understanding of materials and their composition to the application of materials in the world of work. The use of technology to pursue mathematical investigations by way of learning aids was encouraged because the impact of technology on education today cannot be ignored. A group of students from two classes were involved in the implementation of the package to determine its effectiveness, for a duration of eight weeks. By applying the pre-experimental design methodology to the study, pre-test and post-test were used to measure students' cognitive and affective changes. Mathematics proficiency in the categories of procedural skills, conceptual understanding and problem solving abilities were measured and examined by comparing students' pre- and post-test results. Other forms of assessment such as projects and graded class-work (and homework) and also the communication that took place between the students during discussions were analysed to further validate their mathematical understanding. The learning environment and attitude factors mentioned were identified and validated through surveys, observations and interviews. A learning environment instrument called the College Classroom Environment Inventory (CCEI) was adapted for the purpose of measuring students' perception of the learning environment. Another instrument named the Attitude Towards Mathematics survey was designed to measure students' attitude towards mathematics. Both instruments were created, validated and then used to measure students' affective changes (before and after package implementation) and thus evaluate the efficacy of the package. Besides the quantitative data obtained, the qualitative data from observations and interviews was used to confirm, explain and verify results. The results obtained from this study demonstrated students' improved cognitive outcome in all areas of mathematical proficiency measured. As for the affective outcome, there were improvements in students' perception of the classroom environment and also in the attitude category of 'Importance' where more post-test than pre-test students agreed on the importance of mathematics in everyday life. The result also indicated associations between cognitive outcomes and a number of the learning environment scales. Students who experienced the package also demonstrated better mathematical understanding compared to those who did not. Students, instructors, curriculum developers and administrators should benefit from the results of this study. The study also provides a starting point for more research of this kind to be carried out for the benefit of technical students in Brunei in particular, and for mathematics students generally.
As a result of two years working with the pre-service primary teachers in a College in Fiji the author became aware of the difficulty many of the students were having understanding the primary school mathematics they would be required to teach. During that time she had attempted to help them overcome the difficulties by using different teaching approaches and activities but was far from satisfied with her efforts. Hence she decided to make a concerted effort to help the students by planning, implementing and partially evaluating a mathematics education unit, known as the Teaching Program for the first semester of their course. This work formed the basis of this study. For the Teaching Program a constructivist teaching approach was chosen with number sense as the underlying theme. To examine the aspects of the Program the author's observations and those of the students (reported in their mathematics journals) were used. To evaluate the effectiveness of the Teaching Program quantitative data was collected and analysed from traditional testing of the class of forty students as well as data from case studies of six of the pre-service teachers in the class. Case studies were used as the main source of data to determine what features of the Teaching Program were linked to positive changes. The findings suggested that a significant development of the cognitive aspects of the students' number sense did occur during the time of the Teaching Program but not as much as was hoped for. As a result of the analysis of the data the author came to a greater realisation of the importance of the non-cognitive aspects of number sense and the necessity for a greater consideration of them in the development of a Program. A major development that occurred was in the author's understanding of the knowledge and learning of mathematics. Her ideas of a teaching paradigm of social constructivism had not guided her sufficiently to incorporate activities and procedures to develop the non-cognitive aspects. She suggests that a paradigm which extends the theory of social constructivism to give greater consideration of these aspects of learning in general, and hence numeracy and number sense in particular, was needed. As a result of this study, her introduction to the theory of enactivism appears to be giving her some direction in this search at this stage.
While the Direct Instruction experimental intervention employed in this thesis was based on the Engelmann model it differs in fundamental aspects. Specifically designed to cater for the diverse academic levels present in any given classroom it aimed to accommodate and elevate every student's academic skill level. Satisfactory academic performance is composed of a balance of, on the one hand possessed skills and on the other a certain belief in self. Given that self-efficacy is well accepted as an accurate predictor of academic performance the study also examined the effects of the intervention on students' self-efficacy from the perspective of Bandura's social cognitive theory. Since the decline in student self-belief over the transition years has long been recognised as a problem, the study was conducted in 54 regular Year 7 mathematics classrooms comprising 967 students. With at risk students forming a subsidiary focus, socioeconomic status was a relevant consideration in the selection of schools. Employing a pretest-posttest control group design, the experimental intervention was implemented in the first 15 minutes of the regular mathematics lesson. The data were collected immediately prior to administering the experimental intervention and shortly after the trial period concluded. Pretesting both groups enabled the scores to be used as a statistical control, to analyse gain scores. Analysis of the questionnaire data showed no significant change in the self-efficacy beliefs of the control group, whereas in contrast, there was a significant gain in the self-efficacy beliefs of the experimental group. Analysis of the mathematics assessment data showed a significant growth in mathematics achievement for both the control and experimental groups. Pretest comparison showed that the difference in the means for the two groups was statistically significant in favour of the control group, whereas the posttest difference was trivial and not statistically significant. This revealed a particularly significant achievement overall in favour of the experimental group. Significantly, the biggest growth in mathematical achievement in the entire study appeared in the experimental group regarded most at risk. Overall it was found the behaviourally based Direct Instruction intervention had a positive effect on mathematical achievement and self-efficacy. The findings in this study add to the existing body of evidence attesting to the effectiveness of competently designed, properly implemented teacher-directed programs in the important though often neglected mathematical domain of laying the foundational skills. It is to be hoped they also contribute to the long-standing debate between teacher-directed and constructivist student-directed learning adherents by illustrating that some skills are better acquired through one approach and some through the other. The research and literature reviewed herein shows that in the employment and cultivation of higher order skills where reasoning and reflection are required, a constructivist approach would seem more appropriate. But when it comes to the acquisition of basic mathematical skills the findings in this study clearly show a competently designed, properly implemented teacher-directed approach is ideally suited.
The research reported in this thesis is an in-depth study of science education reform in a transitional society. The society in transition is Rwanda - one of the world's poorest countries - a tiny central African nation adversely affected by major social, political, economic, and ethnic upheaval. Rwanda is faced with the challenge of ensuring rehabilitation after the genocide of 1994 and has adopted the following national goals: implementation of a durable educational policy, eradication of illiteracy, national capacity building in science and technology and reinforcing the teaching of mathematics and sciences. The objective of this research is to describe, discuss and analyse information on the status of science education in Rwanda, from the perspective of primary and secondary science teachers, students, education personnel and the author's personal in-field observations and analysis. This research analyses the constraints in the implementation of educational policies and a relevant science education in a climate of social, political, cultural, ethnic and economic uncertainty. The research used a case study methodology and utilised quantitative and qualitative methods to examine how teachers' and students' knowledge, perceptions and experiences impact on the school learning environment. The study made use of a questionnaire that was administered to teachers and students in Rwanda. English and French versions of a modified School Level Environment Questionnaire (SLEQ) and a modified Teacher Beliefs Instrument (STEBI) were administered to teachers. Two scales derived from the Test of Science Related Attitudes (TOSRA) were adapted for use in Rwandan classes. The qualitative component of the research made use of interviews, classroom observations, personal reflexivity, historical and curriculum document analysis and vignettes. To enable an interpretation of the quantitative data from questionnaires in a meaningful manner, the socio-cultural, gender and ethnic perspectives of policy makers, teachers and students were examined through interviews and classroom observations of science lessons. The author's personal experiences and reflections also were used to understand science education reform in Rwanda. The qualitative and quantitative findings of the research identified factors that influence the science education reform process and make meaningful interpretations of background, culture and the situation in Rwanda. Document analysis indicated that there is a need for greater access to secondary education. Interviews and science lesson observations indicated that it is necessary to develop a curriculum that is contextually relevant and to redefine science teacher training programmes. The findings of the research identified the constraints, dilemmas and tensions in the implementation of the educational reform process as young and inexperienced teachers, most of whom do not have university degrees and have difficulties in implementing the curriculum effectively. Further constraints included work pressures due to the examination system, an acute, as well as a lack of material resources and finances required to reconstruct and improve educational institutions. The research investigates the impact of the transition on science education in Rwanda. The research designed to examine the science education reform process in the transitional Rwandan society and economy studied the complex cultural, historical and educational factors that influence science education. Using multiple research methods, this study is an analysis of the author's understanding of the changes that have taken place in science education, the impediments to these changes and the identification of aspects that may enhance the prospect for future science education reform, especially in the areas of the science curriculum reform, assessment procedures and teacher professional development.
The thesis investigates the role a calculator can play in the developing number knowledge of three girls and three boys as part of their mathematics program, during their first two years at primary school. Random sampling was used initially to select six girls and six boys from the twenty-four children entering a 1993 prep class These twelve children were interviewed on entrance to school and based on the performance of the twelve children on the initial interview, a girl and a boy were chosen from the higher, middle and lower achievers to take part in the full study. The class teachers involved were previously participants in the Calculators in Primary Mathematics research program and were committed to the use of calculators in their mathematics program. A case study approach using qualitative methods within the activity theory framework is used to collect relevant data and information. An analysis of five interviews with each child and observations of the children in forty-one classroom lessons provides comprehensive data on the children's developing number knowledge during the two years. The analysis questionnaires establishes each teacher's perceptions of the children's number learning at the beginning and end of each year, compares teacher expectations with children's actual performance for the year and compares curriculum expectations with children's actual performance. A teacher interview established reasons for changes in teaching style; teacher expectations; children's number learning; and was used to confirm my research findings. An activity theory framework provides an appropriate means of co-ordinating perspectives within this research to enable a description of the child's number learning within a social environment. This framework allows for highlighting the mediation offered by the calculator supporting the children's number learning in the classroom. Levels of children's developing number knowledge reached when working with a calculator and as a result of calculator use are mapped against the levels recommended in Mathematics in the National Curriculum (National Curriculum Council, December 1988), and the Curriculum and Standards Framework: Mathematics(Board of Studies 2000). Findings from this comparison illustrate that the six children's performance in number was enhanced when using a calculator and indicate that on-going development and understanding of number concepts occurred at levels of performance at least two years in advance of curriculum recommendations.
There has been widespread interest in the potential impact of the graphics calculator on system wide 'high stakes' end of secondary school mathematics examinations. This thesis has focused on one aspect, the way in which examiners have gone about writing examination questions in a graphics calculator assumed environment. Two aspects of this issue have been investigated. The first concerns the types of questions that can be asked in a graphics calculator assumed environment and their frequency of use. The second addresses the level of skills assessed and whether with the introduction of the graphics calculator has been associated with an increase in difficulty as has been frequently suggested. A descriptive case study methodology was used with three examination boards, the Danish Ministry of Education, Victorian Curriculum and Assessment Authority and the International Baccalaureate Organization. Four distinct categories of questions were identified which differed according to the potential for the graphics calculator to contribute to the solution of the question and the freedom the student was then given to make use of this potential. While all examination boards made use of the full range of questions, the tendency was to under use questions in which required the use of the calculator for their solution. In respect to the level of skills assessed, it was found that both prior to and after the introduction of the graphics calculator, all three examination boards used question types that primarily tested the use of lower level mathematical skills. With exceptions, where graphics calculator active questions have been used, the tendency has been to continue to ask routine mechanistic questions. In this regard, there is no evidence of the introduction of the graphics calculator being associated with either lowering or raising of the level of the mathematical skills assessed. For all cases studied, the graphics calculator was introduced with minimal change to the curriculum and examination policies. The role of the graphics calculator in the enacted curriculum was left implicit. The resulting examinations were consistent with the stated policies. However, the inexperience of some examiners and a general policy of containment or minimal change enabled examiners to minimise the impact of the introduction of the graphics calculators on assessment.
This study analyses the effect of introducing student portfolios as a means of assessing the learning of mathematics. It examines the intended and the unforeseen outcomes in terms of the students, the caregivers, and the teachers involved, using quantitative data to match classroom environments with the response to the innovation. A major focus of the qualitative aspect of the study is the decision-making process that was associated with the implementation of change. For this study, all the junior students in a New Zealand secondary school were asked to compile portfolios of their mathematical work. The portfolios were graded by the teachers, the marks contributing to the students' assessments for the year's work. At the outset, the plan was to survey the 510 students involved to determine their attitude towards mathematics, survey them again once the innovation was in place to quantify the classroom environment, then repeat the first survey. Analysis was expected to reveal whether classroom environments that approximated a 'portfolio culture' contributed to an improved attitude towards mathematics. This quantitative approach was supplemented with taped interviews of students and teachers, ongoing records of less formal interactions, review of examination marks and school reports, and questionnaires mailed to the homes of a sample of the students. As the study progressed, it emerged that the major impact was on the teachers, and the focus shifted to them. For four years, follow-up surveys were conducted with teachers, including those who had transferred to other schools. The study found that all students can benefit from portfolios, both in terms of skills and attitude towards mathematics. Portfolios legitimated the involvement of caregivers, a positive change that provided greater links between classroom activity and the world of employment. The professional practice of teachers was affected by portfolios, prompting development of new classroom resources and techniques, increased collegial cooperation, and well-informed reflection on teaching and assessment. Teachers maintain great influence on classroom culture, and for many of those involved in the study, portfolios prompted a renewed interest in the process undertaken by students as they develop mathematical ideas, and a change in the relationship between teacher and students. The 'portfolio culture' resulted in students improving in their appreciation of mathematics, and a changed role for the student within the social environment of the classroom.
Research suggests that many high school students are not learning mathematics of value from a personal or an employment perspective. School mathematics often consists of applying memorised algorithms to exercises that do not meaningfully connect with the student's experience, and hence do not lead to the construction of meaningful mathematics concepts by the student. Moreover, most high school mathematics curricula give students a false idea of the essence of mathematics: Instead of understanding mathematics as another powerful lens through which to view the world, and a creative, enjoyable endeavour, it is seen as mere calculation or esoteric gobbledegook. Authentic learning experiences involve a different perspective on both what passes as mathematics and how students learn to mathematise. The study examined high school mathematics knowledge from several perspectives, and sought, through an empirical study, to enhance student learning and attitude towards mathematics through authentic learning. A class of Year 8 students learnt several units of mathematics primarily by authentic methods, using problems or interesting phenomena in the students' own experience, or otherwise meaningful to the student. Qualitative data was collected by multiple methods, including video recordings. Surveys were administered to five classes of Year 8 students and their parents at the beginning and at the end of the semester in which most of the empirical research took place. This allowed a comparison of attitudes towards mathematics between the experimental class and the other classes. A comparison of achievement was also made. The results indicate that employing authentic learning experiences may enhance learning and attitude towards mathematics. However, prior transmission teaching methods presented a significant barrier to student acceptance of authentic learning. Furthermore, there remain grave problems with other aspects of current high school mathematics curricula, specifically the mathematics content and the assessment style, which act against the full implementation of authentic learning. These problems are investigated and possible future paths considered.
The purpose of this study was to establish an action research plan for teachers to improve student outcomes by assessing, describing, and changing their classroom environments. This study relied on student perceptions, using survey responses, to assess and describe the classroom environment. Teachers used this information to develop intervention strategies designed to change the students' perceptions of their actual classroom environment to more closely mirror their preferred classroom environment perceptions. More than forty years of classroom environment research has proven the importance of the classroom environment in developing positive student outcomes. Additional research has established the reliability of student perceptions of their learning environment. Previous research has developed several dependable student survey instruments to measure student perceptions of their classroom environment. This study was conducted in a Title I elementary school in the United States over a seven month period. Two intermediate level mathematics teachers participated in the project. Both quantitative data, using the My Classroom Inventory (MCI) and the School Level Environment Questionnaire (SLEQ), and qualitative data, teachers' case studies, were collected and analysed. The study established that an action research plan for teachers to assess, describe, and change their classroom environments could be developed. However, even though teachers realised the benefits, for their students and themselves, in changing their classroom environments, school level environment demands negatively influenced their willingness to implement changes to their classroom environments.
More than half of Australian primary teachers have negative feelings about mathematics. This research study investigates whether it is possible to change negative beliefs and anxieties about mathematics in preservice student teachers so that they can perceive mathematics as a subject that is creative and where discourse is possible. In this study, sixteen maths-anxious preservice primary education student teachers were engaged in computer-mediated collaborative open-ended mathematical activities and discourse. Prior to, and after their mathematical activity, the students participated in a short thirty-second Online Anxiety Survey based on ideas by Ainley and Hidi and Boekaerts, to ascertain changes to their beliefs about the various mathematical activities. The analysis of this data facilitated the identification of key episodes that led to the changes in beliefs. The findings from this study provide teacher educators with a better understanding of what changes need to occur in pre-service mathematics education programs, so as to improve perceptions about mathematics in maths-anxious pre-service education students and subsequently primary mathematics teachers.