published_or_final_version / Education / Master / Master of Education

Law, Helen. / "August 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 78-84). / Abstracts in English and Chinese. / ABSTRACT --- p.i / ACKNOWLEDGEMENTS --- p.v / LIST OF TABLES AND FIGURES --- p.viii / Chapter CHAPTER ONE --- INTRODUCTION --- p.1 / Chapter 1.1 --- Background of Study --- p.1 / Chapter 1.2 --- Research Problems and Objectives --- p.3 / Chapter 1.3 --- Layout of Thesis --- p.5 / Chapter CHAPTER TWO --- LITERATURE REVIEW --- p.6 / Chapter 2.1 --- Explaining the Gender Gap in Math Achievement: A Brief Overview of Previous Studies --- p.6 / Chapter 2.2 --- Gender Stratification Hypothesis --- p.9 / Chapter 2.3 --- Role of Parents --- p.11 / Chapter 2.4 --- Role of Single-Sex Schooling --- p.12 / Chapter 2.5 --- Focus of this Study --- p.16 / Chapter CHAPTER THREE --- ROLE OF FAMILY BACKGROUND AND SINGLE-SEX SCHOOLING IN THE GENDER GAP IN MATH TEST SCORES IN SIXTEEN COUNTRIES --- p.18 / Chapter 3.1 --- Hypotheses --- p.18 / Chapter 3.2 --- Data and Method --- p.19 / Chapter 3.3 --- Results --- p.23 / Chapter 3.4 --- Discussion --- p.40 / Chapter CHAPTER FOUR --- THE GENDER GAP IN MATH TEST SCORES IN ALL COUNTRIES PARTICIPATING IN PISA 2006 --- p.50 / Chapter 4.1 --- Data and Method --- p.51 / Chapter 4.2 --- Results --- p.57 / Chapter 4.3 --- Discussion --- p.63 / Chapter CHAPTER FIVE --- CONCLUSION --- p.67 / Chapter 5.1 --- Summary of Findings --- p.67 / Chapter 5.2 --- Theoretical Implications --- p.69 / Chapter 5.3 --- Empirical Implications --- p.70 / Chapter 5.4 --- Limitations and Suggestions for Future Research --- p.71 / APPENDIX A: Description of dependent variables and student-level independent variables --- p.75 / APPENDIX B: Description of school-level independent variables --- p.76 / REFERENCES --- p.78

The early years of schooling are a crucial part of a student’s education. Recent years have seen the implementation of new literacy and numeracy programs in primary school classrooms. The key area of mathematics (numeracy) has been closely monitored and funded by political and educational bodies (Clarke, Cheeseman, Gervasoni, Gronn, Horne, McDonough, Montgomery, Roche, Sullivan, Clarke, & Rowley, 2002; Association of Independent Schools of South Australia, 2004). The new numeracy programs have been introduced into the school curriculum to ensure that all students’ needs are catered for in the classroom program. However, standardised testing using pencil and paper is still being used as the accepted form of assessment. The Victorian State Government uses the Achievement Improvement Monitor (AIM) to assess students’ mathematical achievement levels. This pencil and paper test is conducted for students in years three, five, seven and nine and is used to sort the students into a percentile group. Other than the ‘Early Numeracy in the Classroom’ program (2002) used by Victorian schools as a prep. to three program, where a one-on-one interview is used as a form of assessment, there is currently no program that offers students the opportunity to choose how best to represent their own mathematical understanding. Although, the learning needs of students are being better catered for within the classroom, students are being disadvantaged by the way in which they are assessed.

Text in Afrikaans / 'n Leerling se wiskunde-selfkonsep wys heen na die konsep wat hy van homself op wiskundige vakgebied het. Die kwaliteit van hierdie konsep word bepaal deur die kwaliteit van sy eie betrokkenheid by, belewing van en sin- en betekenisgewing aan wiskundige vakinhoud. Wanneer die kwaliteit van 'n leerling se wiskunde-selfkonsep ontoereikend is, word sy onvermoe om op daardie tydstip sukses op wiskundige vakgebied te behaal, geopenbaar. Dit plaas die opvoeder voor die opgawe om bemoeienis met die leerling te maak en hom ten aansien van sy probleem te help. In die lig hiervan is 'n hulpverleningsprogram ter bevordering van die wiskunde-selfkonsep ontwerp. Aangesien leerlinge in Suid-Afrikaanse skole tans gedurende die st.7-skooljaar die besluit neem om die studie van wiskunde te staak of daarmee voort te gaan, is die inhoud van die program derhalwe op die st.7-leerling van toepassing gemaak. Spesifieke doelsteilings wat in die ontwerp van die program nagestreef is, is die volgende: Om die leerling te begelei tot insig in en die begryp van die kwaliteit van sy eie wiskunde-selfkonsep en grondliggende oorsake vir die vorming daarvan, ten einde hom in staat te stel om sy eie situasie in perspektief te plaas. Om die leerling te begelei tot die ontwikkeling van spesifieke vaardighede aan die hand waarvan hy homself op 'n meer selfstandige wyse kan handhaaf ten aansien van die begripmatige bemeestering van wiskunde as vak. By wyse van 'n loodsondersoek is die toepasbaarheid van die onderhawige program ondersoek. Uit die terugvoergesprekke met die leerlinge tydens die groepsessies en die inligtingstukke wat hulle voltooi het, blyk dit dat hulle baat gevind het by hulle deelname aan die program. Met die oog op moontlike toekomstige navorsing is spesifieke leemtes ten opsigte van die onderhawige studie uitgelig en aanbevelings gedoen wat as verdere riglyne geimplementeer kan word. / A pupil's mathematical self-concept is the concept a pupil has of himself in the sphere of Mathematics as a subject. The quality of this concept is determined by the quality of his own involvement in, live-experiencing of, and significance attribution in respect of mathematical subject content. When the quality of a pupil's mathematical self-concept is inadequate, his inability is manifested in his failure to master Mathematics as a subject. This confronts the educator with the task of becoming involved with the pupil and helping him with his problem. In view of this, an aid programme was designed to improve the mathematical self-concept. Owing to the fact that, at present, pupils in South African schools have to decide during their Std 7 school year whether they are going to continue with their study of Mathematics or discontinue these studies, the content of the programme was aimed at the Std 7 age group. The following are the specific aims that were pursued in the designing of the programme: To guide the pupil to insight in and understanding of the quality of his own mathematical self-concept and its underlying causes, in order to enable him to place his own situation in perspective. To guide the pupil in the development of specific skills to help him cope more independently with the successful mastery of Mathematics as a subject. The possibility of implementing such a programme in practice was established by means of a pilot investigation. From feedback discussions with the sample group during group sessions and from questionnaires they filled in, it appears that they benefited from their participation in the programme. With a view to possible future research, specific shortcomings with respect to the investigation were highlighted and recommendations made which can be implemented as further guidelines. / Psychology of Education / M. Ed. (Sielkundige Opvoedkunde)

published_or_final_version / Clinical Psychology / Doctoral / Doctor of Psychology

The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in comparison to those of other countries. Based on these observations, the present study was an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of the study was to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study paid more attention to mathematics education in real life situations.

The role of memory as measured by the Wide Range Assessment of Memory and Learning (WRAML) was studied in an outpatient clinic sample of 62 arithmetic disabled children.

This study compared the estimates of reliability made using one, two, three, four, five, and unlimited consecutive failures as ceiling rules in scoring a mathematics achievement test which is part of the Iowa Tests of Basic Skill (ITBS), Form 8. There were 700 students randomly selected from a population (N=2640) of students enrolled in the eight grades in a large urban school district in the southwestern United States. These 700 students were randomly divided into seven subgroups so that each subgroup had 100 students. The responses of all those students to three subtests of the mathematics achievement battery, which included mathematical concepts (44 items), problem solving (32 items), and computation (45 items), were analyzed to obtain the item difficulties and a total score for each student. The items in each subtest then were rearranged based on the item difficulties from the highest to the lowest value. In each subgroup, the method using one, two, three, four, five, and unlimited consecutive failures as the ceiling rules were applied to score the individual responses. The total score for each individual was the sum of the correct responses prior to the point described by the ceiling rule. The correct responses after the ceiling rule were not part of the total score. The estimate of reliability in each method was computed by alpha coefficient of the SPSS-X. The results of this study indicated that the estimate of reliability using two, three, four, and five consecutive failures as the ceiling rules were an improvement over the methods using one and unlimited consecutive failures.

Since the 1960s, the advocacy of teaching mathematics so as to be useful is not without hindrance in school curricula, partly due to the lack of appropriate assessment tools. Practical approaches have been accumulating quickly, but researchers showed that they are not satisfactory in testing students’ ability to apply mathematical knowledge, be they “word problems” in school textbooks, national tests, or large-scale international assessments. To understand the causes behind the dissatisfaction, there is a need to reveal (1) the theories that are used in the test designs, and (2) what the actual assessments are in various curricula. This motive leads to the purpose of the current study, which is to identify empirically consistent theories about students’ ability to apply; the results can be organized as a framework to analyze assessment tools such as PISA, as well as various curricular materials. Based on the current theories, a framework of assessment analysis is created in order to study the coverage of modeling steps of public assessment items. This study finds that, though many education systems have claims of introducing modeling and application into their curricula, high-stake assessments mostly involve a small fraction of the steps that are required in a full modeling cycle. It furthers an earlier result that certain textbooks, though claiming the importance of modeling, almost ignored the first and last steps of modeling. It is found in this study that public assessments are even more limited: most test items that are supposed to test students’ knowledge of application involve only one or two steps of modeling. Furthermore, the tool “modeling spectrum” that is used in the analysis does not only reveal how modeling steps are covered, but can also assists educators to improve or create problems with modeling and application.

This thesis reports data gathered through case studies of ten of the students who took part in a survey of secondary school students who had been invited to camps at which the New Zealand teams were chosen for the International Mathematical Olympiad (IMO) in the first five years of this country�s participation in the IMO. The case studies data gave individuals� narratives that were captivating yet complex, unique yet universal, clear yet not easily described all of apiece. I read widely in response to the information they offered and found that reflection and a narrative style of presentation assisted the grasping of nuances and implications of the students� narratives. Few of the parents of the students were particularly competent in mathematics or able to account for their child�s curiosity, concentration and skills in pursuing a fascination with number. In most of the families, all members were encouraged to follow their own inclinations and interests, to respect the maintenance of a balance of cultural and physical activities, to regard books and play as normal life supports, and to believe that discovery, enchantment and pleasure were both goals and accomplishments of everyday life. Most of the students experienced less encouragement at school than they might have expected, and unpleasant experiences could be linked with a teacher�s apparent lack of appreciation of a student�s mathematical ability. Both the case studies and the initial survey suggested that most teachers, at any level of formal education, were doing all they were capable of doing in mathematics, and that the students responded to opportunities to self-select subjects and topics that interested them and to the help and company offered by mentors and peers who had flair and competence in appropriate subject areas. Few of the case studies students were motivated by strategies dependent on a high level of competition or a 'sorting' of that offered in formal education (through attitudes and practical organisation such as timetabling) into either Arts or Science subjects. Most were attracted to the study of languages and/or philosophy and some to that of computer science. Most showed interest and some prowess in individual cultural and physical activities requiring perseverance. Largely, they were motivated by finding fresh or novel ways of integrating diverse knowledge, and by associating with peers. They enjoyed and valued self-awareness, intellectual independence, chances to empathise with ideas and people, and tasks that were in harmony with the dictates of their own volition. Evidence of differences among the case studies students - even though they had all been identified as very able in mathematics - led me to Vadim Krutetskii�s theories of the components of mathematical ability and their functioning and thus to new views, first, of the interplay between aptitude and languages of perception, inner comprehension and outer expression and, second, of the relationships between giftedness and other attributes of human abilities and endeavours. These appreciations suggested that the models of education and support commonly exhibited in the case studies students� families and in the environments of their extra-school activities had been more encouraging of their gifts, talents and personal growth than those often exhibited in the schools they attended.