Master of Education

In Singapore schools, many students study simple theoretical probability in Secondary 4, (15-16 year olds) and in the junior colleges (16-18 year olds). This present study aims to identify and explain the errors and misconceptions that junior college students have when they learn probability through formal instruction.

The Mathematics syllabi, based on the requirements of the Singapore-Cambridge General Certificate in Education Ordinary Level and Advanced Level for the secondary level and the junior college level respectively, stipulated certain requirements. A review of the past literature also indicated several misconceptions such as the use of judgemental heuristics and the assumption that random events were equally probable. The course requirements and the review of the literature resulted in four research questions. First, were junior college students able to reason with proportions and give examples of certain and impossible events? Second, were junior college students able to solve questions which required the skills and concepts taught in the Probability course in the secondary school and in the junior college and what errors would they commit? Third, what would be the main errors when second year students solve problems on conditional probability? Finally, do students use judgemental heuristics and exhibit the biases and fallacies reported in the literature?

Two minor areas were also investigated. One of them was the errors and misconceptions that occur when students use combinatorics. Another was students' verbal explanation of working. Data collection was divided into two parts. The first part consisted of written tests and a second consisted of interviews. The subjects consisted of 216 first year students (16-17 year olds) and 209 second year students (17-18 year olds). The focus of the study was on the second year students who had completed the Probability course in the junior college. The errors that surfaced would be used to improve the teaching programme. The first year students had received formal instruction on probability only at the secondary level. They would provide a convenient sample to which the second year students could be compared. The comparisons focused on the different types of errors and approaches for both groups.

This study found that both cohorts were able to reason with proportions although when considering a proportion of area, some students were affected by the physical appearances. There appeared to be a confusion between certain events and possible events and one reason was that an event was thought to consist of only one outcome.

Questions which concerned a conjunction of events were generally well done. However, when given empirical data, there was a tendency for students to compute a conjunction, assuming that the events were independent events when there was evidence to indicate that they were not.

The complementary rule was applied in questions where its use would make the solution easier. The main error was in defining a single complementary event.

Questions which involved a consideration of mutually exclusive but not equally likely cases brought out a few difficulties. One was the tendency to consider only one case out of several possibilities. This type of error was more prevalent amongst the second year students than the first year students. One reason for this error was that students did not consider the situation thoroughly and only arrived at a partial solution.

When the empirical probability of a union of 2 non-mutually exclusive events was required, students tended to assume that they were mutually exclusive although the evidence indicated otherwise. During the interviews, there was evidence to show that these students knew what "mutually exclusive" meant.

Conditional probability was difficult for many second year students especially when a backward conditioning event was given. Two main errors were the computation of a conjunction instead of a conditional probability and computing P(X) instead of P(X\Y) when event X preceded event Y.

Judgemental heuristics and biases existed amongst several students. This occurred to a greater extent amongst the first years. For the second year students, there was evidence that even though the probability of the event was correctly found, students did not use it to make a decision. The error of assuming that random events were equally likely was prevalent in both cohorts. For the second year students, one reason was because students thought it was only necessary to consider one outcome that satisfied the requirements.

Several second year students had difficulties with permutations and combinations when they used them to count the number of distinct outcomes. First year students who simply listed the cases fared better.

Students were generally uncomfortable with writing down explanations. During the interviews, students preferred to explain their working in terms of arithmetic operations, multiplication and addition, instead of formal terms like "intersection", "union" or "independent". There were subjects who did not associate terms like "and" and "or" with a conjunction or a union respectively. Instead, they associated them with the operations of multiplication and addition.

The study concluded with a discussion on implications for teaching and for further research.

Against the backdrop of the existential global environmental crisis and the ambitious targets outlined by the UN Sustainable Development Goals (SDGs), this study investigates the critical significance of picturebooks in shaping childhood understandings of human-nature relationships. In this study, I analyse how words and images portray the interaction of characters and nature in the narrative and their embedded environmental ideologies. In this study, I chose a qualitative case study approach to enhance my in-depth understanding of the context. I selected two case studies using a purposeful sampling strategy. In this study, a mul*modal content analysis is used to offer new perspectives derived from the use of traditional content analysis. This multimodal content analysis, henceforth referred to as MMCA, combines social semiotic and content-based analysis. In the semiotic analysis, I examine communication across semiotic modes, including linguistic and non-linguistic elements. Meanwhile, in the content-based analysis, I examine environmental ideologies based on themes that emerged from semiotic findings. This multimodal analytical approach aims to explore all potential meaning-making modes in text, visuals, and their inter-semiosis with each other. The themes that emerged from the multimodal findings provide valuable insights into gender roles, religious perspectives, and sustainable behaviours, which are essential considerations for discovering transformative environmental ideologies. The findings reveal a tendency within these narratives to prioritize individual actions over fostering awareness of systemic thinking, including social collaboration and cooperation. The findings highlight discernible disparities and notable oversights in portraying environmental ideologies of deep ecology, ecofeminism, value ethics, and sustainability. As climate change continues to threaten global human health and well-being, Education for Sustainable Development Goals also referred to as ESD aims to empower populations, including children, with the knowledge, skills, values, and behaviours required for sustainable development. It is imperative that literature wri0en for children evolves and socializes children towards a comprehensive understanding of human nature relationships and sustainable development.

This study is a multimodal critical discourse analysis of ten promotional videos of different cities in China, and aims to explore how China’s soft power is conveyed through these videos. This study adopts Fairclough’s (1989) three-dimensional analytical model as the theoretical framework and utilizes various multimodal analytical approaches including Baldry and Thibault’s (2006) phasal analysis and Burn’s Metamodal Kineikonic framework (2013) to analyse the videos. The analysis identifies key aspects of China’s soft power, encompassing its rich cultural heritage, economic and technological prowess, environmental achievements, high quality of life and international connectivity. The study finds that the videos employ a purposeful integration of various semiotic modes to construct an appealing multimodal narrative that promotes these aspects of China’s soft power. The findings are interpreted within the broader socio-cultural context of China and global trends, revealing that the videos serve as strategic tools for China to project its soft power globally, impact international perceptions, and bolster its global influence.

Alternative conception (AC) refers to any discrepant understanding harboured by an individual that is not considered acceptable by the experts. The literature reveals high school teachers rate genetics as one of the most difficult topic in Biology. The numerous ACs documented in the literature and Cambridge examiner reports together with the lack of local studies on this topic warrant a need to develop a diagnostic instrument to identify alternative conceptions in genetics. The development of Genetics Concept Test (GCT) took place over three phases: preliminary study, pilot study and main study. The final version contained 20 four-tier multiple choice (4TMC) items, each comprising an answer tier, confidence rating of answer, reason tier and confidence rating of reason. The responses were analysed based on the cognitive scores and confidence ratings. GCT also included two open-ended questions to examine students’ understanding of the theory of evolution and sexual reproduction.

This research study aims to address the following questions: (1) To what extent is GCT a valid and reliable instrument to evaluate A-level students’ understanding of the concepts in genetics? (2) What are some common alternative conceptions on genetics held by A-level students in Singapore? (3) What are the different types of views held by students regarding natural selection and sexual reproduction? (4) What are common alternative conceptions harboured by students regarding the concepts of natural selection and sexual reproduction?

GCT reported Cronbach α value of 0.73 and 0.65 in pilot and main study respectively. The mean facility index and discrimination index for both studies were acceptable. Students in the main study obtained a mean score of 63% and 41.6% for the answer tier alone and for both tiers respectively. The overall difficulty level and discriminating power of GCT were considered fair. Our findings suggested that GCT is a reliable and valid instrument to diagnose students’ ACs.

The use of confidence ratings allowed us to delve deeper into the nature of students’ learning difficulties, which would not be possible with the use of test scores alone. A total 34 ACs were reported to be significant using the 4TMC items. 20 of the significant ACs could be considered genuine with mean confidence rating of more than 3.50. We attributed these ACs to confusion over genetic terminology, poor understanding of hydrogen bonding, difficulties with concepts on homologous chromosomes, poor understanding of meiosis and mitosis, limited understanding of differential gene expression, and difficulties in understanding mechanisms underlying heredity.

Our findings from the open-ended items suggested most students had limited understanding of genetics, which prevented them from developing the correct conceptual models and ontological views to understand the process of evolution and sexual reproduction. A total of 28 ACs were identified and two of them could be considered significant. These ACs could have resulted from poor understanding of inheritance, limited understanding of the role of natural selection, simplified and deterministic view of gene, and poor understanding of the factors affecting fertilisation.

This study of adolescent thinking in secondary school considers the involvement of the last two Piagetian stages and the transition from one to the other. The move from concrete operations to formal operations should be demonstrated by the emergence of operations hitherto not evident or evident only in a limited sense. In contrast to Piaget's Identity, Negation, Reciprocity, Correlativity grouping (INRC) and the propositional logic model which he postulated as the structures present in formal operations, this study will look into Acceptance of Lack of Closure (ALC) and Multiple Interacting Systems (MIS) as formulated by E Lunzer. ALC and MIS are seen in the light of alternative structures that appear in the thinking of adolescents.

The adolescents who takes the given content as decisive, who fails to or will not reconcile opposing conclusions, and who does not conceive of unstated possibilities, is performing a kind of "premature closure". In so doing, he is still controlled by concrete thinking. The adolescent, however, who takes account of all evidence, measures the inadequacy of such evidence and supplements it or acknowledges its lack from his store of general knowledge has shown greater tolerance for unclosed operations. He can withhold closing while he considers the different variables in the problem.

MIS, on the other hand, is closely bound with abstraction. When more than one system is involved, as in MIS, variables have no direct correspondence with objects or stipulated events. Instead, the adolescent reconstructs objects as variables according to perceived laws and then tests his hypothesis against alternatives. As such, the adolescent will see abstract statements and generalisations as more meaningful than statements of association and membership.

This study therefore focuses on students' ability to judge and the extent to which their judgment is guided by possibilities other than those given. The study also attempts to measure the preference of a student for more abstract and generalised statements rather than specific statements of incidental association.

The study is also undertaken to see if the two characteristics mentioned are developmental, and if so, whether the developmental trend differs in boys and girls. The study also attempts to see if this developmental trend has any relationship with home background, measured in terms of parents' educational level, and with academic achievement.

Use has been made of two instruments initially developed by E A Peel and refined by his research students in the School of Education, University of Birmingham. One of these instruments has been expanded and labelled in this study as the Test of Judgmental Ability. The TOJA, as it is referred to in the study, uses (a) fixed and (b) flexible responses on the students' part to measure their tendency towards quoting given circumstances or invoking other possibilities. The other instrument, the Sentence Preference Test (SPT) has been largely adopted from Peel and only modified for cultural references. This latter test gives students four types of statements ranging from the incidental to the abstract, and measures their preference of level of generality by their choice.

Both tests have been intended for estimating the tolerance secondary school students have towards lack of closure in verbal situations and their degree of preference for abstract as opposed to concrete terms.

This is an exploratory study on the relationship between academic performance and health status of a sample of primary six students in Singapore. The contributions of the health variables to academic performance were also examined.

Data collected from 496 primary six students were analyzed using correlational, multiple regression and canonical correlation analyses. The criterion variables comprised the Primary School Leaving Examination (PSLE) T-scores and performance in the PSLE subjects of English Language, second language, mathematics and science. The predictor variables were the socio-demographic variables and health status indicators of height, weight, body composition, fitness status=us and performance in power, strength, endurance and flexibility items.

The study revealed statistically significant relationship and sex differences between academic performance and health status.

Fitness status and body composition correlated significantly with the academic performance of the boys. For the girls, height was the only variable which correlated positively to academic performance.

Overall fitness status and performance in six or nine minute run ( a measure and cardiovascular fitness), flexed arm hang ( a measure of strength ), and sit and reach ( a measure of flexibility ) were significant contributors to academic performance.

The study estimated that for the boys an increase in one centimeter in height, PSLE T-scores would increase by 0.472 points. However for the girls, the same increase would result in a decrease by 0.179 points. Likewise, a one percent increase in body mass index would result in an increase of1.111 points for the girls and for the boys, a decrease of 0.116 points.

Health status' contribution towards academic performance was more positive and substantial for the boys. Estimation using multiple regression techniques indicated that 18 percent and 15 percent of the boys' and the girls' performance in PSLE T-scores were respectively explained by the health status indicators.

Apart from the overall PSLE performance, achievement in mathematics was the most important criterion variable, in terms of the magnitude of the correlations and variance explained.

When the health variables were analyzed together in multiple regression analyses, the physical status indicators of height and body composition seemed to have contributed more significantly than the fitness indicators. As fitness performance was also significantly related to these physical variables, its contribution to academic performance was in fact greater.

Hence, programmes aim at improving fitness performance would need to ensure significant change to the physical status before a change in the academic performance could be experienced. It also implies that if activities to improve fitness could be supplemented by appropriate activities to change the physical status, particularly height and body composition, the impact on academic performance is likely to be even more substantial.

People with disabilities are one of the most inactive groups in society, with the majority not obtaining the recommended amount of physical activity needed to enjoy the associated fitness and health benefits and prevent secondary conditions. Research shows that access to fitness and recreation facilities is a major barrier to physical activity for people with disabilities.

The purpose of this study was to assess the level of accessibility of community sports and recreation centres (SRCs) for people with physical disabilities in Singapore. A set of valid, reliable and generalisable instruments called Accessibility Instruments Measuring Fitness and Recreation Environments (AIMFREE) was used as the assessment instrument.

A survey of three Sports and Recreation Centres (SRCs) was carried out by two evaluators with physical disabilities. At each SRC, the swimming pool, gym and indoor sports hall were evaluated for their accessibility using the AIMFREE instruments. Accessibility points were awarded based on the AIMFREE criterion. After each survey was completed, the evaluators completed a post-survey questionnaire. Data was also collected through a focus group discussion with a group of five wheelchair basketball players.

The overall level of accessibility at SRC-1 and SRC-2 was found to be above average. For SRC-1, an accessibility score of more than 50 was achieved in four out of seven survey sections. For SRC-2, a score of more than 50 was achieved in six of the seven survey sections. SRC-3 had a below average level of accessibility, with a score of more than 50 in two out of six survey sections. The accessibility score indicates how accessible a facility is, and a score of more than 50 indicates above-average levels of accessibility, while a score of below 50 indicates below-average levels of accessibility.

Facilities fared poorly with regard to accessibility features in the survey that are harder to implement, such as, automatic doors and pool lifts. Barriers identified in the post-survey questionnaire closely matched the barriers that were identified in the onsite survey of the SRCs, and data resulting from the focus group interview. Areas of concern include the bathroom and shower facilities, the gym and exercise equipment, and the swimming pool. Barriers identified by the focus group participants were similar to the barriers identified in the survey, and matched the more difficult accessibility features in the survey.

This study found that while SRCs are generally accessible to people with physical disabilities, there are existing physical and structural barriers that make some areas in the SRCs inaccessible and affect the participation of people with disabilities in specific sports and recreation activities. Data from this study may be used to improve accessibility standards of community sports facilities in Singapore for people with disabilities.

The paper examines the effectiveness of c-operative learning approaches and traditional approaches on achievement, interpersonal relationships and academic self-concept in economics on a group of boys in a junior college. The co-operative learning programme was implemented in two second year science classes over a period of seven weeks. The achievement outcome was measured using three tests: multiple-choice tests, data response tests and an essay test. The students in the co-operative group performed significantly better in both the multiple-choice test and the data response test. The performance of the group in the co-operative learning environment was better than the group in the traditional learning condition but the difference was not significant. With respect to interpersonal relationships and academic self-concept in economics, significant effects of co-operative learning approaches over the traditional learning learning approaches was not found, though the results were in the desired direction, with the students in the co-operative learning environment showing a greater liking for their peers and the teacher as well as a move positive attitude towards economics. The results of the study show some advantages of co-operative learning approaches over traditional approaches. They suggest that students can gain academically, socially and psychologically through the use of co-operative learning in the teaching and learning of Economics.

This study investigated patterns of acquisition of English and Mandarin by a Singaporean child who has been raised in a code-switching type of speech environment. The relation of code-switching to the acquisition of bilingualism was analyzed too. The speech of the subject, a 23-month-old boy in a middle class trilingual family, was recorded and analyzed for seven months. Results indicate that: (1) the absence of tense and number markers in the English data was due to the variety of Singapore Colloquial English the child was exposed to in his environment; (2) the use of pragmatic particles and the lack of clear developmental pattern in the English interrogatives were linked to the Singapore Colloquial English usage in the input; (3) the English-language acquisition pattern shows a similar pattern as those in other comparable studies done in Singapore; (4) the order of the grammatical morphemes in the Mandarin data follows the similar pattern as other monolingual children reported on ; (5) code-switching and code-mixing were directly affected by social factors: interlocutor, norm of the speech situation and his language dominance; (6) code-switching also occurs for many reasons related to language use; and (7) the child's language development has been affected by the varying amount of input. The study concluded that code-switching did not lead to any negative consequences, but on the contrary, seems to be the only viable means of developing bilingualism in Singapore, where multilingualism is a norm and code-switching is an integral part of the single complex culture.

This study was focused on a mathematics teacher’s use of differentiated instruction strategies for teaching two units in geometry to a class of lower secondary normal students in a Singapore school. A total of 39 students with diverse academic background participated in this three-part action research study. The first study (Study 1) obtained a profile of the students in terms of their academic background as well as learning needs, learning styles and interest. In the second study (Study 2), the teacher designed lessons based on van Hiele’s levels of geometrical understanding and instructional strategies that were differentiated in one or more aspects, namely, content, process and product to provide students of different ability in mathematics with multiple options for taking in information, making sense of ideas, and expressing what they learn (Tomlinson, 2000). These include differentiated assignments (tiered worksheets), flexible groupings (whole group, small group, individual) and other strategies. A pre-post test design was used to collect the data on students’ learning achievement and their attitudes towards mathematics learning. These collected data together with the teachers’ observation and student interviews were used in a final study (Study 3) to evaluate the effectiveness of the two-month long implementation of differentiated lessons. Though the observed gains in students’ learning are not conclusive given the single group pre-post design used for study, a triangulation with the results of the attitudinal survey and other informal feedback/observation shows that differentiated instruction holds promise as a pedagogical approach for reaching out to students with diverse learning needs. Implications of the findings on differentiated instruction for classroom teachers are discussed and directions for future research are also delineated.

This action research studies how creative drama impacts upon the social development of young children in Singapore. Specifically, it addresses how the drama instructor, as well as a structured programme, influences the development of a young child's social skills and self-confidence.

The need for particular research findings in the local context arises because formalised creative drama curriculum has yet to gain recognition in Singapore's early childhood education setting. It is hoped that the findings here will allow for more research studies to be undertaken, specifically those with a focus on creative drama. Ultimately, there needs to be greater awareness and acceptance of the role of creative drama in early childhood development.

This action research, with an embedded case study, was implemented through ten sessions sited in an 'anchor operator' preschool. The demographics of the student population in an 'anchor operator' preschool, is made up primarily of Singaporean children, hence the choice of such a preschool.

The methodology was as follows. A teacher-researcher implements a prescribed creative drama curriculum, while observing the children's responses. Video recordings along with the class-teacher's observations and reflections are also documented and triangulated with the teacher-researcher's observations.

Overall, the findings indicated a growth in the children's social skills and self-confidence. Any curriculum is ineffective if the instructor is unable to look beyond the given structure and adapt to the needs of the class. A prescribed curriculum, flexibility in executing the lesson and focused lesson objectives is necessary to empower creative drama instructors. A creative drama programme that incorporates drama conventions, such as improvisation, teacher-in-role and personal reflection also allows participants to connect with the lesson at a deeper level, hence fostering social development. It is hoped that early childhood educators, equipped with such knowledge, will now be more receptive (and more able) to use creative drama effectively to develop social skills and self-confidence in young children.

Singapore secondary students are familiar with two part linear inequalities such as αx + 𝑏 > 𝑐x + 𝑑, three part inequalities αx + 𝑏 < 𝑐x + 𝑑 < 𝑒x + 𝑓, and quadratic inequalities αx² + 𝑏x + 𝑐 > 0. However compound linear inequalities with connective words such as and and or do not receive much attention. Such inequalities include αx + 𝑏 + 𝑐 and 𝑑x + 𝑒 < 𝑓 or αx + 𝑏 + 𝑐 or 𝑑x + 𝑒 < 𝑓. Depending on the conditions, some compound linear inequalities with the connective word and may not have any solutions and those with the connective word or may have solutions which are union of the two sets or the entire number line.

The objectives of this study are twofold. The first is to identify whether students were aware of these differences and if they were not, could they be helped to construct new understanding of compound inequalities. The study comprising two phases was conducted to identify the difficulties students have with compound linear inequalities. In Phase One, 57 Secondary Three Express provided written responses to a 14-item Written Task. In Phase Two, 20 of the 57 students were interviewed. The objective of Phase Two was to determine whether these students were able to construct a better knowledge of compound linear inequalities.

The study found that although students were able to solve compound linear inequalities involving connective word and, there was floor effect with compound linear inequalities involving the connective word or. However through appropriate prompts students constructed a better understanding of compound inequalities involving the connective words and and or. The study showed that the affordance of number line aided students in their construction of knowledge. The study argued that teachers and textbook writers should address students’ difficulties with compound linear inequalities.

This case study research aims to analyze the impacts and influences of an arts mentorship scheme on two schools after being completed for a year. Using Banduras self-efficacy theory as an overarching framework, the study explores the impact an artist-mentor has on art teachers in three areas. Firstly, the changes in teachers’ self-efficacy in art skills and lesson delivery. Secondly, the teachers’ impact on their students, and thirdly, the motivations to create art for themselves. The findings showed that after the mentorship programme, the teachers became more competent in their technical art skills and lesson delivery. During the mentorship, they had gained insights into new approaches and had the opportunity to practice skills they were weak at. In addition, they were able to expand their knowledge into lesson design and lesson delivery. Students taught by these teachers showed abilities to adapt their skills to other art disciplines. On inspiring teachers to take on more art activities, the mentorship did not bring about a significant impact. The teachers had already established their routines. Moreover, they quoted the lack of time and space as limitations. Moving forward, the teachers recommended expanding the mentorship scheme to include regular reviews and prolonged engagement with the artist-mentor. There were also suggestions to integrate studio space into the school and more time for professional development. In the last chapter, suggestions were offered to respective bodies to help future mentorship programmes.

In 1905, Albert Einstein produced five historic papers that shattered the foundations of Newtonian Physics. One of those papers introduced the theory of special relativity as well as the legendary, and probably the most famous equation in Physics, E = mc2. Interestingly, after 100 years of discovering this equation, the conceptual framework behind the conversion of mass and energy is still in dispute. One facet of the debate is on the absolute notion of mass, the invariant mass as compared to relative notion of mass, sometimes known as relativistic mass or velocity-dependent mass. In a sense, this may arise from the inadequate understanding of the concepts about absolute motion and relative motion. Indeed the present debate is related to the different views between Newton's absolute space and Leibniz's relational space.

Alternative conception, in the usual context, refers to experience-based explanations constructed by a learner to make a range of natural phenomena and objects intelligible, but it also confers intellectual respect on the students or experts who hold those ideas because it implies that alternative conceptions are contextually valid and rational and can lead to even more fruitful conceptions. The present research will focus on the "alternative conceptions" of Einstein's energy-mass equivalence rather than the previously dominant term, misconception. Though the initial intention was to study the student's alternative conceptions, the subsequent discovery of the alternative views of many experts and textbooks suggested that the nature of the controversy is more complicated that it seems, to the physicists and physics teachers. Hence, this study is restricted to the alternative conceptions presented by the textbook authors and physicists.

The objectives of this study are to identify the major areas of alternative conceptions covered in the literature; suggest how the alternative conceptions can be categorized in four different perspectives; investigate the alternative conceptions of E = mc2 from experts and textbooks; discuss the implications to curriculum and assessment and suggest future directions for research. In this study, the focus is on selected textbooks from United States and United Kingdom. This is because they are commonly available in Singapore, and they are also influential and well established.

The research findings indicate that US textbooks have all the concepts in the suggested four perspectives "permutated" in almost all possible ways. However, it is observed that most of the UK textbooks are, somewhat more consistent, following the same traditional view.

This study suggests that educators should be aware of the difference in textbooks from US and UK. While consensus may not be reached in the near future, we suggest that there are a number of issues which the educators need to be cognizant of in introducing this mass-energy relationship into any curriculum. That is, the educators should be aware of the limitations in scientific knowledge, conceptual difficulties, pedagogical challenges and assessments issues. Future research should also be carried out on other concepts to investigate the subtle differences between textbooks which pose further challenges to physics teachers.

The purpose of this study is to examine the level of critical thinking by analysing the pre-service teachers’ message postings, comparing between both text-input and audio-input in an asynchronous discussion forum.

This study involved two groups of students who were pre-service teachers to participate in, two types of asynchronous online discussion – text-input and audio-input. The online discussion was being done over a semester and the message postings from their discussion were being taken down and recorded for further analysis. Both groups of students were given the same topic for discussion, as well as similar duration of time for the discussion.

The results of a chi-square analysis suggested that students produced more than expected higher critical thinking level during asynchronous audio discussion. On the other hand, more lower critical thinking levels than expected were produced during asynchronous text discussion. There were positive results and benefits of the audio-input online asynchronous discussion that motivated the students to actively participate in the audio-input online asynchronous discussion. Students generally were able to contribute more postings in an audio-input online asynchronous discussion.

This dissertation introduces two methodologies - Knowledge Construction – Message Map (KCMM) and Knowledge Construction – Message Graph (KCMG), for analyzing knowledge-construction as well as mis-construction occurring in an online asynchronous discussion forum that could potentially advance understanding of these processes. The ubiquitous adoption of online asynchronous discussion forum in the field of Computer Supported Collaborative Learning (CSCL) has far outpaced the understanding of how this dynamic and collaborative learning tool should best be used to promote independent and higher-order learning. The adoption of an asynchronous discussion forum provides opportunities for in-depth analyses of students’ transcripts to understand peer interaction and knowledge construction in learning. This study introduces instruments for tracing the communication patterns and knowledge construction as well as mis-construction processes of students working in groups, whilst discussing subject-related content using an innovative approach to map the messages of students’ postings. With the focus of this research on what happens to learning within a collaborative and interactive environment, it is hoped that the authentic data collected will reveal the dynamics of the asynchronous discussion forum and how it may facilitate student’s knowledge construction. In addition, this will encourage educational practitioners and researchers to describe on-line interaction with a more systematic approach and adopt a measurement methodology that is more effective rather than necdotal.

Integration is part of the Additional Mathematics syllabus required for the Singapore-Cambridge General Certificate in Education Ordinary Level Examination and is a topic that students generally find difficult to understand. The aim of this study was to pursue an answer to the following general questions :

1. Given the various objectives with respect to integration in the calculus component of the Additional Mathematics syllabus, what is the degree of understanding of integration concepts among Secondary Four school students in Singapore?

2. What are common errors and misconceptions that secondary school students have with respect to integration?

For this study, the data collection involved the use of a six-question test to determine students' performance, degree of understanding and to identify students' learning difficulties. After an analysis of the data collected from the diagnostic test, seven students were interviewed to clarify and elaborate their written answers. Data collected from the interviews also provided information on students' degree of understanding of integration and students' learning disabilities.

With respect to students' performance, students in this study did well with questions involving integration of sums of terms in powers x excluding 1 / x and functions of the form (ax + b)n . They were also adept at evaluating definite integrals. Questions involving integration of trigonometric functions were not as easy for students. The most difficult questions involved applying integration to evaluate plane areas. With regards to application of differentiation and integration to kinematics problems, students fared better when the functions involved were polynomial rather than trigonometric functions.

As for degree of understanding, the students seemed to focus on the procedural aspects of integration far more than on the conceptual aspects. Nevertheless, students generally lacked both conceptual and procedural understanding of integration.

Students committed a large number of conceptual errors, particularly when applying integration to evaluate plane areas. They made about twice as many procedural errors. The procedural errors were mainly due to their confusion over the algorithms for performing integration and differentiation, and also because of their failure to put the constant c in indefinite integrals. However, the largest numbers of errors committed were technical errors which were primarily attributed to the students' lack of mathematical content knowledge in other topics required for integration.

The study concluded with a discussion on the implications for teaching.