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 (Keller, 1983b) 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.

Thesis (Ph. D.) -- University of Tennessee, Knoxville, 2006. / Title from title page screen (viewed on Feb. 2, 2007). Thesis advisor: Vena M. Long. Vita. Includes bibliographical references.

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.