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Students often find it extremely difficult to memorise a host of formulae and more importantly to use them in context when required. By identifying a wide variety of different three variable formulae and commenting on their uses, this article seeks to reinforce basic scientific principles and simultaneously make connections using real life, everyday situations. The paper followed numerous cohorts of students from different countries in several continents over a 45-year period. The triangulation theme is emphasised and derivations from sample fundamental equations are discussed. Results showed that apart from bringing together commonalities, the dangers of compartmentalisation are minimised. This article also serves to encourage thinking outside the box. By requesting that three variable relationships be identified in as many subject areas as possible, the reader is forced to bring together ideas from different subjects, thereby undermining the tendency to compartmentalise. It is hoped that readers will become more sensitive to the threesome nature of basic scientific laws that govern the universe and find science much more engaging and exciting. Educators might consider paying specific attention to the triangulation pattern in relationships in order to improve teaching practices and enhance learning.

A focus group of 18 faculty members at Campus O of a higher educational institution and another focus group of 16 faculty members at Campus S of the same institution comprised the sample, representative of close to 100% of their respective populations. Independently, both groups were engaged in interactive Problem-Based Learning sessions. They subsequently completed two evaluation instruments. One evaluation instrument had five items (05ITEMS), and the other had ten items (10ITEMS). Each evaluation instrument had two forms; one used a five point Likert scale and the other a ten point Likert scale. Identical participator satisfaction ratings were recorded using 05ITEMS and 10ITEMS instruments at the 99%, 98% and 95% confidence intervals (t = 0.59, [alpha]= 0.01, df = 34). Participants expressed satisfaction in a number of areas like clear delivery by workshop facilitator; capturing their interest; gaining knowledge; and obtaining useful handouts. Implications for improving teaching and learning in higher educational institutions through Problem-based Learning, engaging participants and saving time and cost are discussed. (Contains 5 tables.)

Defining self assessment as the involvement of students in identifying standards and/or criteria to apply to their work and making judgements about the extent to which they have met these criteria and standards, this paper seeks to highlight the gestalt effect of self assessment. The total effect of self assessment on the learner is greater than the sum of the individual effects of self assessment. A Posttest-Only Control-Group Experimental Design was used for the conduct of a comprehensive study, with self assessment training as the experimental variable and the posttest as the results of the external examinations. Both treatment groups were selected from the same high schools, with the design duplicated across the 10 schools, controlling for socioeconomic status and other school variables that might otherwise influence differences between the treatment groups. Students reported feeling less threatened by other so-called superior students. The paper uses empirical evidence from the comprehensive study which showed that high school students trained in self assessment skills outperformed their untrained counterparts in external examinations in all areas of the school curriculum. This summary is hoped to bring changes to current practice and provoke much needed research in this field.

This paper seeks to show how self assessment facilitates student-centred learning (SCL) and fills a gap in the literature. Two groups of students were selected from a single class in a tertiary educational institution. The control group of 25 was selected randomly by the tossing of an unbiased coin (heads = control group). They were trained in the traditional manner (TCL) using mostly chalk and talk with numerous textbook examples for practice. The experimental group of 25 representing the remaining students in the selected class was trained using a SCL focus with emphasis on self assessment. Both groups were exposed to the Mathematical topic of "Piecewise Graphing." Their scores on ten compulsory identical textbook questions on the topic of "Piecewise Graphing" were compared. Comparison of the scores of students exposed to both approaches of learning showed that generally students of the experimental group outperformed their counterparts at all achievement levels (top, middle and bottom). Students of the experimental group were able to pin point their specific areas for improvement whilst those of the control group took no interest in determining ways for improvement. Because SCL places the learner at the centre of the learning process, giving him autonomy and responsibility for his own learning this research has added value to industry personnel. The emphasis on being customer focused in industry may have translated itself to being student focused in education. It is hoped that readers would use the ideas offered to improve their practice. A bibliography is included. (Contains 1 table.)

Offering meaningful service to the community while engaging in active learning is a pedagogical strategy that has come to be known as service-learning. Both learner and the community are mutual recipients of benefits derived from the process. The fundamental question that remains is, "How do we assess the learner in this non traditional scenario?" For this pilot study this present paper attempts to provide readers with some contemporary tried-and-tested ways for assessment of service-learning based on the researcher's experiences with learners at a tertiary educational institution in a Caribbean setting where tourism is the main source of foreign exchange. It is hoped that the varied methods discussed serve as a catalyst for developing innovative methods of assessment in service-learning thereby advancing knowledge in this field. (Contains 6 exhibits.)

This paper examines the relationship between objective academic achievement (OAA) and subjective well-being (SWB). Using a sample of 515 adolescents from ten different high schools across a small country, semi-structured interviews, academic records and observations provided relevant data for the study. OAA was measured from examination results and SWB was measured using with permission Jackson's Personality Research Form (PRF)-Form E. Allowing for psychological factors, qualitative and quantitative results showed that high achievers felt better about themselves compared to their low achieving counterparts. Strategies for assisting low achievers are discussed. Further research unraveling how OAA impacts SWB could assist policy makers and curriculum planners in being more student focused. Successful implementation of teaching innovations like self assessment in the classroom requires that early attention be paid to potential sources of student resistance. It is hoped that this research would serve as a catalyst for further studies in this area. A bibliography is included. (Contains 3 tables.)

Socializing is an integral part of human relations and auger well for the human development. Defined as "the involvement of students in identifying standards and/or criteria to apply to their work and making judgments about the extent to which they have met these criteria and standards", self assessment by its nature teaches students how to socialize in appropriate ways within and without the classroom. High school teachers and students became partners in the process of assessment and self directed learning. The questions that teachers asked a class served as models for questions that learners asked themselves in self assessment. The implications for healthy social interactions are far reaching especially when there is so much turmoil in today's family. As family members try to reach consensus they are better able to understand each other and appreciate and celebrate diversity and individual differences that redound to less internal stress and promote harmony.

This paper investigates self assessment using dual scaling which is a descriptive, optimal, non linear multidimensional and multivariate method that may be used to analyze nonlinear multivariate data "very effectively and exhaustively". Self assessment was defined as "the involvement of students in identifying standards and/or criteria to apply to their work and making judgements about the extent to which they have met these criteria and standards". The participants for the study comprised 515 high school students (approximately aged 14-16 years old), representing more than a quarter (25.2%) of the school leaving cohort under study. Two hundred and thirty three were males. All participants were engaged in the same programme of studies. Dual scaling accounted for individual differences instead of averaging out responses and facilitated the examination and judgement of unexpected "attitude" categories. The effect of individual differences in a study of this kind is important because fundamental variations among and between individuals are often obscured by averaging. Observations have implications for research where individual differences are important. (Contains 1 table, 1 figure, and a bibliography.)

Discovery learning in higher education has been reported to be effective in assisting learners to understand difficult concepts and retain long term information. This paper seeks to illustrate how one self assessment model may be used to demonstrate discovery learning in a collaborative atmosphere of students sharing and getting to know each other. Three research questions were posed to drive the research. A researcher designed instrument was used as the pre activity instrument with which the students worked in collaboration with presentations and break our group activities supported by trained proctors. Results indicated that participants experienced the discovery process through the medium of the designed model. They reported learning to work in a collaborative atmosphere where they appreciated and respected each other. This researcher hopes to stimulate readers to experiment with different models for demonstrating discovery learning. "Measurement, Assessment and Evaluation Activity" is appended. A bibliography is included. (Contains 13 tables.)

This article seeks to address a common problem that many Mathematics students have with directed numbers. Directed numbers are either positive or negative. More importantly, many students seem to think that directed numbers have no tangible significance in real life. The paper uses a student-made manipulative to encourage students to appreciate that they could be an integral part of the teaching/learning process. The manipulative comprises a self made ruler with a zero mark and positive and negative numbers on either side of the zero. A "mover" or slider also made from Bristol Board moves smoothly along the ruler. The manipulative is used to calculate commonly met textbook problems on directed numbers. Common every day examples serve to bring to real life the value of directed numbers. Practitioners could use this article a stimulus to formulate manipulatives that they could use in their classroom practice and relate mathematics to real life situations. (Contains 4 figures.)

The study designed to contribute to existing research on Problem-Based Learning (PBL) chose a focus group comprising 16 MSc. Petroleum Engineering students (six females). Using PBL as the method of instruction, students examined a real-life petroleum engineering problem that highlighted numerous areas of their existing curriculum. They worked in three small groups. Communication, management, editing, civic-mindedness, critical thinking and presentation skills were some of the hones skills. A pre and post test using a 15 item dichotomous opinionnaire revealed that student views did not change on issues like PBL being considered a fad, PBL being unsuitable for first year students, students need prior content knowledge and attitude towards PBL determined their success. On the other hand, there was an overall decrease in the number of students who felt that PBL was inappropriate for some disciplines, sufficient content was not taught using PBL and assessment in PBL was a complicated activity. More than 20% of students felt more confident about PBL and no one felt that PBL was too time consuming after the PBL experience. Further research on the long term effects of PBL usage would shed more light on the value of this teaching /learning methodology. Appended are: (1) The first PBL Problem; and (2) Instrument for evaluation of Group Presentations. (Contains 5 tables.)

This paper examines similarities and differences in faculty and student perceptions to PBL training. Faculty at a newly formed university participated in a four day PBL [Problem-Based Learning] workshop. A cohort of MSc [Master of Science] Petroleum Engineering students were PBL trained. Results from the pre/post test using a 15 item dichotomous opinionnaire revealed that there was an overall decrease in the number who felt that PBL was inappropriate for some disciplines, sufficient content was not taught and PBL assessment was a complicated activity. Twenty percent of participants felt more confident after training. Training eroded common myths. Students embraced change more easily than faculty. Implications for teaching and learning in the classroom are discussed. Further PBL research may be used to improve teaching and learning in the classroom. (Contains 2 tables.)

Purpose of Study: This paper seeks to explore the relationship between career aspirations (CA) and academic achievement (AA) for business management technicians (BMTs) from state-run technical institutions (SRTIs) in The Republic of Trinidad and Tobago in the West Indies. Methodology: For the purposes of this study, AA was defined as "task oriented behavior that allows the individual's performance to be evaluated according to some internally or externally imposed criterion that involves the individual in competing with others, or that otherwise involves some standard of excellence" (Spence, 1983, p. 43). AA was measured as a nominal variable (1 = successful completion of the BMT program, 0 = unsuccessful completion of the BMT program). CA referred to the expressed future career wishes of the BMTs. Using a non-convenience, cross-cultural random sample of 500 participants, a questionnaire, semi-structured interviews and academic records provided relevant data. Analysis: Basic descriptive statistical analysis included cross tabulation tables indicating percentages. Qualitative analysis using the unitizing and categorising method provided additional useful information. Research Findings: Results showed that CA appeared to be related to AA. Those BMTs who completed their BMT programs had higher career aspirations than those who did not. Neither age, gender, time to get the job, present job status or area of specialization appeared to affect respondents' career aspirations. CA also appeared to be related to perceived career opportunities at the work place and the fringe benefits received, suggesting the need for employer support. Conclusion/Implications: This paper is particularly valuable to students in their quest for suitable career opportunities to match their academic achievements. Aligning career aspirations with reality could avoid disappointments and unnecessary worry. A new value-based approach to the job search process may be possible with empirical information from this under-researched area of study. (Contains 4 tables.)

Step-by-step teaching is a researcher-designed innovative process that takes the adult learner, step-by-step, from his present level of understanding to the required level. The technique is based on well-researched and accepted pedagogical practices set in their psychological, sociological, and andragogical perspectives. Using a convenience sample of 35 students and a pretest, posttest, control group quasi-experimental design with semistructured interviews and unobtrusive observation, the experimental group outperformed their untrained counterparts. They reported gains in their understanding of fundamental concepts that hitherto had presented them challenges for several years. There was an overall positive change in mathematical achievement, attitudes, beliefs, and self-confidence toward mathematics learning. This research could be a catalyst for more work in this understudied area.