| The rate at which we proceed with reforms in the mathematics high school curriculum suggests that there might be a need for long term effects assessment of programs prior to the implementation of new ones. To this end, the present study constitutes an assessment of mathematical competences of college students (as displayed in solving applied math problems encountered in their current courses), and explores possible linkages with educational history. The study was conducted at the beginning of Year 2000 with forty students in three mathematics-intensive majors: engineering, business and computer science.; By combining results of research in mathematics education on problem solving (Polya, 1945; Schoenfeld, 1985) with those of research in labour sociology (de Terssac, 1996), we designed a grid for classifying errors made by students in solving their applied math problems. This classification allowed assessment of student competencies and identification, through correlation analysis, of possible linkages with individual educational history components (as obtained from a questionnaire). Results showed that students with an inclination towards procedural approach in learning math were the ones who had most troubles in identifying underlying concepts and deciding of a solving strategy. The use of the grid, while proving its value in helping analyze the reasons behind the errors, also showed the inherent difficulties of evaluating competencies: the process is time-consuming and not entirely free from subjective interpretation.; Through qualitative analysis of students' productions and testimonies, we have been able to circumscribe the effects of the procedural orientation of the mathematics curriculum designed in the 80's, and the roles played by application and technology in developing their competencies in mathematics. The results clearly showed that a good performance in mathematics within a curriculum (or a course) designed from a procedural orientation is by no means an indicator of mathematical competence, as one can limit oneself, within such environment, to associating questions and procedures, rely on solved problems for validation, and bypass the meaning of the concepts used.; The use of real-life applications can encourage some students to engage actively in understanding the meaning of the mathematical concepts and their span of application, but the motivation required for this to happen relies heavily on the interest to the students of the applications presented.; The impact of the use of computer software tools on student mathematical competencies appears to depend on the duration of the period of use, the possibility of using these tools at evaluation time, and the degree of analysis required by the learning tasks. At the same time, the presence of these tools in the work environment may well require an increase in mathematical knowledge in order to ensure a degree of autonomy in using them and judging of the validity of the output produced. Finally, the study has shown the differences that exist between the logic of proving and the logic of programming, and the advantage of having developed rigorous deductive thinking in mathematics prior to programming.; Based on the results, we conclude with some curriculum proposals expected to improve the understanding and structuring of mathematical concepts necessary to develop the competencies that are now required in fields where mathematics are being used. |
