Le programme -Une école adaptée à tous ses élèves-, qui s'inscrit dans la réforme actuelle de l'éducation au Québec, nous a amenée à nous intéresser aux représentations dans les grandeurs en mesure en mathématiques des élèves en difficulté d'apprentissage. Nous nous sommes proposés de reconduire plusieurs paramètres de la recherche de Brousseau (1987, 1992) auprès de cette clientèle. La théorie des champs conceptuels (TCC) de Vergnaud (1991), appliquée aux structures additives, a été particulièrement utile pour l'analyse et l'interprétation de leurs représentations. Comme méthode de recherche, nous avons utilisé la théorie des situations didactiques en mathématiques (TSDM), réseau de concepts et de méthode de recherche appuyé sur l'ingénierie didactique qui permet une meilleure compréhension de l'articulation des contenus à enseigner. Grâce à la TSDM, nous avons observé les approches didactiques des enseignants avec leurs élèves. Notre recherche est de type exploratoire et qualitatif et les données recueillies auprès de 26 élèves de deux classes spéciales du deuxième cycle du primaire ont été traitées selon une méthode d'analyse de contenu. Deux conduites ont été adoptées par les élèves. La première, de type procédural a été utilisée par presque tous les élèves. Elle consiste à utiliser des systèmes de comptage plus ou moins sophistiqués, de la planification aux suites d'actions. La deuxième consiste à récupérer directement en mémoire à long terme le résultat associé à un couple donné et au contrôle de son exécution. L'observation des conduites révèle que les erreurs sont dues à une rupture du sens. Ainsi, les difficultés d'ordre conceptuel et de symbolisation nous sont apparues plus importantes lorsque l'activité d'échange demandait la compétence "utilisation" et renvoyait à la compréhension de la tâche, soit les tâches dans lesquelles ils doivent eux-mêmes découvrir les rapports entre les variables à travailler et à simuler les actions décrites dans les énoncés. En conséquence, les problèmes d'échanges se sont révélés difficiles à modéliser en actes et significativement plus ardus que les autres. L'étude des interactions enseignants et élèves a démontré que la parole a été presque uniquement le fait des enseignants qui ont utilisé l'approche du contrôle des actes ou du sens ou les deux stratégies pour aider des élèves en difficulté. Selon le type de situation à résoudre dans ces activités de mesurage de longueur et de masse, des mobilisations plurielles ont été mises en oeuvre par les élèves, telles que la manipulation d'un ou des étalon(s) par superposition, par reports successifs, par pliage ou par coupure lorsque l'étalon dépassait; par retrait ou ajout d'un peu de sable afin de stabiliser les plateaux. Nous avons également observé que bien que certains élèves aient utilisé leurs doigts pour se donner une perception globale extériorisée des quantités, plusieurs ont employé des procédures très diverses au cours de ces mêmes séances. Les résultats présentés étayent l'hypothèse selon laquelle les concepts de grandeur et de mesure prennent du sens à travers des situations problèmes liées à des situations vécues par les élèves, comme les comparaisons directes. Eles renforcent et relient les grandeurs, leurs propriétés et les connaissances numériques. / -An education system adjusted to all its pupils-, in line with the present reform of the education system of Québec has led us in this project, to examine how students with learning problems deal with numbers and measurements in mathematics. In the present study, our purpose is to double-check many of the parameters defined in the work of Brousseau (1987, 1992). The theory of the conceptual fields of Vergnaud (1991)applied to the additives structures, was particularly useful in our analysis of the facts and the interpretation of their representations. In this work, the methodology we adopted is the Didactic engineering, wich allow a better understanding in articulating the contents to each. Using Theory of didactic situations in mathematics, we examined the didactic approaches the teachers have in their relationship with their students. The data for our study, which is of the exploratory and qualitative type, was collected with twenty six students of the second cycle of the primary school. That data was analysed in conformity with a medthodology of content analysis. The examination of the student's behavior revealed two attitudes. Almost all the students used the first attitude, which is of the procedural type. It consisted in using counting systems more or less sophisticated from the planning to the folowing actions involved. The second attitude implied memorizing for the long term, the result associated with a specific couple of actions and the control of their execution. The observaton of the student's attitudes reveals that the errors they made are related to a semantic disruption in their interpretation of the varied tips and strategies the teachers tried to help them with to solve the different problems. Thus, it appeared to us that the difficulties at the conceptual and symbolization levels were more important when the exchange activity involved their competence to evaluate and activity related to the understanding to the task to achieve. In other terms, they had more difficulty with the tasks where they had to establish by themselves to link between the variables, and simulate the actions involved by those tasks. Consequently, the tasks involving exchange operations happened to be more difficult to translate into actions, and were clearly more problematic than the other tasks. The study of the interaction between teachers and students revealed that only teachers used words in the process, where they used the approach of the control of the actions, or the approach of control of the meaning or both strategies to help students with problems. Depending on the type of problem encountered during these activities of measurements of length and masses, the students had recourse to numerous experiments such as manipulation of the standard measure(s). They proceeded by superimposing, by successive deferments, by folding, by cutting when the standard was exceeding in size; or by reduction or addition of some amount of sand to bring into balance the scale. We noticed also that despite the fact that certain students used their fingers to have a global idea of the external measures of the quantities, many of those same students had recourse to a diversity of other procedures during the same test. The result presented here support the hypothesis that says that the concepts of size and measurement get more meaning in a specific context, where they relate to real situations lived by the students, as well as by direct comparisons. They reinforce and establish links between the so-called sizes, their properties and the numeric knowledge.

There are numerous problems associated with the teaching of Euclidean geometry at secondary schools today. Students do not see the necessity of proving results which have been obtained intuitively. They do not comprehend that the validity of a deduction is independent of the 'truth' of the initial assumptions. They do not realise that they cannot reason from diagrams, because these may be misleading or inaccurate. Most importantly, they do not understand that Euclidean geometry is a particular interpretation of physical space and that there are alternative, equally valid interpretations. A possible means of addressing the above problems is tbe introduction of nonEuclidean geometry at school level. It is imperative to identify those students who have the pre-requisite knowledge and skills. A number of interesting teaching strategies, such as debates, discussions, investigations, and oral and written presentations, can be used to introduce and develop the content matter. / Mathematics Education / M. Sc. (Mathematics)

This study examines stresses experienced by primary school learners with learning problems in inclusive classrooms in an Independent School. Literature suggests that learners with learning problems experience more academic, emotional and social difficulties at school than do their peers without learning problems. The Transactional Model of stress was used as a point of departure for the qualitative empirical study to understand stress as it is experienced by three Grade 4 learners. Several school stresses were identified which contributed to unmet emotional and social needs. The three central sources of stress were classified as S1 (Inability to meet perceived/anticipated demand), S2 (Overload – too much expected) and S3 (Selfexpectations not met). The learners’ own suggestions regarding the relief of these stresses were examined and contributed to guidelines to assist teachers in relieving these stresses experienced by learners with learning problems in the inclusive classroom. / Psychology of Education / M. Ed. (Guidance and Counselling)

This study examines stresses experienced by primary school learners with learning problems in inclusive classrooms in an Independent School. Literature suggests that learners with learning problems experience more academic, emotional and social difficulties at school than do their peers without learning problems. The Transactional Model of stress was used as a point of departure for the qualitative empirical study to understand stress as it is experienced by three Grade 4 learners. Several school stresses were identified which contributed to unmet emotional and social needs. The three central sources of stress were classified as S1 (Inability to meet perceived/anticipated demand), S2 (Overload – too much expected) and S3 (Selfexpectations not met). The learners’ own suggestions regarding the relief of these stresses were examined and contributed to guidelines to assist teachers in relieving these stresses experienced by learners with learning problems in the inclusive classroom. / Psychology of Education / M. Ed. (Guidance and Counselling)

After the dispensation of the White Paper 6 in schools, there were no detailed guidelines to accommodate the learners with invisible impairments like absence epilepsy, especially those who live in underprivileged communities. Affected learners are still struggling and not receiving proper instruction in ordinary schools because of the nature of absence epilepsy. It seems like it is unknown that they are suffering, because the symptoms are absent. These learners are performing poorly; they are having learning and behavioural problems. At home parents are ignorant of their plight, teachers are oblivious of their problems and at schools they are being discriminated against by other children. As a result, they repeat grades and some end up leaving school to join the unemployed. They have a low self-esteem and remain unsociable. This is because they suffer from absence epilepsy which is a medical problem. Absence epilepsy is unknown to both parents and teachers in these communities. Cultural beliefs and ignorance prevent parents from taking these children to clinics for identification, which results in them not being supported in schools. / Inclusive Education / M. Ed. (Inclusive Education)

Summaries in English and Afrikaans / Practical research has shown that children with learning disabilities often experience psychosocial problems. These problems not only have an influence on the parent-child relationship, but also impact negatively on the psychological development of the child. The objective of this study is to explore these psychosocial problems by investigating the personal experiences of the learning disabled child within his immediate family. The literature study on learning disabilities shows that it is a complex condition that not only manifests in learning problems, but which can also adversely affect the child in totality. The Relation theory, an educational psychological perspective, functions as a theoretical framework for exploration, and is discussed with reference to psychosocial problems of the learning disabled child. In the empirical study, the researcher has primarily employed projection techniques to investigate the child's experiences of himself and his relationships with family members, from his internal frame of reference. From these findings, recommendations are proposed for psychotherapy. / Uit die praktyk blyk dit dat leergestremdheid by kinders dikwels met psigososiale probleme gepaard gaan. Nie alleen beinvloed hlerdie problema die ouer~kindverhouding nie, maar dit het ook 'n negatiewe invloed op die psigiese ontwikkeling van die kind. Die doel van die studie is om die persoonlike belewenisse van die leergestremde kind binne die gesin te verken. Die meratuurstudie wat oor die verskynsel van leergestremdheid gedoen is, het getoon dat dit 'n kompleksa toestand is wat nie aileen met leerprobleme gepaard gaan nie, maar ook die kind in sy totallteit nadelig bei'nvloed. Die Relasieteorie, 'n opvoedkundig-sielkundige perspektief, wat as teoretiese raamwerk vir verkenning dien, is bespreek en waar toepaslik is na die psigososiale problema van die leergestremde kind verwys. In die empiriese ondersoek is hoofsaaklik van projeksietegnieke gebruik gemaak om vanuit die leergestremde kind se interne verwysingsraamwerk sy persepsies en belewenisse ten opsigte van homself en sy verhoud!ngs in die gesin te verken. Na aanleiding hiervan is aanbevelings vir terapeutiese hulpverlening gemaak. / Educational Studies / M. Ed. (Specialisation in Guidance and Counseling)

Summaries in English and Afrikaans / Practical research has shown that children with learning disabilities often experience psychosocial problems. These problems not only have an influence on the parent-child relationship, but also impact negatively on the psychological development of the child. The objective of this study is to explore these psychosocial problems by investigating the personal experiences of the learning disabled child within his immediate family. The literature study on learning disabilities shows that it is a complex condition that not only manifests in learning problems, but which can also adversely affect the child in totality. The Relation theory, an educational psychological perspective, functions as a theoretical framework for exploration, and is discussed with reference to psychosocial problems of the learning disabled child. In the empirical study, the researcher has primarily employed projection techniques to investigate the child's experiences of himself and his relationships with family members, from his internal frame of reference. From these findings, recommendations are proposed for psychotherapy. / Uit die praktyk blyk dit dat leergestremdheid by kinders dikwels met psigososiale probleme gepaard gaan. Nie alleen beinvloed hlerdie problema die ouer~kindverhouding nie, maar dit het ook 'n negatiewe invloed op die psigiese ontwikkeling van die kind. Die doel van die studie is om die persoonlike belewenisse van die leergestremde kind binne die gesin te verken. Die meratuurstudie wat oor die verskynsel van leergestremdheid gedoen is, het getoon dat dit 'n kompleksa toestand is wat nie aileen met leerprobleme gepaard gaan nie, maar ook die kind in sy totallteit nadelig bei'nvloed. Die Relasieteorie, 'n opvoedkundig-sielkundige perspektief, wat as teoretiese raamwerk vir verkenning dien, is bespreek en waar toepaslik is na die psigososiale problema van die leergestremde kind verwys. In die empiriese ondersoek is hoofsaaklik van projeksietegnieke gebruik gemaak om vanuit die leergestremde kind se interne verwysingsraamwerk sy persepsies en belewenisse ten opsigte van homself en sy verhoud!ngs in die gesin te verken. Na aanleiding hiervan is aanbevelings vir terapeutiese hulpverlening gemaak. / Educational Studies / M. Ed. (Specialisation in Guidance and Counseling)