A subject didactic analysis of the development of the spatial knowledge of young children through a problem-centred approach to mathematics teaching and learning Researchers and educators are in agreement that it is very important that the spatial knowledge of the young child should be developed from the first years of school. In order to develop these skills the appropriate materials and activities need to be designed. This can only be realised through proper research methods that not only acknowledge the cognitive abilities of the young child, but also the social and cultural backgrounds of the children. This implies that due attention should be given to language, beliefs, cognitive skills, socio-economic background, schooling and teaching systems. The immediate worlds of the children should be used in developing the spatial skills of these children. The work that is described in this document is an effort to describe the complexity of such a research endeavour. The development of the spatial skills of young children were investigated through three different instructional/executional media namely language, drawing/writing and physical constructions. The three major variables that were described as influencing the spatial development in the different media were the task that was given to the children, the objects that the children worked with and the dimension and viewpoints of the objects and situations. It was clear from the research that in the development of the spatial skills of children, attention should. be given to: the real-world of the children, hands-on-experiences of the children, the cultural background, the language of instruction, the socio-economic background the classroom culture, the media of instruction and the cognitive skills of the children. / Proefskrif (PhD (Didaktiese Opvoedkunde))--PU vir CHO, 1997

A subject didactic analysis of the development of the spatial knowledge of young children through a problem-centred approach to mathematics teaching and learning Researchers and educators are in agreement that it is very important that the spatial knowledge of the young child should be developed from the first years of school. In order to develop these skills the appropriate materials and activities need to be designed. This can only be realised through proper research methods that not only acknowledge the cognitive abilities of the young child, but also the social and cultural backgrounds of the children. This implies that due attention should be given to language, beliefs, cognitive skills, socio-economic background, schooling and teaching systems. The immediate worlds of the children should be used in developing the spatial skills of these children. The work that is described in this document is an effort to describe the complexity of such a research endeavour. The development of the spatial skills of young children were investigated through three different instructional/executional media namely language, drawing/writing and physical constructions. The three major variables that were described as influencing the spatial development in the different media were the task that was given to the children, the objects that the children worked with and the dimension and viewpoints of the objects and situations. It was clear from the research that in the development of the spatial skills of children, attention should. be given to: the real-world of the children, hands-on-experiences of the children, the cultural background, the language of instruction, the socio-economic background the classroom culture, the media of instruction and the cognitive skills of the children. / Proefskrif (PhD (Didaktiese Opvoedkunde))--PU vir CHO, 1997

Orientador: Marcia Regina Ferreira de Brito / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-05T04:06:21Z (GMT). No. of bitstreams: 1 Viana_OdaleaAparecida_D.pdf: 13457630 bytes, checksum: cf0ae91ebe117f9120972fbd9fc97dc2 (MD5) Previous issue date: 2005 / Resumo: Considerando a influência de fatores cognitivos e afetivos no desempenho escolar em geometria, este trabalho teve como objetivos analisar o componente espacial da habilidade matemática e verificar a existência de relações entre este componente, o raciocínio espacial, as atitudes em relação à matemática e à geometria e o desempenho escolar. Foram sujeitos 177 alunos de ensino médio de uma escola particular, tendo sido aplicadas duas provas tipo lápis e papel, um teste psicológico de raciocínio espacial e duas escalas de atitudes em relação à matemática e geometria. A análise fatorial das operações do componente espacial da habilidade matemática (contagem de cubos, formação e identificação de polígonos no espaço, secção, planificação, projeção e revolução) indicou a existência de um único fator, o que comprova que a prova avaliou a habilidade geral dos sujeitos em lidar com conceitos geométricos espaciais trabalhados no ensino médio, com base nas tarefas propostas. As atitudes em relação à matemática estavam relacionadas com as atitudes em relação à geometria. O desempenho em geometria estava relacionado com o raciocínio espacial, com o componente espacial da habilidade matemática e com as atitudes em relação à geometria. O trabalho faz referência aos processos de formação, inspeção e transformação de imagens mentais evidenciados nas fases de obtenção e de processamento da informação geométrica de problemas. As representações pictóricas externas demonstradas na solução de problemas geométricos com estrutura espacial foram classificadas de acordo com a funcionalidade, coerência e detalhamento, sendo que os dados mostraram que sujeitos mais habilidosos elaboram representações parciais e coerentes e não as utilizavam com a função de assistência perceptual.Psicologia da educação matemática; ensino de geometria; habilidade matemática; raciocínio espacial; habilidade visual / Abstract: In considering the influence of cognitive and affective factors in academic achievement of geometry, the objectives of this work were to analyze the spatial component of mathematical ability and to verify the existence of relations among this component, the spatial sense, the attitudes toward Mathematics and Geometry and the academic performance. The subjects of this research were 177 students, from three grades of a particular school from Mogi das Cruzes ¿ SP. Two questionnaires with pencil and paper, one spatial sense test and two attitudes scales toward mathematics and geometry were applied. The factorial analysis of spatial component operations of mathematics ability (counting of cubes, formation and identification of polygon in space, section, planning, projection and rotation) indicated the existence of one factor. It proved that the test evaluated the general ability to deal with geometric concepts that are taught in the secondary school, taking into account the proposed tasks. The attitudes toward Mathematics were related to the attitudes toward geometry. The geometry performance was related to the spatial sense, to the spatial component of mathematical ability and to the attitudes toward mathematics and geometry. This work made reference to the formation, inspection and transformation of visual mental images, whose processes were evidenced in the phases of acquisition and processing of problems geometrical information. The external graphical representations that were evidenced in the solution of geometry problems with the spatial structure were classified according to the function, coherence and detailing, and the dates indicated that the most talented students made partial and coherent representations and did not utilize them as perceptual assistance.Psychology of Mathematics Education; geometry teaching; mathematical abilities; spatial sense / Doutorado / Educação Matematica / Doutor em Educação

Ce mémoire, se situant dans le champ de la didactique des mathématiques, contribue à l’avancement des connaissances sur le développement des connaissances spatiales (CS) des élèves au primaire. Bien que le développement de ces connaissances soient importantes pour surpasser plusieurs difficultés scolaires (Duval, 2005; Ekimova-Boublil, 2005), peu de recherches se sont intéressées au développement de celles-ci en situation de jeu et de mouvement qui ont tous deux été révélés comme des pratiques gagnantes pour accroitre les connaissances spatiales. L’objectif de cette recherche est donc d’enrichir les connaissances entourant le développement des CS lors d’un jeu en mouvement auprès d’élèves du primaire. Pour ce faire, nous avons utilisé l’outil développé par Marchand (2020) et Marchand et Munier (2021), la « Structure génératrice d’activités » (SGA) pour rendre compte des CS employées par les élèvesselon les trois balises de cet outil, soit les composantes des CS, les niveaux d’abstraction et les variables entourant la situation, et plus particulièrement les tâches effectuées. De plus, afin de définir le jeu en mouvement, nous nous sommes inspirées des travaux de Sauvé et al. (2007), de Pelczer (2013) et de Héroux et Proulx (2015). Afin de mettre en place notre contexte, nous avons effectué un Teaching experiment (TE) particulier. Ce TE a pris la forme de trois séances d’une trentaine de minutes auprès de douze élèves d’une classe primaire. Une analyse détaillée de ces trois séances nous a permis d’établir une relation existante entre les composantes de CS et les différents niveaux d’abstraction utilisés. Les élèves se sont alors vu.es utiliser des niveaux d’abstraction de plus en plus complexes en réalisant des activités visant à développer leurs CS. Ces résultats ont également montré que les catégories de tâches utilisées par les élèves influencent le développement des CS, selon l'activité proposée. Finalement, l’analyse de ce TE nous a permis de ressortir quelques retombés, limites et prolongements possibles. / This dissertation, in the field of mathematics didactics, contributes to the advancement of knowledge on the development of spatial knowledge (SK) in primary school learners. Although the development of this knowledge is important for overcoming many academic difficulties (Duval, 2005; Ekimova-Boublil, 2005), little research has focused on the development of this knowledge in situations of games and movement. However, both of which have been shown to be winning practices for increasing spatial knowledge. The aim of this research is to expand our knowledge of the development of SK in moving game with elementary school students. To achieve this, we used the tool developed by Marchand (2020) and Marchand and Munier (2021), the "Structure génératrice d'activités" (SGA), to reflect the CS employed by students according to the three markers of this tool, namely the components of SK, the levels of abstraction and the variables surrounding the situation, and more specifically the tasks performed. In addition, in order to define moving game, we relied on the work of Sauvé et al. (2007), Pelczer (2013) and Héroux and Proulx (2015). In order to implement our context, we carried out a special teaching experiment (TE). This TE took the form of three 30-minute sessions with twelve elementary school students. A detailed analysis of these three sessions enabled us to establish an existing relationship between SK components and the different levels of abstraction used. The students were seen to employ increasingly complex levels of abstraction as they carried out activities aimed at developing their SK. These results also showed that the task categories used by students influence the development of SK, depending on the activity proposed. Finally, our analysis of this TE has enabled us to identify a number of possible spin-offs, limitations and extensions.

Text in Afrikaans / Die doel van hierdie navorsing was om vas te stel of leerders in Graad R die nodige wiskundige vaardighede deur gestruktureerde spel bemeester het wat as grondslag vir verdere wiskunde-onderrig kan dien. In die literatuurstudie is die verskillende wiskunde konsepte in diepte ondersoek. Daar is ook gefokus op die oordra van wiskunde konsepte aan jong leerders. Verder is daar in die literatuurstudie ondersoek ingestel na die doel, waardes, tipes, ontwikkeling van spel asook spel in die moderne era. Vir die empiriese ondersoek is 103 Graad R-leerders van ses verskillende skole betrek. Daar is gebruik gemaak van ʼn ewekansige steekproef by die skole wat bereid was om aan die studie deel te neem. Die ondersoek het plaasgevind deur die gebruik van die positivistiese kwantitatiewe navorsingsmetode. Daar is gebruik gemaak van vraelyste om te bepaal wat die bemeestering van wiskundige vaardighede by Graad R-leerders is. Gestruktureerde spel is as hulpmiddel gebruik vir die insameling van die navorsingsmateriaal. Die resultate is bekom deur die vraelyste statisties te verwerk. Daar is ook vraelyste aan die onderwysers gegee om meer agtergrond oor hulle onderrigmetodes asook die onderwysers se eie gevoel teenoor en kennis van wiskunde te bekom. Die navorsingsresultate bevestig dat die meerderheid van die Graad R-leerders oor ʼn goeie wiskundige grondslag beskik. Dus is daar deur die studie gevind dat dit belangrik is dat jong kinders baie moet speel om nuwe vaardighede aan te leer, maar ook die geleentheid moet hê om die vaardighede te beoefen. / The purpose of this research was to determine whether learners in Grade R mastered the necessary math skills through structured play that could serve as a basis for further mathematics training. In the literature various math concepts were studied in depth. The main focus was on the transfer of math concepts to young learners. The literature study further focussed on the purpose, values, and types of play, development of play and play in the modern era. An empirical study using random sampling was done using 103 Grade R learners from six different schools who were willing to participate in the study. The study was done using the positivism quantitative research methodology. Questionnaires were used to determine the mastery of mathematical skills by Grade R learners. Structured play was used as a tool to collect the research material. The results were obtained by processing the questionnaires statistically. Questionnaires were also completed by the teachers to confirm their background knowledge, teaching methods as well as to determine the teachers‟ own feelings towards and their knowledge of mathematics. The research results confirm that the majority of Grade R learners have obtained a good math foundation. The study also confirmed that it is important that young children need to play to learn new skills and must have the opportunity to practise the new skills. / Psychology of Education / D. Ed. (Sielkundige Opvoedkunde)

Text in Afrikaans / Die doel van hierdie navorsing was om vas te stel of leerders in Graad R die nodige wiskundige vaardighede deur gestruktureerde spel bemeester het wat as grondslag vir verdere wiskunde-onderrig kan dien. In die literatuurstudie is die verskillende wiskunde konsepte in diepte ondersoek. Daar is ook gefokus op die oordra van wiskunde konsepte aan jong leerders. Verder is daar in die literatuurstudie ondersoek ingestel na die doel, waardes, tipes, ontwikkeling van spel asook spel in die moderne era. Vir die empiriese ondersoek is 103 Graad R-leerders van ses verskillende skole betrek. Daar is gebruik gemaak van ʼn ewekansige steekproef by die skole wat bereid was om aan die studie deel te neem. Die ondersoek het plaasgevind deur die gebruik van die positivistiese kwantitatiewe navorsingsmetode. Daar is gebruik gemaak van vraelyste om te bepaal wat die bemeestering van wiskundige vaardighede by Graad R-leerders is. Gestruktureerde spel is as hulpmiddel gebruik vir die insameling van die navorsingsmateriaal. Die resultate is bekom deur die vraelyste statisties te verwerk. Daar is ook vraelyste aan die onderwysers gegee om meer agtergrond oor hulle onderrigmetodes asook die onderwysers se eie gevoel teenoor en kennis van wiskunde te bekom. Die navorsingsresultate bevestig dat die meerderheid van die Graad R-leerders oor ʼn goeie wiskundige grondslag beskik. Dus is daar deur die studie gevind dat dit belangrik is dat jong kinders baie moet speel om nuwe vaardighede aan te leer, maar ook die geleentheid moet hê om die vaardighede te beoefen. / The purpose of this research was to determine whether learners in Grade R mastered the necessary math skills through structured play that could serve as a basis for further mathematics training. In the literature various math concepts were studied in depth. The main focus was on the transfer of math concepts to young learners. The literature study further focussed on the purpose, values, and types of play, development of play and play in the modern era. An empirical study using random sampling was done using 103 Grade R learners from six different schools who were willing to participate in the study. The study was done using the positivism quantitative research methodology. Questionnaires were used to determine the mastery of mathematical skills by Grade R learners. Structured play was used as a tool to collect the research material. The results were obtained by processing the questionnaires statistically. Questionnaires were also completed by the teachers to confirm their background knowledge, teaching methods as well as to determine the teachers‟ own feelings towards and their knowledge of mathematics. The research results confirm that the majority of Grade R learners have obtained a good math foundation. The study also confirmed that it is important that young children need to play to learn new skills and must have the opportunity to practise the new skills. / Psychology of Education / D. Ed. (Sielkundige Opvoedkunde)