This item was digitized by the Internet Archive. Thesis (Ed.D.)--Boston University / https://archive.org/details/decimalusageinoc00russ

Thesis (M.Ed.)--University of Waikato, 2008. / Title from PDF cover (viewed April 27, 2009) Includes bibliographical references (p. 184-199)

The increasing emphasis on teaching arithmetic meaningfully intensifies the search for materials of instruction which can effectively communicate arithmetical understandings to children. Though manipulative aids are widely approved as effective teaching media for achieving this purpose, most of the endorsements are subjective opinions rather than objective evaluations based on experimentation. This study is an attempt to determine the effectiveness of group instruction use of certain manipulative aids in teaching decimal fraction concepts to Grade VII pupils. The effectiveness was determined by comparing the achievement of two unselected groups, randomly assigned, on a test of understanding of the processes involved in decimal fractions. The two groups were given teaching treatments identical except in so far as the materials of instruction were concerned. One group used manipulative aids; the other used static representations of these aids. These materials were intended to differ only with respects to the characteristic of manipulability. Since manipulability of concepts is the most essential property of manipulative aids, it was isolated as the experimental variable. Because the groups were randomly assigned, analysis of covariance was selected to control statistically the initial differences between groups in the four variables considered likely to influence achievement on the criterion test: initial understanding of the processes involved in decimal fractions, computational ability in decimal fractions, mental ability, and reading ability. The data obtained from the investigation were analyzed and the following conclusions reached. 1. The pupils taught by means of group instruction with the manipulative aids used in this investigation did not acquire a significantly better understanding of decimal fractions than did the pupils taught with static representations of these aids. In other words, the manipulation of the concepts, performed by using the manipulative aids in group demonstrations, was not effective in contributing to the pupils’ understanding of these concepts. 2. A study of the correlations for both treatment groups between achievement on the criterion variable and achievement on each of the independent variables indicates that the manipulative aids proved to be neither more nor less effective than the static representations as media for conveying an understanding of decimal fractions to pupils of any particular ability in the areas represented by the independent variables. 3. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, used exclusively by the teacher for group demonstration purposes, would be applicable also to similar materials if they were used in a teaching procedure in which the pupils themselves, participated individually in the manipulative activity. It must not be inferred that any generalization concerning the effectiveness of these specific materials of instruction, which were used in a brief teaching assignment devoted exclusively to the rationalization of processes, would be applicable also to the same materials if they were used in a teaching assignment of longer duration, and/or a teaching assignment in which the emphasis on the WHY of the processes was taught concurrently with, or preceded, the emphasis on the HOW of the processes. 5. Independently of treatment groups, the achievement on the initial test of understanding of the processes involved in decimal fractions was the variable most predictive of achievement on the final test of understanding. Computational ability in decimal fractions and mental ability each shared approximately one-half the predictive capacity of the initial test of understanding. Reading ability was a negligible predictor of achievement on the final test of understanding. / Education, Faculty of / Graduate

Thesis (MEd)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: Research shows that misconceptions about calculations develop in many classrooms without being noticed and these are not corrected by repeated routine exercises. The misconceptions formed are at times the result of inappropriate models used to solve problems. An even bigger concern is that these particular models sometimes provide the correct answers by accident. This may result in the learner's belief in the models being reinforced, as described by Swan (n.d.). The aim of this study is to identify the misconceptions related to the use of decimal fractions by Grade 8 and 9 learners and then, through the use of an intervention program, to address the learners' misconceptions and attempt to correct them. Two schools were involved in this study. The group of learners from school A served as a control group to determine the success of the intervention in learners from school B. The results of school A, the frequency and nature of errors were compared with the test results of school B as well as described by interviews with learners from school B. After the diagnostic tests and interview, the learners' answers were compared with those already described in literature. The learners from school B participated voluntarily in the intervention program. Learners from both schools wrote a post-test and the results were compared with those of a pre-test. The conclusion of this study is that there are misconceptions concerning calculations with decimal fractions at Grade 8 and 9 level. These misconceptions are formed during the intermediate phase and are not suitably corrected. The intervention program, for various reasons, had limited success. These reasons are discussed and recommendations are made for future intervention programs. / AFRIKAANSE OPSOMMING: Navorsing toon dat wanbegrippe ten opsigte van berekeninge in baie klaskamers onopgemerk verbygaan en dat dit nie reggestel word deur herhaalde roetine oefeninge nie. Wanbegrippe wat kinders vorm is onder andere die gevolg van onvanpaste modelle wat gebruik word vir die oplos van probleme. 'n Groter gevaar is dat hierdie onvanpaste modelle toevallig die regte antwoord lewer. Dit kan dan veroorsaak dat die leerder se vertroue op die modelle net versterk word, soos Swan (s.j.) dit beskryf. Die doel van hierdie studie is om wanbegrippe ten opsigte van bewerkings met desimale breuke by Graad 8 en 9 leerders te identifiseer en dan deur middel van 'n intervensieprogram die leerders se wanbegrippe aan te spreek en te probeer regstel. Twee skole is by hierdie studie betrek. Die groep leerders van skool A sou dien as 'n kontrolegroep om die intervensie-sukses van die leerders van skool B te bepaal. Die skool A resultate en frekwensie van foute asook die aard daarvan is vergelyk met die toetse van skool B en beskryf op grond van onderhoude met die leerders van skool B. Ná die diagnostiese toets en onderhoud is die leerders se antwoorde vergelyk met dié wat reeds in die literatuur beskryf is. Die leerders van skool B is op vrywillige basis by 'n intervensieprogram betrek. Beide skole se leerders het daarna 'n natoets geskryf en die resultate is vergelyk met dié van die voortoets. Die gevolgtrekking wat uit hierdie studie gemaak word, is dat daar wanbegrippe ten opsigte van bewerkings met desimale breuke op graad 8 en 9 vlak aanwesig is. Hierdie wanbegrippe is in die intermediêre fase gevorm en nie reggestel nie. Die intervensieprogram het om verskeie redes slegs beperkte sukses gehad. Hierdie redes word bespreek en aanbevelings word gemaak vir toekomstige intervensieprogramme.

As the electronic industry advances rapidly, the dimensions of the semiconductor products keep on being shrunk and that leads to more stringent requirement on process control and quality assurance. In particular, area array packages like BGA, CSP, flip chips, wafer bumping and wafer-level packaging need to have the 3D quality of some micro-surfaces inspected accurately and efficiently. An example of the micro-surfaces is the solder bumps for direct die-to-die bonding, which are of size as small as 60 to 600 microns in diameter. However, the tiny size and often highly specular and textureless nature of the surfaces make the inspection difficult. In addition, the size of the inspection system is required to be small so as to minimize restraint, on the operation of the various moving parts involved in the manufacturing process. / Experimental results with image data of a variety of objects have positively demonstrated the feasibility of the proposed methodology. / In the mechanism the inspection speed is governed by the number of needed images which also equals the number of spatial shiftings of the grating. This thesis also addresses how the grating, as well as its spatial shifting, can be designed optimally for minimizing this image number for faster inspection speed. An optimal solution to shifting strategy optimization is proposed that is applicable to any pattern on the fringe grating. A design method is also introduced for optimal pattern design, which has higher efficiency than brute-force searching. To reduce image number furthermore, bit-pairing codification mechanism and color-encoded pattern are proposed and verified to be more efficient. / In this thesis, I propose a new methodology for reconstructing micro-surfaces in 3D. The mechanism is based upon the familiar concept of binary structured-light, projection, but adapted, for the purpose of greatly reducing the system size, from the traditional setup of an array of multiple light sources to one with a single light source. The mechanism consists of a single light source in combination with a binary grating for projecting a binary pattern onto the target surface, and of a camera for capturing image of the illuminated scene. By shifting the binary grating in space and in every drifting taking a separate image of the illuminated surface, each position on the illuminated surface will be attached with a string of binary code over the sequence of captured images. With a suitable design of the binary grating, the binary code string can be made unique for each bump surface position, allowing exact correspondence between the binary pattern and image data, and subsequently 3D determination through triangulation. With such a bright-or-dark world for each image position, the issues of image saturation, image noise, and textureless nature of the target surfaces are avoided. / Jun Cheng. / "June 2006." / Adviser: Ronald Chi-kit Chung. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6499. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (p. 107-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

M.A. Epstein. / "March 14, 1958"--Cover. "Reprinted from the 1958 IRE National Convention Record, Part 4"--P. 69. / Bibliography: p. 66. / Army Signal Corps Contract DA36-039-sc-64637. Dept. of the Army Task 3-99-06-108 and Project 3-99-00-100.

Shannon showed that the codes with random-like codeword weight distribution are capable of approaching the channel capacity. However, the random-like property can be achieved only in codes with long-length codewords. On the other hand, the decoding complexity for a random-like codeword increases exponentially with its length. Therefore, code designers are combining shorter and simpler codes in a pseudorandom manner to form longer and more powerful codewords. In this research, a method for designing non-binary compound codes with moderate to high coding rate is proposed. Based on this method, non-binary single parity-check (SPC) codes are considered as component codes and different iterative decoding algorithms for decoding the constructed compound codes are proposed. The soft-input soft-output component decoders, which are employed for the iterative decoding algorithms, are constructed from optimal and sub-optimal a posteriori probability (APP) decoders. However, for non-binary codes, implementing an optimal APP decoder requires a large amount of memory. In order to reduce the memory requirement of the APP decoding algorithm, in the first part of this research, a modified form of the APP decoding algorithm is presented. The amount of memory requirement of this proposed algorithm is significantly less than that of the standard APP decoder. Therefore, the proposed algorithm becomes more practical for decoding non-binary block codes. The compound codes that are proposed in this research are constructed from combination of non-binary SPC codes. Therefore, as part of this research, the construction and decoding of the non-binary SPC codes, when SPC codes are defined over a finite ring of order q, are presented. The concept of finite rings is more general and it thus includes non-binary SPC codes defined over finite fields. Thereafter, based on production of non-binary SPC codes, a class of non-binary compound codes is proposed that is efficient for controlling both random-error and burst-error patterns and can be used for applications where high coding rate schemes are required. Simulation results show that the performance of the proposed codes is good. Furthermore, the performance of the compound code improves over larger rings. The analytical performance bounds and the minimum distance properties of these product codes are studied. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2013.

As escritas numéricas e o valor posicional do número são o tema desta pesquisa que tem como objetivos: investigar concepções construídas na interação criança-escrita numérica que contribuem para a construção do valor posicional característico do sistema de numeração decimal; identificar contribuições das notações de números multidígitos à conceituação do valor posicional do número, e verificar as formas cognitivas por meio das quais estas contribuições se efetivam. Consiste num estudo de análise qualitativa.Fundamenta-se na concepção epistemológica construtivista, e volta-se para as microaprendizagens presentes no processo de construção da compreensão do valor posicional e de apropriação da escrita numérica convencional de multidígitos. Envolveu nove alunos da segunda série do Ensino Fundamental de uma escola estadual do município de Erechim-RS, selecionados por sorteio a partir da realização de pré-testes com 44 crianças de três turmas nos quais foram avaliadas noções de composição aditiva, domínio da escrita numérica de multidígitos e do valor posicional. Os critérios utilizados para a seleção foram: compreensão da composição aditiva, não-compreensão do valor posicional e o não-domínio das escritas numéricas de multidígitos. Os alunos participantes da pesquisa, organizados em trios, participaram de onze situações didáticas ao longo do segundo semestre letivo do ano de 2005. A pesquisa evidenciou um processo construtivo não linear, no qual as crianças construíram concepções próximas ao valor posicional, à medida que as situações didáticas provocavam reflexões e sucessivas tomadas de consciência sobre as notações em si e sobre as relações entre escritas e agrupamentos. No que se refere ao valor posicional, a escrita numérica não sugeriu, de imediato, a possibilidade de formarem agrupamentos de acordo com as propriedades do sistema de numeração decimal, do mesmo modo que os agrupamentos (organizados dentro destes princípios) não sugeriram, num primeiro momento, a escrita numérica correspondente. Ambos, escritas e agrupamentos, num primeiro momento, significaram para as crianças a quantidade total representada tanto pelas escritas numéricas quanto pelos agrupamentos. Observou-se uma construção incipiente e progressiva dos princípios aditivo e multiplicativo do sistema, bem como da compreensão da organização do sistema em potências de dez, elementos fundamentais ao reconhecimento do valor relativo do algarismo. As notações, por si só, não foram “transparentes” às crianças e o aprendizado do valor posicional ocorreu a partir da reflexão sobre as relações entre os resultados das ações e sobre as próprias reflexões realizadas por abstrações reflexionantes e tomadas de consciência. / Numeric writings and the number place value are the theme of this research, which aims: to investigate conceptions built on the children-numeric writing interaction that contributes for the construction of place value characteristic of the decimal system; to identify contributions of multidigit numbers to the conceptualization of the number place value and; to verify the cognitive forms through which these contributions are effective. It is a study of qualitative analysis. It is grounded on the constructivist epistemological conception, and it turns to micro-learnings present in the process of construction of place value comprehension and of appropriation of the conventional numeric writing of multidigits. Nine fundamental second grade students from a public state school in the town of Erechim/RS were involved in the research, selected by assortment after the accomplishment of pre-tests with 44 children from three classes in which notions of additive composition, the understanding of numeric writing of multidigit and place value were evaluated. The criteria used for the selection were: comprehension of additive composition, the non-comprehension of place value and the non-dominance of numeric writings of multidigits. The participants of the research, organized in triads, participated in eleven didactic situations during the second school semester of 2005. The research evidenced a constructive, non-linear process, in which children built conceptions close to the place value, as the didactic situations provoked reflections and successive consciousness about notations and about the relations between writings and groupings. Regarding place value, the numeric writing did not suggest, at first, the possibility of forming groups according to the properties of decimal system, in the same manner that the groupings (organized within these principles) did not suggest immediately the correspondent numeric writing. In a first moment, both, writings and groupings, meant for the children the total quantity represented as for numeric writings as for groupings. An incipient and progressive construction of additive and multiplicative principles of the system was observed, as well as the comprehension of the system organization in potencies of tens, fundamental elements for the recognition of the number relative value. The notations, by themselves, were not “transparent” for the children and the learning of place value took place from the reflection about relations between action results and about the reflections accomplished by reflexive abstractions and consciousness. / Las escritas numéricas y el valor posicional del número son temas de esta pesquisa, que tiene como objetivos: investigar concepciones construidas en la interacción niñoescrita numérica que contribuyen para la construcción del valor posicional característico del sistema de numeración decimal; identificar contribuciones de las notaciones de números multidígitos a la conceptuación del valor posicional del número y verificar las formas cognitivas a través de las cuales estas contribuciones se efectúan. Consiste en un estudio de análisis cualitativo. Se fundamenta en la concepción epistemológica constructivista y se vuelve para los microaprendizajes presentes en el proceso de construcción de la comprensión del valor posicional y de apropiación de la escrita numérica convencional de multidígitos. Involucró nueve alumnos del segundo año de la Enseñanza Primaria – 2ª série do Ensino Fundamental – de una escuela estadual del municipio de Erechim-RS, seleccionados, por sorteo, a partir de la realización de pré-testes con 44 niños de tres grupos en los cuales fueron evaluados nociones de composición aditiva, el dominio de la escrita numérica de multidígitos y del valor posicional. Los criterios utilizados para la selección fueron: comprensión de la composición aditiva, no comprensión del valor posicional y el no dominio de las escritas numéricas de multidígitos. Los alumnos participantes de la pesquisa, organizados en triades, participaron de once situaciones-didácticas a lo largo del segundo semestre lectivo del año de 2005. La pesquisa evidenció un proceso constructivo, no linear, en el cual los niños construyeron concepciones próximas al valor posicional, a la medida que las situaciones didácticas provocaban reflexiones y sucesivas tomadas de conciencia sobre las notaciones en si y sobre las relaciones entre escritas y agrupamientos. A lo que se refiere al valor de posición, la escrita numérica no sugirió, de inmediato, la posibilidad de formar agrupamientos de acuerdo con las propiedades del sistema de numeración decimal, del mismo modo que las agrupaciones (organizados dentro de estos principios) no sugirieron de inmediato la escrita numérica correspondiente. Ambos, escritas y agrupamientos, en un primer momento, significaron para los niños la cuantidad total representada tanto por las escritas numéricas, cuanto por los agrupamientos. Se observó una construcción incipiente y progresiva de los principios aditivo y multiplicativo del sistema, bien como de la comprensión de la organización del sistema en potencias de diez, elementos fundamentales al reconocimiento del valor relativo del guarismo. Las notaciones, tan sólo, no fueron “transparentes” los niños y el aprendizaje del valor posicional ocurrió a partir de la reflexión sobre las relaciones entre los resultados de las acciones y sobre las propias reflexiones realizadas por abstracciones reflexionantes y tomadas de conciencia.

As escritas numéricas e o valor posicional do número são o tema desta pesquisa que tem como objetivos: investigar concepções construídas na interação criança-escrita numérica que contribuem para a construção do valor posicional característico do sistema de numeração decimal; identificar contribuições das notações de números multidígitos à conceituação do valor posicional do número, e verificar as formas cognitivas por meio das quais estas contribuições se efetivam. Consiste num estudo de análise qualitativa.Fundamenta-se na concepção epistemológica construtivista, e volta-se para as microaprendizagens presentes no processo de construção da compreensão do valor posicional e de apropriação da escrita numérica convencional de multidígitos. Envolveu nove alunos da segunda série do Ensino Fundamental de uma escola estadual do município de Erechim-RS, selecionados por sorteio a partir da realização de pré-testes com 44 crianças de três turmas nos quais foram avaliadas noções de composição aditiva, domínio da escrita numérica de multidígitos e do valor posicional. Os critérios utilizados para a seleção foram: compreensão da composição aditiva, não-compreensão do valor posicional e o não-domínio das escritas numéricas de multidígitos. Os alunos participantes da pesquisa, organizados em trios, participaram de onze situações didáticas ao longo do segundo semestre letivo do ano de 2005. A pesquisa evidenciou um processo construtivo não linear, no qual as crianças construíram concepções próximas ao valor posicional, à medida que as situações didáticas provocavam reflexões e sucessivas tomadas de consciência sobre as notações em si e sobre as relações entre escritas e agrupamentos. No que se refere ao valor posicional, a escrita numérica não sugeriu, de imediato, a possibilidade de formarem agrupamentos de acordo com as propriedades do sistema de numeração decimal, do mesmo modo que os agrupamentos (organizados dentro destes princípios) não sugeriram, num primeiro momento, a escrita numérica correspondente. Ambos, escritas e agrupamentos, num primeiro momento, significaram para as crianças a quantidade total representada tanto pelas escritas numéricas quanto pelos agrupamentos. Observou-se uma construção incipiente e progressiva dos princípios aditivo e multiplicativo do sistema, bem como da compreensão da organização do sistema em potências de dez, elementos fundamentais ao reconhecimento do valor relativo do algarismo. As notações, por si só, não foram “transparentes” às crianças e o aprendizado do valor posicional ocorreu a partir da reflexão sobre as relações entre os resultados das ações e sobre as próprias reflexões realizadas por abstrações reflexionantes e tomadas de consciência. / Numeric writings and the number place value are the theme of this research, which aims: to investigate conceptions built on the children-numeric writing interaction that contributes for the construction of place value characteristic of the decimal system; to identify contributions of multidigit numbers to the conceptualization of the number place value and; to verify the cognitive forms through which these contributions are effective. It is a study of qualitative analysis. It is grounded on the constructivist epistemological conception, and it turns to micro-learnings present in the process of construction of place value comprehension and of appropriation of the conventional numeric writing of multidigits. Nine fundamental second grade students from a public state school in the town of Erechim/RS were involved in the research, selected by assortment after the accomplishment of pre-tests with 44 children from three classes in which notions of additive composition, the understanding of numeric writing of multidigit and place value were evaluated. The criteria used for the selection were: comprehension of additive composition, the non-comprehension of place value and the non-dominance of numeric writings of multidigits. The participants of the research, organized in triads, participated in eleven didactic situations during the second school semester of 2005. The research evidenced a constructive, non-linear process, in which children built conceptions close to the place value, as the didactic situations provoked reflections and successive consciousness about notations and about the relations between writings and groupings. Regarding place value, the numeric writing did not suggest, at first, the possibility of forming groups according to the properties of decimal system, in the same manner that the groupings (organized within these principles) did not suggest immediately the correspondent numeric writing. In a first moment, both, writings and groupings, meant for the children the total quantity represented as for numeric writings as for groupings. An incipient and progressive construction of additive and multiplicative principles of the system was observed, as well as the comprehension of the system organization in potencies of tens, fundamental elements for the recognition of the number relative value. The notations, by themselves, were not “transparent” for the children and the learning of place value took place from the reflection about relations between action results and about the reflections accomplished by reflexive abstractions and consciousness. / Las escritas numéricas y el valor posicional del número son temas de esta pesquisa, que tiene como objetivos: investigar concepciones construidas en la interacción niñoescrita numérica que contribuyen para la construcción del valor posicional característico del sistema de numeración decimal; identificar contribuciones de las notaciones de números multidígitos a la conceptuación del valor posicional del número y verificar las formas cognitivas a través de las cuales estas contribuciones se efectúan. Consiste en un estudio de análisis cualitativo. Se fundamenta en la concepción epistemológica constructivista y se vuelve para los microaprendizajes presentes en el proceso de construcción de la comprensión del valor posicional y de apropiación de la escrita numérica convencional de multidígitos. Involucró nueve alumnos del segundo año de la Enseñanza Primaria – 2ª série do Ensino Fundamental – de una escuela estadual del municipio de Erechim-RS, seleccionados, por sorteo, a partir de la realización de pré-testes con 44 niños de tres grupos en los cuales fueron evaluados nociones de composición aditiva, el dominio de la escrita numérica de multidígitos y del valor posicional. Los criterios utilizados para la selección fueron: comprensión de la composición aditiva, no comprensión del valor posicional y el no dominio de las escritas numéricas de multidígitos. Los alumnos participantes de la pesquisa, organizados en triades, participaron de once situaciones-didácticas a lo largo del segundo semestre lectivo del año de 2005. La pesquisa evidenció un proceso constructivo, no linear, en el cual los niños construyeron concepciones próximas al valor posicional, a la medida que las situaciones didácticas provocaban reflexiones y sucesivas tomadas de conciencia sobre las notaciones en si y sobre las relaciones entre escritas y agrupamientos. A lo que se refiere al valor de posición, la escrita numérica no sugirió, de inmediato, la posibilidad de formar agrupamientos de acuerdo con las propiedades del sistema de numeración decimal, del mismo modo que las agrupaciones (organizados dentro de estos principios) no sugirieron de inmediato la escrita numérica correspondiente. Ambos, escritas y agrupamientos, en un primer momento, significaron para los niños la cuantidad total representada tanto por las escritas numéricas, cuanto por los agrupamientos. Se observó una construcción incipiente y progresiva de los principios aditivo y multiplicativo del sistema, bien como de la comprensión de la organización del sistema en potencias de diez, elementos fundamentales al reconocimiento del valor relativo del guarismo. Las notaciones, tan sólo, no fueron “transparentes” los niños y el aprendizaje del valor posicional ocurrió a partir de la reflexión sobre las relaciones entre los resultados de las acciones y sobre las propias reflexiones realizadas por abstracciones reflexionantes y tomadas de conciencia.

As escritas numéricas e o valor posicional do número são o tema desta pesquisa que tem como objetivos: investigar concepções construídas na interação criança-escrita numérica que contribuem para a construção do valor posicional característico do sistema de numeração decimal; identificar contribuições das notações de números multidígitos à conceituação do valor posicional do número, e verificar as formas cognitivas por meio das quais estas contribuições se efetivam. Consiste num estudo de análise qualitativa.Fundamenta-se na concepção epistemológica construtivista, e volta-se para as microaprendizagens presentes no processo de construção da compreensão do valor posicional e de apropriação da escrita numérica convencional de multidígitos. Envolveu nove alunos da segunda série do Ensino Fundamental de uma escola estadual do município de Erechim-RS, selecionados por sorteio a partir da realização de pré-testes com 44 crianças de três turmas nos quais foram avaliadas noções de composição aditiva, domínio da escrita numérica de multidígitos e do valor posicional. Os critérios utilizados para a seleção foram: compreensão da composição aditiva, não-compreensão do valor posicional e o não-domínio das escritas numéricas de multidígitos. Os alunos participantes da pesquisa, organizados em trios, participaram de onze situações didáticas ao longo do segundo semestre letivo do ano de 2005. A pesquisa evidenciou um processo construtivo não linear, no qual as crianças construíram concepções próximas ao valor posicional, à medida que as situações didáticas provocavam reflexões e sucessivas tomadas de consciência sobre as notações em si e sobre as relações entre escritas e agrupamentos. No que se refere ao valor posicional, a escrita numérica não sugeriu, de imediato, a possibilidade de formarem agrupamentos de acordo com as propriedades do sistema de numeração decimal, do mesmo modo que os agrupamentos (organizados dentro destes princípios) não sugeriram, num primeiro momento, a escrita numérica correspondente. Ambos, escritas e agrupamentos, num primeiro momento, significaram para as crianças a quantidade total representada tanto pelas escritas numéricas quanto pelos agrupamentos. Observou-se uma construção incipiente e progressiva dos princípios aditivo e multiplicativo do sistema, bem como da compreensão da organização do sistema em potências de dez, elementos fundamentais ao reconhecimento do valor relativo do algarismo. As notações, por si só, não foram “transparentes” às crianças e o aprendizado do valor posicional ocorreu a partir da reflexão sobre as relações entre os resultados das ações e sobre as próprias reflexões realizadas por abstrações reflexionantes e tomadas de consciência. / Numeric writings and the number place value are the theme of this research, which aims: to investigate conceptions built on the children-numeric writing interaction that contributes for the construction of place value characteristic of the decimal system; to identify contributions of multidigit numbers to the conceptualization of the number place value and; to verify the cognitive forms through which these contributions are effective. It is a study of qualitative analysis. It is grounded on the constructivist epistemological conception, and it turns to micro-learnings present in the process of construction of place value comprehension and of appropriation of the conventional numeric writing of multidigits. Nine fundamental second grade students from a public state school in the town of Erechim/RS were involved in the research, selected by assortment after the accomplishment of pre-tests with 44 children from three classes in which notions of additive composition, the understanding of numeric writing of multidigit and place value were evaluated. The criteria used for the selection were: comprehension of additive composition, the non-comprehension of place value and the non-dominance of numeric writings of multidigits. The participants of the research, organized in triads, participated in eleven didactic situations during the second school semester of 2005. The research evidenced a constructive, non-linear process, in which children built conceptions close to the place value, as the didactic situations provoked reflections and successive consciousness about notations and about the relations between writings and groupings. Regarding place value, the numeric writing did not suggest, at first, the possibility of forming groups according to the properties of decimal system, in the same manner that the groupings (organized within these principles) did not suggest immediately the correspondent numeric writing. In a first moment, both, writings and groupings, meant for the children the total quantity represented as for numeric writings as for groupings. An incipient and progressive construction of additive and multiplicative principles of the system was observed, as well as the comprehension of the system organization in potencies of tens, fundamental elements for the recognition of the number relative value. The notations, by themselves, were not “transparent” for the children and the learning of place value took place from the reflection about relations between action results and about the reflections accomplished by reflexive abstractions and consciousness. / Las escritas numéricas y el valor posicional del número son temas de esta pesquisa, que tiene como objetivos: investigar concepciones construidas en la interacción niñoescrita numérica que contribuyen para la construcción del valor posicional característico del sistema de numeración decimal; identificar contribuciones de las notaciones de números multidígitos a la conceptuación del valor posicional del número y verificar las formas cognitivas a través de las cuales estas contribuciones se efectúan. Consiste en un estudio de análisis cualitativo. Se fundamenta en la concepción epistemológica constructivista y se vuelve para los microaprendizajes presentes en el proceso de construcción de la comprensión del valor posicional y de apropiación de la escrita numérica convencional de multidígitos. Involucró nueve alumnos del segundo año de la Enseñanza Primaria – 2ª série do Ensino Fundamental – de una escuela estadual del municipio de Erechim-RS, seleccionados, por sorteo, a partir de la realización de pré-testes con 44 niños de tres grupos en los cuales fueron evaluados nociones de composición aditiva, el dominio de la escrita numérica de multidígitos y del valor posicional. Los criterios utilizados para la selección fueron: comprensión de la composición aditiva, no comprensión del valor posicional y el no dominio de las escritas numéricas de multidígitos. Los alumnos participantes de la pesquisa, organizados en triades, participaron de once situaciones-didácticas a lo largo del segundo semestre lectivo del año de 2005. La pesquisa evidenció un proceso constructivo, no linear, en el cual los niños construyeron concepciones próximas al valor posicional, a la medida que las situaciones didácticas provocaban reflexiones y sucesivas tomadas de conciencia sobre las notaciones en si y sobre las relaciones entre escritas y agrupamientos. A lo que se refiere al valor de posición, la escrita numérica no sugirió, de inmediato, la posibilidad de formar agrupamientos de acuerdo con las propiedades del sistema de numeración decimal, del mismo modo que las agrupaciones (organizados dentro de estos principios) no sugirieron de inmediato la escrita numérica correspondiente. Ambos, escritas y agrupamientos, en un primer momento, significaron para los niños la cuantidad total representada tanto por las escritas numéricas, cuanto por los agrupamientos. Se observó una construcción incipiente y progresiva de los principios aditivo y multiplicativo del sistema, bien como de la comprensión de la organización del sistema en potencias de diez, elementos fundamentales al reconocimiento del valor relativo del guarismo. Las notaciones, tan sólo, no fueron “transparentes” los niños y el aprendizaje del valor posicional ocurrió a partir de la reflexión sobre las relaciones entre los resultados de las acciones y sobre las propias reflexiones realizadas por abstracciones reflexionantes y tomadas de conciencia.