Submitted by Caroline Falcao (caroline.rfalcao@ufpe.br) on 2017-06-19T17:49:08Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) 2011-Dissertacao-Tatyane-Veras-De-Queiroz.pdf: 1221590 bytes, checksum: 8a4a86ea3d37c88bdae2dfff9f39feee (MD5) / Made available in DSpace on 2017-06-19T17:49:08Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) 2011-Dissertacao-Tatyane-Veras-De-Queiroz.pdf: 1221590 bytes, checksum: 8a4a86ea3d37c88bdae2dfff9f39feee (MD5) Previous issue date: 2011-05-27 / Estudo envolvendo a compreensão dos conceitos matemáticos emcrianças e adolescentes surdos tem se tornado relevantedevido à proposta de uma educação inclusiva. A presente pesquisa tem porobjetivoinvestigar o efeito de diferentes formas de apresentação de problemas (português, interlíngua e Libras) e dos suportes de representação (material concreto definido, lápis e papel e representação visual) na resolução de problemas de multiplicação por crianças surdas. Para tal foram entrevistados 88 estudantes, surdos e ouvintes, do Ensino Fundamental de escolas públicas do Recife, alocadosigualmente em quatro grupos (G1 –surdos sem instrução; G2 –surdos com instrução; G3 –ouvintes sem instrução; G4 –ouvintes com instrução), que realizaram quatro tarefas (T1-Sondagem, T2-Português, T3-Interlíngua e T4-Libras, sendo esta última aplicada apenas com os surdos). Os principais resultados foram os seguintes: (a) o efeito da forma como o problema é apresentado:os participantes apresentaram desempenhos diferentes em relação às tarefas (T2, T3 e T4), diferindo em relação àforma como o problema estava escrito ou era apresentado. A forma escrita da Tarefa 2 favoreceu o desempenho dos ouvintes enquanto aforma da Tarefa 3 e Tarefa 4 favoreceu aos surdos; (b) efeito dos suportes de representação de acordo com as situações propostas:osdados apontaram que os suportes interferiram no desempenho juntamente com a forma escrita dos problemas, ou seja, nas tarefas em que o grupo teve dificuldade em relação à escrita, o suporte parecia auxiliar na resolução, como o lápis e papel para os surdos na Tarefa 2. Nas Tarefas 3 e 4, em que os grupos não apresentaram dificuldades, o desempenho em relação aos suportes era semelhante, não havendo diferenças significativas; (c) estratégias adotadas por surdos:dependia do nível de instrução de cada grupo e da situação proposta em cada tarefa, assim, as estratégias mais elaboradas emergiram nos grupos com instrução formal da multiplicação, enquanto que as estratégias mais simples foram adotadas por grupos sem instrução. A partir desses resultados, é possível dizer que aproximar a forma de apresentação dos enunciados matemáticos à realidade dos surdos contribui para o desempenhoe para o surgimento de estratégias mais elaboradas, principalmente quando associada a alguns suportes de representação, como o material concreto definido (para os sem instrução) e o lápis e papel (para os com instrução). Portanto, é necessário pensar em rotas alternativas de ensino, em salas de aula inclusivas, para aquisição de conceitos matemáticos por surdos. / Studies involving the understanding of mathematical concepts in deaf children and teenagers have become increasingly relevant due to the proposed inclusive education. This research aims to investigate the effect of different ways of presenting problems (Portuguese, Interlingua and Sign Language) and the representational supports (specific material, pencil and paper and visual representation) in solving multiplication problems by deafchildren. To this end, 88 deaf and hearing students from Elementary Public Schools in Recife were interviewed and allocated equally into four groups (Group 1 -deaf without instruction; Group 2 -deaf with instruction; Group 3 -listeners without instruction; Group 4 -listeners with instruction) that performed four tasks (T1 -Sounding out, T2 -Portuguese, T3 –Interlingua, T4 –Pounds, latter applied only with deaf people). The main results were as follows: (a) the effect of how the problem is presented: the participants had different performances related to the tasks 2, 3 and 4, according to how the problem was wrote or presented. The written form in Task 2 favored the listeners’ performance while the Task 3 and 4 helped the deaf. (b) the effect of the representational supports according to proposed situations:the collected data indicated that the performance was interfered along with the problems in written form, in other words, the tasks in which the group had writing difficulties, the representation tools seemed to help solving the situation, like the paper and pencil helped the deaf ones in the Task 2. In the tasks 3 and 4, in which the groups had no difficulties, the performance related to the representation supports was similar, not having major differences; (c) the strategies used by the deaf:it depended on the education level of each group and the situation presented on each task, so the most refined strategies appeared in the groups with formal instruction in multiplication, while the simplest strategies have been adopted by groups without instruction. From these results, it is possible to say that making the way of presenting mathematics questions closer to the reality of deaf people helps their performance and the creation of refined strategies, mainly when is using the representational support such as the concret materials (to the deaf without instruction) and pencil and paper (to the deaf with instruction). Therefore, it is necessary to think in new alternative ways of teaching in inclusive classrooms, so the deaf students can understand mathematical concepts.

Primarily via constructivist teaching experiment methodology, units coordination (Steffe, 1992) has emerged as a useful construct for modeling students' psychological constructions pertaining to several mathematical domains, including counting sequences, whole number multiplicative conceptions, and fractions schemes. I describe how consideration of units coordination as a Piagetian (1970b) structure is useful for modeling units coordination across contexts. In this study, I extend teaching experiment methodology (Steffe and Thompson, 2000) to model the dynamics of students' units coordinating activity across contexts within a teaching experiment, using the construct of propensity to coordinate units. Two video-recorded teaching experiments involving pairs of sixth-grade students were analyzed to form a model of the dynamics of students' units coordinating activity. The modeling involved separation of transcriptions into chunks that were coded dichotomously for the units coordinating activity of a single student in each dyad. The two teaching experiments were used to form 5 conjectures about the output of the model that were then tested with a third teaching experiment. The results suggest that modeling units coordination activity via the construct of propensity to coordinate units was useful for describing patterns in the students' perturbations during the teaching sessions. The model was moderately useful for identifying sequences of interactions that support growth in units coordination. Extensions, modifications, and implications of the modeling approach are discussed. / Ph. D.

Multiplicative reasoning permeates many mathematical topics, for example fractions and functions. Hence there is consensus on the importance of acquiring multiplicative reasoning. Multiplication is typically introduced as repeated addition, but when it is extended to include multi-digits and decimals a more general view of multiplication is required. There are conflicting reports in previous research concerning students’ understandings of multiplication. For example, repeated addition has been suggested both to support students’ understanding of calculations and as a hindrance to students’ conceptualisation of the two-dimensionality of multiplication. The relative difficulty of commutativity and distributivity is also debated, and there is a possible conflict in how multiplicative reasoning is described and assessed. These inconsistencies are addressed in a study with the aim of understanding more about students’ understandings of multiplication when it is expanded to comprise multi-digits and decimals. Understanding is perceived as connections between representations of different types of knowledge, linked together by reasoning. Especially connections between three components of multiplication were investigated; models for multiplication, calculations and arithmetical properties. Explicit reasoning made the connections observable and externalised mental representations. Twenty-two students were recurrently interviewed during five semesters in grades five to seven to find answers to the overarching research question: What do students’ responses to different forms of multiplicative tasks in the domain of multi-digits and decimals reveal about their understandings of multiplication? The students were invited to solve different forms of tasks during clinical interviews, both individually and in pairs. The tasks involved story telling to given multiplications, explicit explanations of multiplication, calculation problems including explanations and justifications for the calculations and evaluation of suggested calculation strategies. Additionally the students were given written word problems to solve. The students’ understandings of multiplication were robustly rooted in repeated addition or equally sized groups. This was beneficial for their understandings of calculations and distributivity, but hindered them from fluent use of commutativity and to conceptualise decimal multiplication. The robustness of their views might be explained by the introduction to multiplication, which typically is by repeated addition and modelled by equally sized groups. The robustness is discussed in relation to previous research and the dilemma that more general models for multiplication, such as rectangular area, are harder to conceptualise than models that are only susceptible to natural numbers. The study indicated that to evaluate and explain others’ calculation strategies elicited more reasoning and deeper mathematical thinking compared to evaluating and explaining calculations conducted by the students themselves. Furthermore, the different forms of tasks revealed various lines of reasoning and to get a richly composed picture of students’ multiplicative reasoning and understandings of multiplication, a wide variety of forms of tasks is suggested. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.</p>

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