The aim of this study is to investigate differences between aboriginal and Han fifth graders in problem posing. The objectives of research include: (1) design and implementation of arithmetic problem posing process; (2) investigation of the arithmetic learning condition for aboriginal and Han pupils; and (3) investigation of the misconception presentation difference between aboriginal and Han pupils in problem posing. The problem posing process falls into 3 stages: ¡§problem solving¡¨, ¡§problem posing¡¨, and ¡§problem posing-solving¡¨. This study applied the problem solving and problem posing learning sheets for pupils to engage in individual problem solving and problem posing. Pupils were requested to complete a learning journal after class. As a teacher, the researcher allowed aboriginal and Han pupils to engage in problem solving and problem posing based on 3 types of questions: word algorithm, calculation, and open-end questions; and collected data with learning journals and pupil interviews. Findings include: (1) pupils have different performances when posing different types of problems; (2) both aboriginal and Han pupils can pose feasible and appropriate questions, particularly for word items, though it is not easy for pupils to pose appropriate open-end questions; and (3) the content of problems posed varies as a result of environmental and cultural differences. Additionally, the problem posing teaching allows pupils to feel more interested in learning mathematics, and such a positive learning attitude can enrich the mathematic concepts and enhance the thinking ability of pupils. Keywords: problem posing, four basic operations, aboriginal children

O objetivo deste trabalho é mostrar que variados cálculos tornam-se mais fáceis de ser efetuados realizando operações com números escritos na base dois, com o pressuposto de que se esteja habituado a números nessa base, promovendo um aprofundamento na compreensão das bases e das propriedades utilizadas nas operações. Retomaremos alguns dos principais sistemas de numeração e apresentamos os cálculos de adições, subtrações, multiplicações e divisões com números escritos na base binária. Resgataremos também um antigo, porém eficiente, algoritmo para a extração de raízes quadradas. / The purpose of this work is to show that various calculations become easier to perform by performing operations with numbers written in base two, with the assumption that one is accustomed to numbers in this base, promoting a deeper understanding of the bases and properties used for these operations. We will return to some of the major numbering systems and present the calculations of sums, subtractions, multiplications, and divisions with numbers written on the binary basis. We will also rescue an old but efficient algorithm for the extraction of square roots.

O objetivo deste trabalho é mostrar que variados cálculos tornam-se mais fáceis de ser efetuados realizando operações com números escritos na base dois, com o pressuposto de que se esteja habituado a números nessa base, promovendo um aprofundamento na compreensão das bases e das propriedades utilizadas nas operações. Retomaremos alguns dos principais sistemas de numeração e apresentamos os cálculos de adições, subtrações, multiplicações e divisões com números escritos na base binária. Resgataremos também um antigo, porém eficiente, algoritmo para a extração de raízes quadradas. / The purpose of this work is to show that various calculations become easier to perform by performing operations with numbers written in base two, with the assumption that one is accustomed to numbers in this base, promoting a deeper understanding of the bases and properties used for these operations. We will return to some of the major numbering systems and present the calculations of sums, subtractions, multiplications, and divisions with numbers written on the binary basis. We will also rescue an old but efficient algorithm for the extraction of square roots.

Made available in DSpace on 2014-12-17T15:04:51Z (GMT). No. of bitstreams: 1 MariaCAB.pdf: 633984 bytes, checksum: 9739dba9dc013192725090e07643d0d7 (MD5) Previous issue date: 2008-08-08 / The current research had as main objective to analyze the possibility of knowledge elaboration/re-elaboration about ideas and algorithmic procedures related to basic operations by pupils of the 6th degree fundamental teaching in a significant learning process. This way the study had as basis a methodological intervention developed in a 6th degree class of a Fundamental Teaching Municipal School in the city of Jo?o Pessoa, PB. The research had as central steps the application of pre-tests (1 and 2); the execution of semi-structured interviews with the pupils involved in the theme deep studies; the elaboration and development of teaching activities, having as referential the significant learning and the application of a pre-test. The data collected in the pre-tests (1 and 2) showed a low level of the pupils comprehension about the contents related to the four operations. The answers to the post-test questions were analyzed mainly from the qualitative point of view based on the mathematic concepts comprehension theory proposed by Skemp (1980) having as complementary subsidy data collected through interviews. The analysis of the results obtained in the post-test showed that the major part of pupils reached a relational comprehension about the ideas and algorithmic procedures related to addition, subtraction, multiplication, and division. Such results showed us that the application of a teaching methodology that privileges the content comprehension, considering the pupils previous knowledge and the reflection about the action along the activities proposed, made possible the elaboration or re-elaboration of knowledge by pupils regarding to contents adopted as theme for our research / A presente pesquisa teve como principal objetivo analisar a possibilidade de elabora??o/reelabora??o de conhecimento acerca das id?ias e procedimentos algoritmos relativos ?s opera??es b?sicas, por alunos do 6? ano do Ensino Fundamental, em um processo de aprendizagem significativa. Para tanto, o estudo teve como base uma interven??o metodol?gica desenvolvida em uma turma do 6? ano de uma Escola da Rede Municipal de Ensino Fundamental da cidade de Jo?o Pessoa-PB. A pesquisa teve como etapas centrais a aplica??o de pr?-testes (1 e 2); a realiza??o de entrevistas semi-estruturadas com os alunos envolvidos nos estudos de aprofundamento do tema; a elabora??o e desenvolvimento de atividades de ensino, tendo como referencial a aprendizagem significativa, e a aplica??o de um p?s-teste. Os dados coletados nos pr?-testes (1 e 2) revelaram um baixo n?vel de compreens?o dos alunos acerca dos conte?dos relativos ?s quatro opera??es. As respostas ?s quest?es do p?s-teste foram analisadas principalmente do ponto de vista qualitativo, com base na teoria de compreens?o de conceitos matem?ticos, proposta por Skemp (1980), tendo como subs?dio, complementar dados coletados por meio de entrevistas. A an?lise dos resultados obtidos no p?s-teste revelou que a maior parte dos alunos atingiu uma compreens?o relacional acerca das id?ias e procedimentos algor?tmicos relativos ? adi??o, subtra??o, multiplica??o e divis?o. Tais resultados indicam que ? aplica??o de uma metodologia de ensino que privilegie a compreens?o dos conte?dos, considerando o conhecimento pr?vio dos alunos e a reflex?o sobre a a??o ao longo das atividades propostas, possibilitaram a elabora??o ou reelabora??o de conhecimento por parte dos alunos, pertinentes aos conte?dos adotados como tema para nossa pesquisa