Orientador: Dario Fiorentini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-23T20:37:25Z (GMT). No. of bitstreams: 1 Santos_SuelidosPrazeres_M.pdf: 3248639 bytes, checksum: df5758dccce33b51eb115fa7a654d241 (MD5) Previous issue date: 2013 / Resumo: Este estudo tem como hipótese de trabalho que os erros e dificuldades evidenciados pelos alunos na aprendizagem da matemática estão diretamente relacionados com os modos de conceber e realizar o ensino da álgebra em sala de aula. O objetivo principal deste trabalho é identificar e analisar, em investigações que têm como foco de estudo erros no ensino e aprendizagem da álgebra elementar, as relações que se estabelecem entre as concepções de ensino de álgebra, os tipos de erros cometidos pelos alunos e os modos de os pesquisadores lidarem com eles. Para alcançar tal objetivo, foi realizada uma metanálise qualitativa de nove dissertações brasileiras de mestrado que investigaram erros e dificuldades dos alunos em álgebra elementar. Esse corpus de análise foi constituído de acordo com critérios definidos previamente. A metanálise desse corpus foi desenvolvida com base nas seguintes perspectivas de investigação: identificação dos tipos de erros em álgebra presentes nas pesquisas; os modos de conceber a educação algébrica em cada pesquisa, tendo por base Fiorentini, Miorim e Miguel (1993); e as concepções e os modos de lidar com erros evidenciados nesses estudos. Foram identificadas quatro concepções distintas de erro nessas pesquisas: o erro que deve ser corrigido e identificado; o erro considerado como um obstáculo; o erro como parte integrante do processo de ensino e aprendizagem; e o erro considerado como indicador para avaliar/reavaliar a prática pedagógica. Em relação aos erros identificados, foi possível discutir sobre alguns erros que tiveram um caráter mais procedimental, considerados como erros de sintaxe, e outros erros mais relacionados com a interpretação de significados e de conceitos, considerados como erros de natureza semântica. Percebeu-se, ao final da metanálise, que as pesquisas que apresentaram mais erros de procedimentos, alinhavam-se às concepções de educação algébrica fundamentalista estrutural, fundamentalista analógica e linguístico-pragmática. Entretanto as pesquisas alinhadas à concepção exploratória e de desenvolvimento do pensamento e da linguagem algébricos, e que enfatizavam a produção e negociação de significados e a compreensão dos conceitos algébricos, evidenciaram erros de natureza semântica, mesmo na exploração de situações de natureza sintática. Em síntese, os resultados obtidos reforçaram nossa hipótese inicial de que os tipos de erros cometidos ou destacados em álgebra estão diretamente relacionados à concepção que professores e pesquisadores têm do ensino da álgebra. / Abstract: The hypothesis of this research is that the errors and difficulties of students during mathematical learning are related directly to ways of thinking and teaching algebra in classes. Its main goal is to identify and analyze, in study that have as focus the study errors in the teaching and learning of elementary algebra, relations established among the algebra teaching conceptions, the kinds of errors made by students and the researchers' ways of managing them. To get the goal, it was realized a qualitative meta-analysis of nine master's degree Brazilian theses that studied students' errors and difficulties in elementary algebra. The corpus of analysis was established according to criteria defined previously. The meta-analysis was developed based on the following investigation perspectives: identifying of errors kinds in algebra from researches; the ways of thinking the algebra teaching in each research, based on Fiorentini, Miorim and Miguel (1993); and the conceptions and the ways of managing the errors evidenced in the studies. It was identified four concepts of errors: error that must be identified and corrected; error regarded as an obstacle; error as a part of teaching and learning process; and error regarded as an indicator to evaluate and reevaluate the pedagogical practice. Concerning the identified errors, it was possible to discuss about some errors with procedural feature, regarded as syntax errors, and others related to interpretation of meaning and concepts, regarded as errors with semantic feature. It was perceived that, at the end of meta-analysis, the researches that presented more procedural errors are aligned with structural fundamentalism, analogical fundamentalism and linguistic pragmatic conceptions of algebra teaching. However, the researches aligned with the exploratory conceptions, with algebraic thinking and language developing, that emphasized the production and negotiation of meaning and understanding of algebraic concepts, evidenced errors of semantic feature, even in the investigation of situations with syntax feature. In summary, the obtained results reinforced the initial hypothesis that errors made or showed in algebra are directly related to the conception that teachers and researchers have about algebra teaching. / Mestrado / Ensino de Ciencias e Matematica / Mestra em Multiunidades em Ensino de Ciências e Matemática

The purpose of this study was to investigate the nature of mathematical connections used by selected teachers when teaching the topic of algebra and to investigate their perceptions of their use of connections. The participants were selected on the basis of teaching experience as well as their willingness to share their ideas. An interpretive paradigm was used to collect and analyse data. The data was collected from three participating teachers. These participants were selected from the three secondary schools in the town of Tsumeb in Namibia. I used video recordings of two lessons per teacher as well as semi-structured interviews as my tools to gather data. After the two lessons were video recorded, I conducted a workshop with the teachers to introduce them to the 5 types of mathematical connections pertinent to this study. We analysed the videos together using Businskas' framework as a basis for analysis. This then formed part of the stimulated recall interviews. It was found that, even though teachers were not aware of the concept of mathematical connections before our interactions, there was strong evidence of connections being made and used in their lessons. The two types of connections that were used most frequently (24.1 percent each) were procedural and instruction-oriented connections respectively. Part-whole relationships connections were used the least with a frequency of 12 percent. All three teachers agreed that they needed to make more connections when teaching and that they would think more about connections in future, particularly when preparing their lessons. The study makes recommendations to encourage the continuous use of connections in teaching mathematics.

This dissertation consists of three related papers. The first paper, Rethinking mathematics bridge courses--An inquiry model for community colleges, introduces the activities of conventionalizing and axiomatizing from a practitioner perspective. In the paper, I offer a curricular model that includes both inquiry and traditional instruction for two-year college students interested in mathematics. In particular, I provide both examples and rationales of tasks from the research-based Teaching Abstract Algebra for Understanding (TAAFU) curriculum, which anchors the inquiry-oriented version of the mathematics bridge course. The second paper, the role of past experience in creating a shared representation system for a mathematical operation: A case of conventionalizing, adds to the existing literature on mathematizing (Freudenthal, 1973) by "zooming in" on the early stages of the classroom enactment of an inquiry-oriented curriculum for reinventing the concept of group (Larsen, 2013). In three case study episodes, I shed light onto "How might conventionalizing unfold in a mathematics classroom?" and offer an initial framework that relates students' establishment of conventions in light of their past mathematical experiences. The third paper, Collective axiomatizing as a classroom activity, is a detailed case study (Yin, 2009) that examines how students collectively engage in axiomatizing. In the paper, I offer a revision to De Villiers's (1986) model of descriptive axiomatizing. The results of this study emphasize the additions of pre-axiomatic activity and axiomatic creation to the model and elaborate the processes of axiomatic formulation and analysis within the classroom community.

The questions guiding this research seek to discover the factors that affect high school math course completion and college readiness in a Texas suburban public school district. The first research question examines the relationship between 8th grade completion of Algebra I and high school mathematics course taking patterns and college readiness. The second question evaluates the relationship between race, gender, socioeconomic status and enrollment in the Advancement Via Individual Determination (AVID) program to college math readiness and high school mathematics course completion. Participants included 841 high school graduates of the class of 2006; 76% of the graduates were White, 15% Hispanic and 7% African American. Twenty-three percent of students were economically disadvantaged and 46% of students completed Algebra I in 8th grade. Chi-square, Cramer's V, and multiple regression were conducted to evaluate possible relationships between variables. The Chi-square and Cramer's V showed statistically significant (p<.05) relationships between 8th grade algebra completion and both college readiness and high school math course completion. A significant statistical relationship was also found between college readiness and each of the independent variables, ethnicity, economic status, completion of 8th grade algebra and enrollment in AVID. The number of math courses completed in high school was statistically related to ethnicity and economic status.. The findings of this study indicate that early access to Algebra I can positively affect the number of high school math courses a student completes and the likelihood that the student will be college ready after high school graduation.

The purpose of this study was to investigate the effectiveness of carefully designed teacher training in the use of the computer to teach graphing skills associated with Algebra II conic sections. Three areas were studied: the teachers' attitude toward mathematics, and the effect on students' achievement in the area of graphing skills.

The problems with which this study was concerned were threefold: (a) to design a computer-based graphics presentation on the topics of functions and graphing, (b) to develop the presentation, and (c) to determine the instructional effectiveness of this computer-based graphics instruction. The computerized presentation was written in Authorware for the Macintosh computer. The population of this study consisted of three intermediate algebra classes at Collin County Community College (n = 51). A standardized examination, the Descriptive Tests of Mathematics Skills for Functions and Graphs, was used for pretest and posttest purposes. Means were calculated on these scores and compared using a t-test for correlated means. The level of significance was set at .01. The results of the data analysis indicated: 1. There was a significant difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 2. There was no significant gender difference between the pretest and posttest performance after exposure to the computer-based graphics presentation. 3. There was no significant difference between the pretest and posttest performance of the traditional and nontraditional age students after exposure to the computer-based graphics presentation. Females had a lower posttest score than the mean male posttest score, but an analysis of the differences showed no significance. Traditional age students had a higher posttest performance score than the mean traditional age student posttest score, but their pretest performance scores were higher as well. An analysis of the differences showed no significance. In summary, this computer-based graphics presentation was an effective teaching technique for increasing mathematics performance.

Thesis (MEd)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: According to Prins(1995), readability factors in Mathematics text do not only influence the comprehension of questions, but also have a marked influence on learner achievement levels. Extending on Prins (op cit), this study sought to investigate whether there are any differences in the quality of interpretation and choice of algo-heuristic methods when isiXhosa-speaking learners respond to mathematical word problems set in English and isiXhosa. The study was located within an ethnographic framework, with all of the 109 participants speaking isiXhosa as LI. The participants were in grades 8 (44), Grade 9 (29) and grade 10(36) and all took Mathematics as one of their school subjects. Learners were divided into four groups based on achievement levels in English in June examinations. The study was cross-sectional, with each of the four groups comprising learners who were good achievers, average achievers and under achievers in English second language. A unique methodological and data collection design was undertaken in such a way that each of the participants responded to word problems set in both English and isiXhosa. Two questions were administered to all learners (one in each of the two languages). The two questions were written in two sessions. If a learner responded in English during the first session, s/he will respond in isiXhosa during the second session and vice versa. There was a 5-minute break in between the sessions. Data was analysed both quantitatively and qualitatively. The broad focus of the analyses was on learners' quality of interpretation of the given word problems and the choice of computational methods they employed when they responded to the word problems. Three categories were investigated under each of the focus areas. Categories investigated under the quality of interpretation were: [J Totally false interpretation [J Partially correct interpretation and [J Totally correct interpretation Categories investigated under the choice of computational methods were: [J Standard methods [J Non-standard methods [J Unidentifiable methods The evidence gathered suggested that isiXhosa-speaking learners interpret word problems better when they are set in isiXhosa rather than English. Another important finding was that isiXhosa-speaking learners prefer to use standard methods when they respond to word problems set in English and also prefer to use non-standard methods when they respond to word problems set in siXhosa. / AFRIKAANSE OPSOMMING: Volgens Prins (1995) beïnvloed leesbaarheidfaktore in Wiskundetekste nie net die verstaan van vrae nie, maar het dit ook 'n merkbare invloed op leerders se prestasievlakke. Ter uitbreiding op Prins (op cit) het hierdie studie gepoog om ondersoek in te stelof daar enige verskille in die kwaliteit van interpretasie en keuse van algo-heuristiese metodes is wanneer isiXhosasprekende leerders op wiskundige woordprobleme reageer wat in Engels en isiXhosa gestel is. Die studie is binne 'n etnografiese raamwerk geplaas. Al 109 deelnemers het isiXhosa as eerste taal gepraat. Die deelnemers was in Graad 8 (44), Graad 9 (29) en Graad 10 (36) en het Wiskunde as een van hul skoolvakke geneem. Leerders is in vier groepe verdeel, en die indeling is op prestasievlakke in Engels in die Junieeksamen gebaseer. In hierdie deursneestudie het elk van die vier groepe uit leerders bestaan wat goeie presteerders, gemiddelde presteerders en onderpresteerders in Engels tweede taal was. 'n Unieke metodologiese en data-insamelingsontwerp is op so 'n wyse toegepas dat elkeen van die deelnemers op woordprobleme gereageer het wat in beide Engels en isiXhosa gestel is. Twee vrae is aan elke leerder gestel, een in elk van die twee tale. Die twee vrae is in twee sessies beantwoord. As 'n leerder tydens die eerste sessie in Engels reageer het, sou sy/hy tydens die tweede sessie in isiXhosa beantwoord, en omgekeerd. Daar was 'n pouse van vyf minute tussen die sessies. Data is beide kwantitatief en kwalitatief ontleed. Die breë fokus van die analises was op die kwaliteit van die leerders se interpretasie van die woordprobleme en die keuse van bewerkingsmetodes wat hulle aangewend het wanneer hulle op die woordprobleme reageer het. Drie kategorieë is in elk van die fokusareas ondersoek. Die kategorieë wat onder die kwaliteit van interpretasie ondersoek is, was: Cl 'n Algeheel verkeerde interpretasie Cl 'n Gedeeltelik korrekte interpretasie en Cl 'n Algeheel korrekte interpretasie Kategorieë wat onder die keuse van bewerkingsmetodes ondersoek is, was: u Standaardmetodes u Nie-standaardmetodes en o Onidentifiseerbare metodes Die gegewens wat ingewin is, het daarop gedui dat isiXhosasprekende leerders woordprobleme beter interpreteer wanneer die probleme in isiXhosa eerder as in Engels gestel is. 'n Ander belangrike bevinding was dat isiXhosasprekende leerders verkies om standaardmetodes aan te wend wanneer hulle op woordprobleme wat in Engels gestel is, reageer, en dat hulle ook verkies om nie-standaardmetodes te gebruik wanneer hulle op woordprobleme reageer wat in isiXhosa gestel is.

A report issued in 2012 by the United States Government Accountability Office (US Government Accountability Office, 2012) concluded that the United States is not producing enough graduates in Science, Technology, Engineering, and Mathematics (STEM) to meet the demands of its economy. According to the National Center for Educational Statistics (2001), fewer than fifty percent of students nationally possess a solid command of mathematical content. This study tested whether the insertion of Academic Service Learning (ASL) into intermediate algebra courses improved students’ performance, their motivation to learn the subject, and attitudes towards mathematics learning. ASL is an educational strategy that integrates meaningful community service with instruction and reflection to enrich the learning experience, teach civic responsibility, and strengthen communities (Duffy, Barrington, West, Heredia, & Barry, 2011). The subjects in this study were thirty-four students enrolled in intermediate algebra at a large public university in southeast Florida. The participant group consisted of fifteen students who completed the requirements of the ASL program and the comparison group consisted of nineteen students who initially showed interest in the program but dropped out of the study early in the semester. Through a mixed method analysis, the study found that the proportion of students who passed the course in the ASL group was greater than the proportion of students in the non-ASL group. Similarly, the mean final course grade in the ASL group was higher than the mean final course grade in the non-ASL group. The results of the qualitative analyses showed that all the participants enjoyed the ASL experience. In addition, some participants felt that the ASL project raised their motivation to learn mathematics and increased their competence in mathematics. However, both quantitative and qualitative analyses revealed that the students’ participation in the ASL project did not affect their attitudes towards mathematics learning. The study concluded that Academic Service Learning has the potential to help improve students’ success rates in developmental mathematics courses as well as increase their motivation to learn the subject. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-07-30T12:24:34Z No. of bitstreams: 1 José Roberto de Campos Lima.pdf: 798464 bytes, checksum: 390e74f72d58fa99f1dec2d73f258409 (MD5) / Made available in DSpace on 2018-07-30T12:24:34Z (GMT). No. of bitstreams: 1 José Roberto de Campos Lima.pdf: 798464 bytes, checksum: 390e74f72d58fa99f1dec2d73f258409 (MD5) Previous issue date: 2018-04-09 / In this paper, we present a qualitative research guided by the goal of investigating what the approach given to algebraic thinking in the prescribed curriculum of literacy cycle, which refers to the first three years of elementary school (children from 6 to 8 years old) of two proposals. To this end, we seek to characterize elements of algebraic thinking implicit or explicit in two documents, one of the federal sphere, the National Curricular Common Base (NCCB), and other of the state sphere, the Math Curriculum Guidelines for the Early Years (MCGEY). The NCCB was chosen because it is a document in the implementation phase, which every Brazilian education networks have as a reference for the elaboration of their own curriculum and, in the case of MCGEY, the state of São Paulo has the largest number of enrolments in literacy cycle. In addition, its curriculum is used by a large number of municipalities in the state. Thus, we decided to perform a documental analysis, in which the data collection occurred through content analysis, according to Bardin. We used the usual analytical techniques divided into three phases: pre-analysis, exploration of the material and processing of results, in which, through a “floating reading”, we refined the content until we get a material that met our goal. After this reading, investing in the observation, we established three categories for analysis, one that observes the structure with which the documents were elaborated; another to examine evidences of approach given to the algebraic thinking in different axes or thematic units of math; and, finally, the conceptual, which points to possible concepts involving algebraic thinking, either explicitly or implicitly. By analying the documents, in the NCCB, we identified a conceptual approach to the research area called Early Algebra, which has as its premise the possibility of developing algebraic thinking since the early years of schooling and not just from the final years of primary school, as Lins and Gimenez already pointed out. In MCGEY, we have evidences that can lead to the development of algebraic thinking, but in an implicity way, so this kind of mathematical thinking is hardly mentioned. The algebraic thinking in the literacy cycle is presented as identification, understanding of patterns and regularities in various contexts that can be generalized, without the need for a symbolic algebraic language. Therefore, it was necessary to understand how algebra interacts with other subareas of mathematics. We consider that it is very important to understand the development of algebraic thinking in the prescribed curriculum, both for initial and continuing training of teachers and for the preparation of materials and curricular structures, as well as a possibility that contributes to the mathematical training of students / Neste trabalho, apresentamos uma pesquisa qualitativa norteada pelo objetivo de investigar qual a abordagem dada ao pensamento algébrico no currículo prescrito do ciclo de alfabetização, que se refere aos três primeiros anos de escolaridade do ensino fundamental, ou seja, crianças de 6 a 8 anos, de duas propostas. Para tanto, buscamos elementos caracterizadores do pensamento algébrico de forma implícita ou explícita em dois documentos, sendo um da esfera federal, a Base Nacional Curricular Comum (BNCC), e o outro da esfera estadual, as Orientações Curriculares de Matemática para os Anos Iniciais (OCMAI). A escolha da BNCC se dá por esse ser um documento em fase de implementação, o qual todas as redes de ensino brasileiras têm como referência para elaboração de seus próprios currículos e, no caso do OCMAI, pelo fato de o estado de São Paulo ter o maior número de matrículas no ciclo de alfabetização. Além disso, seu currículo é utilizado por um grande número de municípios do estado. Assim, optamos por realizar uma análise documental, na qual a coleta de dados ocorreu por meio da análise de conteúdo, segundo Bardin. Empregamos as usuais técnicas de análise divididas em três fases: pré-análise, exploração do material e tratamento dos resultados, sendo que, por meio de uma leitura flutuante, refinamos o conteúdo até obtermos um material que atendesse ao nosso objetivo. Após essa leitura, investindo na observação, estabelecemos três categorias para análise, uma que observasse a estrutura com a qual os documentos foram elaborados; outra que analisasse indícios de abordagem dada ao pensamento algébrico nos diferentes eixos ou unidades temáticas da Matemática; e, por último, a conceitual, que aponta para possíveis conceitos que envolvam o pensamento algébrico, seja de forma explícita ou implícita. Ao analisarmos os documentos, identificamos, na BNCC, uma aproximação conceitual à denominada área de pesquisa Early Algebra, que tem como premissa a possibilidade do desenvolvimento do pensamento algébrico desde os primeiros anos de escolaridade e não apenas a partir dos anos finais do ensino fundamental, como já apontavam Lins e Gimenez. Nas OCMAI, temos indícios que podem conduzir ao desenvolvimento do pensamento algébrico, mas de modo implícito, sendo pouco citada essa forma de pensamento matemático. O pensamento algébrico no ciclo de alfabetização é apontado como identificação, compreensão de padrões e regularidades em diversos contextos que possam ser generalizados, sem a necessidade de uma linguagem simbólica algébrica. Sendo assim, fez-se necessário compreender como a Álgebra interage com as demais subáreas da matemática. Consideramos de grande importância a compreensão do desenvolvimento do pensamento algébrico no currículo prescrito, tanto para formação inicial e continuada de professores como para elaboração de materiais e estruturas curriculares, além de ser essa uma possibilidade que contribui para a formação matemática dos estudantes

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