In this study, a community of high school Common Core Algebra I teachers in a socio-economically and racially diverse suburban high school participated in a lesson study process facilitated by an instructional coach to design curriculum for an algebra lab model. The model was intended to address issues of equity and access in mathematics education, which incorporated skills support, social-emotional learning, and authentic tasks to help students needing additional support succeed in a de-tracked Common Core Algebra I course. Pedagogical strategies were examined through the lens of “Danielson’s Framework for Teaching,” an instrument used to promote highly effective instructional strategies and evaluate the quality of teaching; this framework was used as a lens to construct authentic task lessons and assess teacher practice. A major finding was that an emphasis on skills support and social-emotional learning promoted increased participation and student achievement in the Common Core Algebra I course; an overemphasis on authentic tasks in the lab course was found to be counterproductive. Peer observations, collaboration, and instructional coaching were also found to be highly impactful and vital to the curriculum development process and enhancement of teacher practice. To ensure a productive lesson study process, the researcher advises school leaders to consider tenets of adult learning theory and teachers’ capacity for transformational learning when selecting teachers to develop and implement innovative curricular and instructional approaches.

Standardized aptitude and achievement tests are often accompanied by directions which recommend skipping items perceived as difficult and returning to answer them if time permits. Prior to the present study, the only empirical research in this area was a single study concerning the effects of examinee decisions to follow or disregard these instructions. It was the conclusion of this research that it was to the advantage of high ability examinees to follow the instructions to skip but that conformity to the instructions was disadvantageous to middle and low ability examinees. The present study, in contrast, was concerned with the effects of differing instructions concerning skipping and was quasi-experimental in design. The sample consisted of 423 eighth through twelfth grade students of algebra and biology. Intact classes representing three ability levels were assigned at random to treatment conditions consisting of instructions to skip, not to skip, and with no advice concerning skipping (only “skip” and “do not skip” instructions for the algebra classes.) Schoolwide tests were administered using special answer sheets designed to identify skipped items even when examinees later returned and answered some or all previously skipped. The scores from these tests were used in determination of end-of-course grades. The primary dependent variables were number-right test scores and the number of items skipped. For each subject area, two, two-way factorial analyses of variance evaluated the effect of the differing instructions across ability levels, one for the number-right scores and one for the number of items skipped. For the algebra test, there was no significant treatment effect for number-right scores. However, there was a significant interaction (p≤.01) between ability level and treatment, with high ability examinees receiving “do not skip” instructions performing significantly worse than their counterparts who received “skip” instructions. For the biology test scores, the main effect for treatment and its interaction with ability were not significant (p>.05). For the number of skips in both algebra and biology, the main effect for treatment was significant (p<.01), with the fewest skips in the “do not skip” groups. In addition, for the number of skips in algebra, the main effect for ability was significant (p<.05) with the fewest skips in the middle ability group. While the instructions apparently had their intended effect, and while the treatment-ability interaction in algebra was consistent with the findings of prior research, the number of items skipped by groups instructed to do so were not large, and groups instructed not to skip had meaningful number of skips nevertheless. Thus it was not surprising that neither the biology scores nor the algebra scores differed significantly according to treatment. Extensive secondary analyses of item and other statistics provided no basis for explaining the interaction between ability and treatment for the algebra scores. It was concluded that instructions to skip items had relatively little effect for tests of the type employed in this study. / Ph. D.

The purpose of this study was to compare the effects of Web-based learning (WBL) versus those of traditional instructor-based learning (IBL) on student knowledge and satisfaction based on student learning styles. Other goals were to determine if WBL is more effective for those with a particular learning style. The study examined a sample of undergraduate students who were enrolled in the college algebra offered as both oncampus instructor-based (traditional) and Web-based at the university of North Texas (UNT). A total of 36 Web-based students and 58 instructor-based students participated in this study. This study utilized a posttest-only intact group. The Kolb Learning Style Inventory (LSI) measured the learning styles of students. This study used learning methods (Web-based learning (WBL), instructor-based learning (IBL)), and learning styles (Diverger, Converger, Assimilator, and Accommodator) as independent variables. Student knowledge and student satisfaction was measured at the end of the course as independent variables. Based upon the results of the LSI, post-learning exam, and satisfaction a series of two-way analysis of variance (ANOVA 4x2) techniques and independent variable tests was used for each of the dependent variables, knowledge and satisfaction, based on a student's learning styles. The results revealed that students' learning styles were statistically significant for knowledge when learning on the Web versus instructor-led. In addition, the learning style was important factor for Web-based learning. The results indicated students with Assimilator and Converger as learning styles received better result with the Web-based learning method. Furthermore, this study found there is significant difference in student satisfaction based on learning on the Web versus instructor-led. The outcome of the study could be of particular interest in educational institutions; especially those that want to transfer some of their traditional courses onto the Web. The finding also has implications for training organizations as they seek efficient and effective ways to satisfy their training needs.

The problem of this study was to determine the extent to which certain characteristics of teachers of first-year algebra were related to a) their pupils' attitudes toward algebra and b) their pupils' achievements in algebra. An additional aspect of the study was to ascertain and study the differences between Anglo- and Latin-American pupils' attitudes and achievements in algebra.

The effect of an interdisciplinary algebra/science course on students' critical thinking skills was examined. A traditional college algebra course was used as a comparison group. The students in the sample enrolled in college algebra and then half were randomly placed into the interdisciplinary course. A quasi-experimental pretest-posttest comparison group design was used. The Watson-Glaser Critical Thinking Appraisal was used to measure the students' critical thinking skills. This instrument consists of an overall critical thinking score as well as five subscores in the areas of Inference, Recognition of Assumptions, Deduction, Interpretation and Evaluation of Arguments. It was found that the students in the interdisciplinary course made greater gains in the overall critical thinking score as well as in four of the five subscores. However, the differences in the gains made in the two courses were not statistically significant. Disregarding course, other factors that were found to be closely related to critical thinking were Composite ACT, grade received in the course, Math ACT and grade point average. It was also found that students whose majors were in the Schools of Arts and Letters or Science and Technology scored higher on critical thinking than students whose majors were in the Schools of Business or Education. Factors found to have no relationship to critical thinking were ethnicity, gender and classification.

The problem of this study was to determine if the teachers of Algebra I rated highest and lowest according to the Texas Teacher Appraisal System differed significantly in a measure of achievement. The analyses indicated that there were significant differences in achievement between the classes taught by the highest and lowest ranked teachers.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-08-08T11:30:50Z No. of bitstreams: 1 Renata Mendes Soares.pdf: 2927777 bytes, checksum: dcdc528de401d9634fff47e385636acd (MD5) / Made available in DSpace on 2018-08-08T11:30:50Z (GMT). No. of bitstreams: 1 Renata Mendes Soares.pdf: 2927777 bytes, checksum: dcdc528de401d9634fff47e385636acd (MD5) Previous issue date: 2018-05-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Our investigation, which has a qualitative character, has as goal to indicate which aspects related to the development of algebraic thinking are identified by four Mathematic teachers that operate on the second cycle of elementary School in a São Paulo’s public school. For that purpose, Blanton and Kaput; Kieran; Fiorentini, Miorin and Miguel; Fiorentini, Fernandes and Cristóvão; Ponte, Branco and Matos and Blanton were adopted as reference and guided each moment of our research. Initially we proposed to the participants the resolution of three activities that presented an algebraic nature and were destined to the sixth and seventh grades of elementary school, as well as some questions regarding the Algebraic thinking and Algebra teaching. We have done, also, a presentation to the participants about the research’s themes. At last, teachers were interviewed with the intent of clarifying points of their written production or participation on the moment of the presentation, which demanded further explanations. After the analysis of the written production and audio tapes, made during the presentation and interviews, we verified that the participants identified some elements characterizing a work that prioritizes the development of the algebraic thought, as we hoped. Elements such as equivalency of numeric expressions and algebraic; not obligatory use of an algebraic language to resolution of problems; use of different representations; comprehension of the structure of a calculation. However, none of them identified the generalization, element that we hoped they would indicate. This element is already present on three activities chosen as our instrument of data collection / Nossa investigação, de caráter qualitativo, tem o objetivo de identificar quais aspectos relacionados ao desenvolvimento do pensamento algébrico são identificados por quatro professores de Matemática que atuam no segundo ciclo do Ensino Fundamental de uma escola da rede estadual de São Paulo. Para isso Blanton e Kaput; Kieran; Fiorentini Miorin e Miguel; Fiorentini, Fernandes e Cristovão; Ponte, Branco e Matos e Blanton foram tomados como referências e nortearam cada momento de nossa pesquisa: inicialmente propusemos aos participantes a resolução de três atividades que apresentam um cunho algébrico e são destinadas a sexto e sétimo anos do ensino fundamental, alguns questionamentos acerca das atividades propostas, para colher dados sobre seus saberes a respeito do Pensamento Algébrico e ensino de Álgebra; realizamos, também, uma apresentação aos participantes sobre a temática da pesquisa; por fim, foram feitas entrevistas com professores com o intuito de esclarecer pontos de suas produções escritas ou participações no momento da apresentação que demandavam maiores explicações. Após análise das produções escritas e gravações de áudio tomadas na apresentação e entrevistas, constatamos que os participantes identificam alguns elementos caracterizadores de um trabalho que priorize o desenvolvimento do pensamento algébrico que esperávamos, como equivalência de expressões numéricas e algébricas, não obrigatoriedade do uso de uma linguagem algébrica para resolução de problemas, uso de diferentes representações, compreensão da estrutura de um cálculo. No entanto, nenhum deles identificou a generalização, elemento que esperávamos que eles indicassem. Este elemento está presente em três atividades escolhidas para nosso instrumento de coleta de dados

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-09-18T12:29:42Z No. of bitstreams: 1 Ana Paula Teles de Oliveira.pdf: 1429586 bytes, checksum: 83e9261fc458586c93c9fe22bebe556c (MD5) / Made available in DSpace on 2017-09-18T12:29:42Z (GMT). No. of bitstreams: 1 Ana Paula Teles de Oliveira.pdf: 1429586 bytes, checksum: 83e9261fc458586c93c9fe22bebe556c (MD5) Previous issue date: 2017-08-08 / In this research our aim is to investigate and evaluate a collection of data that will help understand the concept of the algebraic group, according to the question: What are the strength and limitations of a group of activities mentioned in examples and counterexamples in the algebraic structure group to generalize and formalize the context referred? It is possible to observe that this concept is organized through the following definitions: axiom and theories both containing examples and counterexamples. Our proposal consists on doing the opposite, meaning through examples and counterexamples it will be possible to study the concept involved. To start the research, we elaborated three activities, reorganized in four subgroups, which were elaborated in numeric and geometric exercises and fundamentals mentioned in Brousseau theories. We implemented the method of Design Experiments which helped us improve the activities, and thus evolve them with five individuals and subdivisions with two teams. This methodology has two perspectives: a prospective – that addresses a study of the activates proposed in the ways that will provide possible answers and further reflections - presenting an analysis of the answers and reflections obtained with the goal of meeting the proposed objective (the concepts of structure in the algebraic group). The people that took part in this research are students enrolled on the post-graduate of Mathematical Education. As a result, we point out as potentiality the movement between the phases of didactic situations in necessary concepts of the group algebraic structure identity element and associative property and also in relation to the worked examples as the reflection, composition of geometric transformations as an operation and when the same is closed in a given set and identity transformation as identity element in the set of geometric transformations. As limitations we observe that the phases of didactic situations did not occur in concepts such as binary and closed operation and the group algebraic structure. The activates done are not self-explanatory and thus needs to be clarified by individuals with the basic idea of element inverse, identity element, commutative and associative properties, composition of functions and symmetries in addition to the algebraic language / Nesta pesquisa nosso objetivo consiste em elaborar e analisar um conjunto de atividades para a constituição do conceito de estrutura algébrica grupo, direcionada pela questão: Quais são as potencialidades e limitações de um conjunto de atividades pautadas em exemplos e contraexemplos particulares de estrutura algébrica grupo para generalização e formalização do referido conceito? Observamos que esse conceito é organizado a partir de definições, axiomas, teorias, seguido de exemplos e contraexemplos. Nossa proposta consiste em fazermos uma inversão, ou seja, a partir de exemplos e contraexemplos estudarmos o conceito. Dessa forma, para iniciar os trabalhos de pesquisa, elaboramos três atividades, reorganizadas em quatro durante a pesquisa, que pautamos em exercícios numéricos e geométricos e fundamentamos teoricamente nas situações didáticas de Brousseau. Empregamos a metodologia Design Experiments, que nos permitiu aprimorar as atividades, e as desenvolvemos com cinco indivíduos, subdivididas em duas equipes. Essa metodologia envolve duas faces: uma prospectiva – que aborda um estudo das atividades propostas no sentido de fornecer possíveis respostas e resoluções, e outra reflexiva – que apresenta uma análise das respostas e resoluções obtidas com a finalidade de atingir o objetivo proposto (constituição do conceito de estrutura algébrica grupo). Os sujeitos de pesquisa, que compuseram as equipes, foram alunos matriculados no curso de pós-graduação em Educação Matemática. Como resultado, apontamos como potencialidade o movimento entre as fases das situações didáticas em conceitos necessários da estrutura algébrica grupo, elemento neutro e propriedade associativa e, ainda, exemplos trabalhados como reflexão, composição de transformações geométricas como uma operação, mesmo que seja fechada em um determinado conjunto, e transformação identidade como elemento neutro no conjunto das transformações geométricas. Em relação às limitações observamos que as fases das situações didáticas não ocorreram em conceitos como operação binária, fechada e a estrutura algébrica grupo. As atividades não são autoexplicativas e precisam ser desenvolvidas por indivíduos com ideias básicas de elemento inverso, elemento neutro, propriedades comutativa e associativa, composição de funções e simetrias, bem como a utilização de linguagem algébrica

Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert consensus protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated to an additional 476 students over two rounds. Through follow-up interviews intended for validation, and test analysis processes, the questions were refined to best target conceptions and strengthen validity measures. The GCI consists of seventeen questions, each targeting a different concept in introductory group theory. The results from this study are broken into three papers. The first paper reports on the methodology for creating the GCI with the goal of providing a model for building valid concept inventories. The second paper provides replication results and critiques of previous studies by leveraging three GCI questions (on cyclic groups, subgroups, and isomorphism) that have been adapted from prior studies. The final paper introduces the GCI for use by instructors and mathematics departments with emphasis on how it can be leveraged to investigate their students' understanding of group theory concepts. Through careful creation and extensive field-testing, the GCI has been shown to be a meaningful instrument with powerful ability to explore student understanding around group theory concepts at the large-scale.

Orientador : Anna Regina Lanner de Moura / Dissertação (mestrado) ¿ Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-09T12:44:29Z (GMT). No. of bitstreams: 1 Scarlassari_NathaliaTornisiello_M.pdf: 1150253 bytes, checksum: 3ff8a24b10e00322ae200a7208de6031 (MD5) Previous issue date: 2007 / Resumo: Esta pesquisa, de caráter qualitativo, tem como objetivo principal discutir Que tipo de dificuldades alunos da 6ª série do Ensino Fundamental apresentam em uma situação B de ensino de álgebra, comparativamente a alunos da mesma série que passaram por uma situação A de ensino de álgebra? As situações de ensino tiveram a seguintes características: A situação A ocorreu em uma escola da rede particular de ensino da cidade de Piracicaba, em 1999, em duas classes de 6ª série e constituiu-se fonte de dados para a nossa pesquisa de Iniciação Científica que versou sobre as dificuldades dos alunos em álgebra. Atuamos como observadoras das aulas de álgebra que foram desenvolvidas numa abordagem tradicional, pela manipulação simbólica, resolução e correção de listas de exercícios na lousa. Os dados foram provenientes das respostas dos alunos a uma lista de exercícios. Dessas respostas analisamos e categorizamos as dificuldades em álgebra, aí manifestas. A situação B de ensino de álgebra ocorreu em uma escola estadual da cidade de Campinas, em duas classes de 6ª série onde atuamos como pesquisadoras e professora das classes pesquisadas. Foram trabalhadas atividades que propunham o desenvolvimento dos nexos conceituais da álgebra elementar, tais como: fluência, variável, campo de variação, linguagem, operacionalidade e unidade. Após esse desenvolvimento solicitamos aos alunos responderem a mesma lista de exercício usada na situação A. Comparamos as dificuldades encontradas nas duas situações para os mesmos exercícios. Esta comparação indica que os alunos da situação B encontraram menos dificuldades para realizar as atividades e que a freqüência dos erros, nessa situação, foi menor. Este trabalho permitiu afirmar que a Situação B de ensino proporcionou uma aprendizagem mais significativa das idéias algébricas correspondentes aos exercícios solicitados do que a Situação A, de abordagem tradicional / Abstract: The main purpose of this research is to discuss under a qualitative aspect What kind of difficulties the sixth-grade students of Elementary school present with regard to the Algebra learning situation B in comparison with those students from the same grade who have experienced the Algebra learning situation A? The learning situations had the following characteristics: The situation A occurred in two sixth-grade classes of one private school located in the city of Piracicaba, Sao Paulo, in 1999, and it has constituted data source for the Undergraduate Research that discussed students' difficulties regarding algebra. We have been acting as observers in the algebra classes, which were prepared according to a traditional approach using symbolic manipulation, resolution, and correction of lists of exercises on the blackboard. The data was gathered from the answers given by the students to a list of exercises, from which we were able to analyze and categorize the difficulties in algebra. The algebra learning situation B happened in two sixth-grade classes of public school in the city of Campinas, São Paulo, where we have acted both as researchers and teachers on the researched classes. Working activities proposed the development of the conceptual nexus of elementary algebra, such as fluency, variable, variation field, language, operationability and unity. Afterwards we invited the students to answer the same list of exercises used in situation A. We compared the difficulties found in both situations considering the same exercises. This comparison shows that the students in situation B found less difficulty to solve this list and there was a fewer occurrence of mistakes compared to situation A. This research allowed us to affirm that the learning situation B has brought a more significant understanding of the algebraic ideas related to the given exercises than the situation A, which considered a traditional learning approach / Mestrado / Educação Matematica / Mestre em Educação