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1
Kersaint, Gladis Swafford Jane. "Preservice elementary teachers' ability to generalize functional relationships the impact of two versions of a mathematics content course /." Normal, Ill. Illinois State University, 1998. http://wwwlib.umi.com/cr/ilstu/fullcit?p9835911.
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Thesis (Ph. D.)--Illinois State University, 1998.Title from title page screen, viewed July 5, 2006. Dissertation Committee: Jane O. Swafford (chair), John A. Dossey, Cheryl Hawker, Cynthia W. Langrall. Includes bibliographical references (leaves 142-158) and abstract. Also available in print.
2
Kaplan, Merve. "Pre-service Elementary Mathematics Teachers." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12613176/index.pdf.
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Mathematics education could and should benefit from technology in order to improve teaching and learning, particularly in topics where visualizations and connections to other concepts are needed. Handheld technologies such as graphing calculators can provide students with visualization, confirmation and exploration of problems and concepts they are learning. Handheld graphing technologies have been taken place widely in elementary and secondary level mathematics courses and considered to be beneficial in various means in mathematics education. Mathematics teachers have a crucial role in the use of GCs in mathematics classrooms. Therefore, pre-service teachers&rsquouse of GCs and their views on the use of the tool in mathematics learning are considered to be valuable. The purpose of this study was to investigate the difficulties pre-service elementary mathematics teachers face, and the benefits and constraints they emphasize while learning elementary school algebra through using the Casio Classpad after receiving an instruction with graphing calculators. The graphing calculator used in the present study is the Casio Classpad 330, which is an evolved handheld device combining features of graphing calculators, dynamic geometry environment, computer algebra systems and more. The following two research problems guided the study: What are the difficulties do pre-service elementary mathematics teachers face while using Classpad in learning elementary school algebra after receiving an instruction with graphing calculators? What benefits and constraints do pre-service elementary mathematics teachers emphasize while learning elementary school algebra through using Classpad after receiving an instruction with graphing calculators? With the aim of investigating the views of a group of pre-service elementary mathematics teachers, qualitative research strategies were used. The data was collected and analyzed by means of a case study design. Classroom observations, a questionnaire, and focus group interviews were the main data sources of the existing study. The study was carried out with 21 pre-service elementary mathematics teachers. In the classroom studies elementary level algebra was taught to the participants with the use of Classpad as a main tool by giving one tool to each of the participants. Classroom observations ended in five weeks &ndash
20 courses &ndash
including one week of a training period. After the classroom observations, participants filled out a questionnaire including five open-ended questions about the classroom studies. Finally, data collection procedure was ended with three focus group interviews. The data was analyzed with qualitative means by transcribing and analyzing the observation records, answers of the questionnaire, and records of the three interviews. Results revealed that pre-service teachers&rsquo
view Classpad in three categories
as a personal tool, as an educational tool, and the relationship between CP and motivation. They viewed CP as a personal tool that they were eager to use the tool in every level of mathematics from elementary to mastering degrees. As an educational tool, they preferred to use the tool as a teacher by giving some cautions that teachers and students should be careful with. Lastly, they considered that the tool has a positive effect on motivation when used appropriately. Pre-service elementary mathematics teachers faced some difficulties in the beginning courses of the classroom studies which was their learning period of how to use CP and they overcome most of the difficulties at the end of the classroom studies. As the new elementary school level mathematics curriculum encourages the use of various technologies in teaching and learning of mathematics, the results of this study will have useful implications for mathematics teachers and curriculum developers.
3
Davis, Ann. "So I'm done because I'm confused now measuring metacognition in elementary algebra community college students /." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=2026651711&sid=4&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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4
Benitez, Dehlly Porras. "A learning guide to improve reading of mathematics : a case study with college remedial students in elementary algebra /." Access Digital Full Text version, 1987. http://pocketknowledge.tc.columbia.edu/home.php/bybib/10732275.
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5
Afonso, Dominique Gabriala. "The development of algebraic thinking in the foundation phase: a comparative study of two different curricula." Thesis, Cape Peninsula University of Technology, 2019. http://hdl.handle.net/20.500.11838/2864.
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Thesis (MEd)--Cape Peninsula University of Technology, 2019.The mathematics results in South Africa are alarmingly low, with a number of high school learners unable to compute basic operations. International test results show South Africa consistently ranks low in comparison to other countries whilst Singapore continues to perform well. Some schools in South Africa have decided to adopt the Singaporean method of teaching mathematics, known as Singapore Maths, in the hope of improving learner results. This study seeks to understand how two different curricula, South African and Singapore, provide opportunity for the development of algebraic thinking in the Foundation Phase. There is ongoing research which suggests a link between algebraic thinking (Early Algebra) and a deeper conceptual understanding of mathematics (Blanton & Kaput, 2003). This study comprises a qualitative case study of two schools using different curricula and textbooks to teach algebraic thinking with a special focus on patterns and functional thinking. Data were gathered using document analysis of curriculum and textbooks; learner tests; semi structured interviews with class teachers and focus group interviews with Grade 3 learners from each curriculum group. The analysis process involved pattern matching and building explanations related to each data collection instrument using Blanton, Brizuela, Gardiner, Sawrey and Newman-Owen’s (2015) levels of sophistication in learner’s thinking about functional relationships. The results of the study suggest that although South African learners have the potential to think algebraically, they are not, however, always offered the opportunities to do so. The importance of suitable mathematical activities and scaffolding is highlighted and the critical need for professional development for teachers in which the importance of Early Algebra is defined and explained. It is imperative that the curriculum and textbooks activities are relooked at to address the development of algebraic thinking in the early grades and shift the focus from an emphasis on arithmetic relationships to thinking in generalised ways about functional relationships.
6
Ledbetter, Lissa S. "A Qualitative Content Analysis of Early Algebra Education iOS Apps for Primary Children." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6884.
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Educational software applications (apps) on multi-touch, mobile devices provide a promising space to help learners work toward long-term educational goals, like learning with understanding (Bransford, Brown, & Cocking, 2000). Such goals are particularly relevant in supporting a learner’s efforts to become more mathematically literate. Yet, a number of current apps do not appear to be living up to this potential. As such, this study drew upon the theoretical framework of Learning Science and the conceptual framework of TPACK theory (Mishra & Koehler, 2006) to define curricular characteristics that ideally support primary children’s potential to learn early algebra concepts with understanding, through multi-touch, mobile, iOS mathematics education apps. Using qualitative content analysis these characteristics, then, were compared to the curricular characteristics of three authentic (i.e., real-world) apps in order to describe the general extent to which the two sets of characteristics aligned. This study found the authentic apps did not align with the majority of curricular characteristics that ideally support learning with understanding. Additionally, a number of qualitative findings emerged from the study that may be used to inform future app design. These ideas include themes related to the kinds of characteristics the authentic apps tended to align with or not, and suggested adaptations to a number of contemporary theories and models related to pedagogical content knowledge and its application toward the goal of learning with understanding. These findings have direct implications for the theory and practice of app design, and suggest revisions to the way in which the field of instructional design, historically, has been approached.
7
Kahn, Eric B. "THE GENERALIZED BURNSIDE AND REPRESENTATION RINGS." UKnowledge, 2009. http://uknowledge.uky.edu/gradschool_diss/707.
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Making use of linear and homological algebra techniques we study the linearization map between the generalized Burnside and rational representation rings of a group G. For groups G and H, the generalized Burnside ring is the Grothendieck construction of the semiring of G × H-sets with a free H-action. The generalized representation ring is the Grothendieck construction of the semiring of rational G×H-modules that are free as rational H-modules. The canonical map between these two rings mapping the isomorphism class of a G-set X to the class of its permutation module is known as the linearization map. For p a prime number and H the unique group of order p, we describe the generators of the kernel of this map in the cases where G is an elementary abelian p-group or a cyclic p-group. In addition we introduce the methods needed to study the Bredon homology theory of a G-CW-complex with coefficients coming from the classical Burnside ring.
8
Howard, Nicol R. "The Influences of Mathematics Self-Efficacy, Identity, Interest, and Parental Involvement on STEM Achievement in Algebra for Female High School Students." Chapman University Digital Commons, 2015. http://digitalcommons.chapman.edu/ces_dissertations/2.
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The purpose of this study was to determine the predictability of STEM achievement in Algebra for female high school students utilizing mathematics self-efficacy, mathematics interest, mathematics identity, and parental involvement. This study employed data from the High School Longitudinal Study of 2009 (HSLS:09/12) which consisted of 3,938 female eleventh-grade participants randomly selected from 944 public and private high schools during the fall 2009 academic year. The results of a hierarchical multiple regression indicated that mathematics identity was the strongest predictor of STEM achievement for female high school students, regardless of race. In spite of this significant relationship, STEM achievement outcomes are impacted by numerous factors. Further explorations of these factors are needed to provide a more accurate model to predict female high school student achievement in STEM.
9
Figueiredo, Auriluci de Carvalho. "Saberes e concepções de educação algébrica em um curso de licenciatura em matemática." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11255.
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Investigations have shown that difficulties experienced by students when dealing with topics of Algebra, across a range of schooling levels, may be rooted in certain conceptions of Algebra Education, either their own or those held by their teachers. These conceptions provide the basis for knowings held by teachers and students in Teaching Degree programs in Mathematics. Given the relevance of this link, the purpose of the present study was to identify knowings and conceptions related to Algebra Education deployed by teachers and students in a Teaching Degree program in Mathematics. To this end, a case study was conducted employing an ethnographic approach at a university located in the state of São Paulo, Brazil. The categorizations developed by Lee and Fiorentini et al. were the primary theoretical framework adopted to identify conceptions held by students and teachers in the program. The teaching-related knowings were analyzed based on two approaches: according to Tardif s perspective, in which the notion of knowing has a wider scope that encompasses, among other aspects, attitudes of professionals; and according to Shulman s perspective, which allows for identification of a repertoire of knowledge held by teachers related to mathematical contents, of which the elementary Algebra topics were our focus of interest. Data were collected from selected documents and by interviewing three 1st-year and five 2nd-year students along with four teachers, one of whom also acted as program coordinator. The Structural-fundamentalist conception (defined by Fiorentini et al.) proved predominant among the teachers, as did Algebra as Language (defined by Lee). Among students, the Linguistic-pragmatic conception (by Fiorentini et al.) and that of Generalized Arithmetic (by Lee) predominated. The investigation enabled identification of a potential for broadening knowings related to the teaching of elementary Algebra topics and linked to Algebra Education. Given that teachers and students lack knowings related to pedagogical, curricular, or content knowledge (defined by Shulman) needed for teaching elementary Algebra topics, across various schooling levels, the participants investigated generate some of the very difficulties they face. If the teachers and students interviewed are to overcome their current situation, they will need at least to enlarge their repertoire of knowings and concurrently examine a range of conceptions of Algebra and Algebra Education not only those available in the literature, but also those held by them. It is the author s belief that further studies involving the school community and carried out under the auspices of an institutional project represent a direction for future investigation. To this end, the present study provides a valuable contribution to the area
Pesquisas indicam que as dificuldades que estudantes vivenciam com tópicos de Álgebra, nos diversos segmentos de ensino, podem advir de determinadas concepções de Educação Algébrica, tanto próprias quanto de seus professores. Essas concepções são subjacentes a saberes de atores de cursos de Licenciatura em Matemática. Pela relevância de tal entrecruzamento, este estudo teve como objetivo detectar que saberes e que concepções de Educação Algébrica estão sendo mobilizados por atores de um curso de Licenciatura em Matemática. Para tanto realizamos um estudo de caso de natureza etnográfica em uma universidade localizada no estado de São Paulo. Para identificar as concepções dos atores desse curso, tomamos como principais referenciais teóricos as categorizações elaboradas por Lee e por Fiorentini et al. Os saberes docentes foram analisados a partir de dois enfoques: sob a ótica de Tardif, segundo a qual a noção de saber tem um sentido amplo que engloba, entre outros aspectos, as atitudes dos profissionais, e sob a ótica de Shulman, que permite identificar um repertório de conhecimento do professor ligado ao conteúdo matemático, no qual destacamos os tópicos algébricos elementares. As informações necessárias à investigação foram obtidas da análise de documentos selecionados e entrevistando-se três alunos de 1.o ano, cinco de 2.o e quatro professores, um dos quais era também o coordenador do curso. As concepções predominantes entre os professores entrevistados foram a Fundamentalista-estrutural (de Fiorentini et al.) e a de Álgebra como Linguagem (de Lee). Entre os alunos, predominaram as concepções Lingüístico-pragmática (de Fiorentini et al.) e de Aritmética Generalizada (de Lee). Esta investigação permitiu-nos vislumbrar a possibilidade de ampliação de saberes relativos ao ensino de tópicos algébricos elementares, que se vinculam a concepções de Educação Algébrica. Por sequer possuírem saberes relacionados aos conhecimentos pedagógicos, curriculares e de conteúdo (de Shulman) necessários à docência de tópicos elementares nos diversos segmentos de ensino, os atores do curso investigado geram algumas das dificuldades experimentadas. Para que esses atores ultrapassem essa condição, precisam, no mínimo, ampliar o repertório de seus saberes, ao mesmo tempo em que examinam concepções de Álgebra e de Educação Algébrica as da literatura e as próprias. Cremos que estudos envolvendo a comunidade escolar desenvolvidos pelo impulso de um projeto institucional possam concretizar tal proposta de investigação futura. Nesse sentido, o presente estudo pode oferecer sua contribuição
10
Lima, José Roberto de Campos. "Pensamento algébrico no currículo do ciclo de alfabetização: estudo comparativo de duas propostas." Pontifícia Universidade Católica de São Paulo, 2018. https://tede2.pucsp.br/handle/handle/21287.
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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
11
Rigdon, Misty B. "The impact of coteaching on regular education eighth grade student achievement on a basic skills algebra assessment." ScholarWorks, 2010. https://scholarworks.waldenu.edu/dissertations/783.
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Coteaching strategies have been implemented in many of the inclusion math classrooms in an attempt to improve the achievement of students. Math achievement continues to be a concern as reported by the National Mathematics Advisory Council in 2007. Educators and previous research reported that coteaching does not improve student achievement. The purpose of this study and the research question was designed to investigate, determine, and examine if coteaching has an impact on regular education students' achievement on an algebra assessment in the eighth grade. This concurrent mixed methods design used test data from a convenience sample of 70 eighth grade students and 6 math coteachers from a small rural middle school in a southern U.S state. The students were divided into a cotaught class (experimental) and a noncotaught class (control group). The teachers' perception and implementation of the coteaching model within the inclusive classroom was determined through interviews using a semi-structured interview guide. Students' achievement was measured based on math scores on a Basic Skills Algebra Assessment given at the beginning and end of 12 weeks. A two-way analysis of variance (ANOVA) was conducted to assess if differences exist on algebra achievement scores by group (control vs. treatment) and time (pretest vs. posttest). The results of the post hoc analysis, consisting of two independent sample t tests and two dependent sample t tests, revealed that significant mean differences did in fact exist on algebra achievement scores for only the experimental group suggesting that scores increased from pre to posttest. The interview data indicated that the teachers' perception of student learning was greater in the cotaught classroom. Evidence is provided to coteachers and administrators in support of implementing the coteaching model. It supports a change in students' attitudes and perceptions of other's differences as well as their ability to learn mathematics.
12
Sert, Ozlem. "Eighth Grade Students'." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608896/index.pdf.
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The purpose of this study was to determine eighth grade students&rsquoskills of translating among different representations
graphic, table, equation, and verbal sentence
of algebraic concepts. Moreover, it was also aimed to investigate if there is any gender difference regarding the translation skills of students translating multiple representations, and their most common errors in making these translations. For data collection, 18 schools were selected randomly from 103 elementary schools in Ç
ankaya district of Ankara. Then all of the eighth grade students in each school were selected as sample. In total 705 eighth grade students were participated in the study. To assess students&rsquo
translation skills &ldquo
Translation among different representations of algebraic concepts test&rdquo
(TADRACT) was developed by researcher. Descriptive statistics were obtained to understand students&rsquo
achievement in translation process. To compare mean scores of female and male students, the statistical analysis of Independent Samples t-test was used. Every question were examined in detail to determine any misconceptions, and most frequent errors students made in translating among different algebraic representations. The results of test indicated that 8th grade students had poor skill in translations of four different representations
verbal statement, equation, table, graphic
in algebraic concepts. There was no significant difference between mean scores of girls and mean scores of boys. The most problematic translations were from other representations
equation, table, graphic
to verbal statement, and translations from other three representations
verbal statement, equation, graphic
to table were the easiest translations.
13
Bortoletti, Anderson de Abreu. "Introdução às expressões algébricas na escola básica : variáveis & células de planilhas eletrônicas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/107253.
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Esta dissertação apresenta o planejamento, a execução e a análise de uma sequência didática que visa introduzir as expressões algébricas aos alunos do 7º ano do Ensino Fundamental. Os estudantes participantes são de uma escola municipal de Porto Alegre. O trabalho desenvolvido foi realizado durante as aulas regulares de matemática, a partir do final de setembro até o início de dezembro de 2013. A metodologia de pesquisa utilizada foi o Estudo de Caso e o referencial teórico é baseado, principalmente, no conceito de pensamento algébrico, desenvolvido por Fiorentini, Miorim e Miguel, concepções de variáveis, apresentado por Usiskin, a teoria dos Registros de Representação Semiótica, desenvolvida por Duval, e a Resolução de Problemas, fundamentada em Polya e também no trabalho de Allevato e Onuchic. Durante o desenvolvimento das atividades planejadas, os estudantes passaram a utilizar variáveis a partir da generalização de determinadas situações numéricas e, posteriormente, as variáveis passaram a ser associadas às células de planilhas eletrônicas. Ao final do trabalho desenvolvido, concluímos que a sequência didática cumpre com os objetivos propostos. Em especial, as atividades oportunizaram aos estudantes o trabalho com as expressões algébricas de forma natural e o desenvolvimento de diversas características necessárias ao pensamento algébrico. Além disso, ao trabalharem com a programação de planilhas eletrônicas, os alunos percebem o quanto o conhecimento da linguagem matemática é importante nos dias atuais.This dissertation presents the planning, implementation and analysis of a didactic sequence, in order to introduce the algebraic expressions to 7th graders of elementary school. The participants are students of a public school in Porto Alegre. The work was conducted during regular math classes, from late September to early December 2013. The research methodology used was the Case Study and the theoretical framework is mainly based on the concept of algebraic thinking developed by Fiorentini, Miorim and Miguel; conceptions of variables presented by Usiskin; Representation Theory of Semiotics Records, developed by Duval; and Troubleshooting, based on Polya and also in the work of Allevato and Onuchic. During the development of the planned activities, the students started to use variables from the generalization of certain numerical situations and, subsequently, the variables were associated to a cell spreadsheet. At the end of the work, we conclude that the instructional sequence meets the proposed objectives. In particular, the activities were able to give these students the chance to work with algebraic expressions in a natural way and the development of several characteristics, which are necessary to algebraic thinking. Additionally, when working with programming spreadsheets, the students realize how much knowledge of mathematical language is important today.
14
Banks, Alberta Diahann. "Effects of Embedded Study-Skills Instruction on High School Students' Attitudes Toward Mathematics." ScholarWorks, 2015. https://scholarworks.waldenu.edu/dissertations/50.
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The target school used embedded study skills in Algebra I classes to improve attitudes toward mathematics. The purpose of this sequential, explanatory mixed-methods study was to examine the effect of embedded study-skills instruction on students' attitudes toward mathematics. Metacognitive theory was used for this study's framework. Participants were 28 Grade 9 and 10 students who repeated Algebra I. Quantitative data from the Attitudes Toward Mathematics Inventory assessed students' pre- and post-instruction attitudes toward mathematics in 4 domains. Data were analyzed using 4 independent samples t tests for students who did and did not receive embedded instruction. Qualitative data were collected through a semi structured group interview to explore 6 students' perceptions on how the intervention affected their attitudes toward mathematics. Open and axial coding strategies were used to develop themes. Quantitative results indicated no significant differences in students' attitudes toward mathematics, while qualitative findings supported the use of the intervention to develop students' positive attitudes in mathematics. A recommendation was that educators undergo professional learning opportunities to increase awareness of the impact of embedded study skills on student learning and how to use this instruction in lessons. Positive social change may occur if educators are provided with insight in embedded study skills that could improve students' attitudes toward mathematics, which ultimately may encourage students to study higher level mathematics and to pursue mathematics-based careers.
15
Nivens, Ryan Andrew. "License Plate Math: Palindromes, Graphing, & Transformations." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etsu-works/231.
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Using license plates as a context, we will analyze patterns. I will share a technique for graphing, and you will design your own license plates with given parameters. Our graphs will offer entry into transformational geometry, and a mapping from letters to numbers allows us to experience early algebra in context.
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Welder, Rachael Mae. "Preservice Elementary Teachers' Mathematical Content Knowledge of Prerequisite Algebra Concepts." Thesis, Montana State University, 2007. http://etd.lib.montana.edu/etd/2007/welder/WelderR0507.pdf.
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Research illustrating that student achievement is affected by teachers' knowledge advocates for K-8 teachers to be knowledgeable regarding prerequisite algebra concepts: (1) numbers (numerical operations), (2) ratios/proportions, (3) the order of operations, (4) equality, (5) patterning, (6) algebraic symbolism (including letter usage), (7) algebraic equations, (8) functions, and (9) graphing. The theoretical framework for the knowledge for teaching mathematics built for this study suggests that the mathematical content knowledge needed for teaching consists of specialized content knowledge in addition to common content knowledge. Specialized mathematical content knowledge extends beyond solving mathematical problems to encompass how and why mathematical procedures work and an awareness of structuring and representing mathematical content for learners. The effects of an undergraduate mathematics content course for elementary education students on preservice teachers' common and specialized content knowledge of prerequisite algebra concepts was investigated, using a pre-experimental one-group pretest-posttest design. A quantitative, 51-item, multiple-choice instrument, developed specifically to measure both types of content knowledge with respect to prerequisite algebra concepts, was constructed from the Learning Mathematics for Teaching Project's Content Knowledge for Teaching Mathematics Measures question bank. This instrument was administered to all students enrolled in Mathematics for Elementary Teachers I (n = 48), at Montana State University, during the fall semester of 2006. Matched pairs t-tests, comparing pretest and posttest scores within the single sample, show significant gains (p = .000) in both common and specialized content knowledge and in all tested aspects of prerequisite algebra knowledge (numbers and equations/functions). Results also suggest a significant correlation (r = .716, p = .000) between preservice teachers' common and specialized content knowledge. Lastly, a oneparameter linear model was constructed to predict the number of participants to incorrectly answer each item, based on item difficulty. Items missed by notably more or less students than predicted were identified and analyzed. The one item students performed better than expected on addresses common content knowledge regarding a linear graph. The set of troublesome items address both common and specialized content knowledge of reading, writing, and representing functions in a variety of contexts and using ratios to write and solve proportions.
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Chang, Hao [Verfasser]. "Varieties of elementary Lie algebras / Hao Chang." Kiel : Universitätsbibliothek Kiel, 2016. http://d-nb.info/1105472140/34.
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Oliveira, Silvio Barbosa de. "As equações diofantinas lineares e o livro didático de matemática para o ensino médio." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11059.
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Previous issue date: 2006-05-24This work involves a qualitative study of how the theme of linear Diophantine equations is approached in mathematics textbooks for high school students. Using the methods associated with content analysis (Bardin, 1977), I search for references, in both explicit and implicit forms, to these equations in two different sets of high school mathematics textbooks, both of which had been approved in the last PNLEM (a national project for the assessment of high school textbooks). Although elementary number theory has been highlighted by researchers in mathematics education, such as Campbell and Zazkis (2002), as a subject apt for the introduction and development of fundamental mathematical ideas in compulsory education, the results of this investigation indicate that it receives little attention in the textbooks analysed
Neste trabalho apresento um estudo qualitativo sobre a abordagem dada pelo livro didático do Ensino Médio ao tema equações diofantinas lineares . Por meio de uma análise de conteúdo, segundo Bardin (1977), busquei o assunto em sua forma explícita e implícita em duas coleções de Matemática para o Ensino Médio, aprovadas no último PNLEM. Embora a Teoria Elementar dos Números venha sendo tratada por pesquisadores de Educação Matemática, como Campbell e Zazkis (2002), como assunto propício para a introdução e desenvolvimento de idéias matemáticas fundamentais, no Ensino Básico, os resultados desta investigação indicam a pouca exploração do assunto por parte das coleções analisadas
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Turner, Sylvia A. "The effects of a constructivist-based fraction intervention on the achievement and self-efficacy beliefs of low socio-economic status students." Scholarly Commons, 2012. https://scholarlycommons.pacific.edu/uop_etds/26.
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Low socio-economic status (SES) students are less likely to gain access to the gatekeeper mathematics courses necessary for high school graduation and entrance to college. This study examined the effects of a constructivist-based fraction intervention on mathematics achievement, self-efficacy beliefs, and Algebra One enrollment of mathematically at risk low SES sixth grade students. Students' fifth grade mathematics CST and sixth grade fraction benchmark scores served as covariates in each analysis. Achievement was measured by the students' scores on their seventh grade fraction benchmark and mathematics California Standards Test (CST). A Fraction Self-Efficacy Survey measured students' beliefs. The sixth grade fraction intervention was a one week, 35 hour program. The experiment included 45 students who attended the intervention and 43 matched students who served as the comparison group. Teacher effects were controlled. The scores of students in the treatment group were significantly higher on both their seventh grade fraction benchmark (p < 0.001) and mathematics CST (p < 0.001). Students in the treatment group scored higher in overall self-efficacy beliefs than students in the comparison group and, although there was a trend towards significance (p = 0.065), the difference was not statistically significant. Additionally, logistic regression was used to determine that students' self-efficacy beliefs partially mediated the relationship between participation in the fraction intervention and their enrollment in Algebra One. Students who attended the intervention were three times as likely to enroll in Algebra One as their matched peers.
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Dumitraşcu, Gabriela Georgeta. "Generalization: Developing Mathematical Practices in Elementary School." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556959.
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The process of generalization in mathematics was identified by mathematics education and educational psychology research, out of many mental actions or operations, as a cognitive function fundamentally required in the thinking process. Moreover, the current changes in education in the United States bring forward the dual goal of mathematics teaching and learning: students should have strong and rigorous mathematical content knowledge and students should be involved in practices that define the status of doing mathematical work. This dual role is totally dependent on the process of generalization. This study uses theories and research findings from the field of algebraic thinking, teaching, and learning to understand how the third grade teacher’s edition textbooks of three mathematics curricula portray the process of generalization. I started my study with the development of a theoretical coding system obtained by combining Kaput’s theory about algebra (Kaput, 2008), Krutetskii’s two way of generalization (Krutetskii, 1976), and the five mathematical representations identified by Lesh, Post, and Behr (1987). Then, I used the coding system to identify tasks that have the potential to involve students in the process of generalization. The findings from my study provide evidence that following a well-structured theory, such as Kaput’s theory about algebra, allows us to identify tasks that support algebraic thinking and to create new ones with higher potential to involve children in the process of generalization. Such tasks may support the development of algebraic thinking as a continuous process that should start from early grades of elementary school.
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Costa, Eduardo Sad da. "As Equações Diofantinas Lineares e o Professor de Matemática do Ensino Médio." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11124.
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Previous issue date: 2007-05-21Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This work involves a qualitative study about whether and how mathematics High-School teachers work with their students the trouble-situations regarding linear Diophantine equations. The study was performed by means of analyzing semi-structured interviews applied on six mathematics teachers from the states of São Paulo and Minas Gerais, teaching at high-school level. The Numbers Elementary Theory has been treated by several researchers on Mathematical Education, as Campbell e Zazkis (2002), Resende (2007), as an adequate subject for the introduction and development of fundamental Mathematical ideas in High- School. However, the results of such investigation show that, although the interviewed teachers affirmed that they did work with problems of discreet mathematics that can be modeled through linear Diophantine equations, none of them seemed to work with their students using the knowledge of these equations properties in order to decide whether they have solution, and what these solutions would be
Neste trabalho apresento um estudo qualitativo sobre se, e como, professores de Matemática do Ensino Médio trabalham com seus alunos situações-problema que recaem em equações diofantinas lineares. O estudo foi feito por meio da análise de entrevistas semi-estruturadas realizadas com seis professores de Matemática dos estados de São Paulo e Minas Gerais que lecionam no Ensino Médio. A Teoria Elementar dos Números vem sendo tratada por diversos pesquisadores de Educação Matemática, como Campbell & Zazkis (2002), Resende (2007), como assunto propício para a introdução e desenvolvimento de idéias Matemáticas fundamentais no Ensino Básico. No entanto os resultados desta investigação indicam que embora os professores entrevistados afirmassem trabalhar com problemas de matemática discreta modeláveis via equação diofantina linear, nenhum deles deu indícios de trabalhar com seus alunos utilizando conhecimentos das propriedades dessas equações para decidir se as mesmas tem solução e quais seriam essas soluções
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Kim, Grace B. "The Effect of E-Based Virtual Manipulative on Third-Grade Elementary Students' Algebraic Thinking in Math Education." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10261327.
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The purpose of this study was to examine the effects of virtual manipulative on children’s algebraic thinking in their early math education. The virtual manipulative is considered as a means of intervention, and its effects is proven to be an effective way through the action research working with the third-grade elementary students. In doing so, this study evaluated the effectiveness of e-based virtual manipulative to support children’s algebraic thinking development in their early math education. Data collected for this study included pre-disposition and post-disposition surveys, pretest and posttest for algebraic thinking, and intervention assignments utilizing online math content materials regarding algebraic thinking. Data was analyzed using a statistical method using SPSS 24.0, including descriptive statistics, Pearson correlation analysis, effective size, and paired t-test. This study found that students’ test scores improved significantly in overall math scores, showing that there was a statistically significant difference between the pretest and the posttest through the intervention using e-based virtual manipulative. This study also found that student’s test scores increased in three algebra thinking content areas such as unknown variables, properties of operations, and arithmetic pattern with a significant difference. This study also found that students’ disposition scores increased in all three areas of attitude, confidence, and belief. This study will benefit students in early-grade levels with positive impact on usage of e-based virtual manipulative intervention activities for better understanding algebraic thinking and effective pedagogy.
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Hayata, Carole Anne. "The Development of Algebraic Reasoning in Undergraduate Elementary Preservice Teachers." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc177211/.
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Although studies of teacher preparation programs have documented positive changes in mathematical knowledge for teaching with preservice teachers in mathematics content courses, this study focused on the impact of a mathematics methods course and follow-up student teaching assignment. The presumption was that preservice teachers would show growth in their mathematical knowledge during methods since the course was structured around active participation in mathematics, research-based pedagogy, and was concurrent with a two-day-per-week field experience in a local elementary school. Survey instruments utilized the computer adaptive test version of the Mathematical Knowledge for Teaching (MKT) measures from the Learning Mathematics for Teaching Project, and the Attitudes and Beliefs (towards mathematics) survey from the Mathematical Education of Elementary Teachers Project. A piecewise growth model analysis was conducted on data collected from 176 participants at 5 time-points (methods, 3 time-points; student teaching, 2 time-points) over a 9 month period. Although the participants' demographics were typical of U.S. undergraduate preservice teachers, findings suggest that initial low-level of mathematical knowledge, and a deep-rooted belief that there is only one way to solve mathematics problems, limited the impact of the methods and student teaching courses. The results from this study indicate that in (a) number sense, there was no significant change during methods (p = .392), but a significant decrease during student teaching (p < .001), and in (b) algebraic thinking, there was a significant decrease during methods (p < .001), but no significant change during student teaching (p = .653). Recommendations include that the minimum teacher preparation program entry requirements for mathematical knowledge be raised and that new teachers participate in continued professional development emphasizing both mathematical content knowledge and reform-based pedagogy to continue to peel away deep-rooted beliefs towards mathematics.
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Ferreira, Carlos Henrique Grossi. "Ferramentas elementares para geometrias classicas e hiperbolica complexa." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307372.
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Orientador: Alexandre AnaninTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatisitca e Computação Cientifica
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Resumo: Esta tese possui quatro partes. A primeira parte apresenta uma construção que permite abordar todas as geometrias clássicas sob um mesmo ponto de vista. Utilizando tal abordagem, expressamos e caracterizamos, de modo simples e isento de coordenadas, vários aspectos destas geometrias, tais como geodésicas distâncias, transporte paralelo, tensores de curvatura e curvaturas seccionais. Esperamos, assim, unificar e facilitar o estudo das geometrias clássicas, evitando a introdução de vários ¿modelos¿ para uma mesma geometria (como é o caso dos modelos de Poincaré, de Siegel e de Klein para as geometrias hiperbólicas) bem como evitando a descrição de métricas através de sistemas de coordenadas específicos. A segunda parte consiste em aplicar as ferramentas desenvolvidas anteriormente para o caso específico da geometria hiperbólica complexa. O foco central é o estudo de configurações de um número pequeno de pontos. Deste modo estudamos propriedades básicas de objetos elementares tais como linhas projetivas, geodésicas e bissetores. Estas propriedades provaram-se essenciais com relação ao nosso principal objetivo, o estudo de grupos discretos de isometrias do plano hiperbólico complexo. A terceira parte consiste em uma versão do Teorema Poliedral de Poincaré em que as exigências sobre a tesselação são suficientemente locais. Além disso, buscamos para o referido Teorema condições simples e verificáveis na prática. A versão apresentada pode ser aplicada em geometrias de curvatura não-constante, nas quais n¿ao podemos explorar, por exemplo, os conceitos de convexidade. Por fim, a quarta parte é um artigo produzido em colaboração com os professores Alexandre Ananin e Nikolai Goussevskii. Neste artigo, novos exemplos de variedades com estrutura hiperbólica complexa s¿ao apresentados, resolvendo alguns problemas da área
Abstract: This thesis consists of four parts. The first part consists of a construction interpreting all classic geometries in the same way. With this construction, we express and characterize various aspects of these geometries, such as geodesics, distances, parallel displacement, curvature tensors, and sectional curvatures, in a simple coordinate-free way. We believe that this approach can unify and simplify the study of classic geometries escaping the use of several ¿models¿ for the same geometry (as Poincaré¿s, Siegel¿s, and Klein¿s models of hyperbolic geometry) as well as avoiding descriptions of metrics in specific coordinates. In the second part we apply the previously developed tools to the case of complex hyperbolic geometry. The guideline is the study of finite configurations of points. From this point of view, we study basic properties of elementary geometric objects such as projective lines, geodesics, and bisectors. These properties turned out to be crucial for our central purpose, the study of discrete groups of isometries of the complex hyperbolic plane. The third part consists of a version of Poincaré¿s Polyhedron Theorem where the conditions concerning the tessellation are sufficiently local. Also, we consider conditions that are simple and verifiable in practice. The proposed theorem can be applied in the case of geometries of non-constant curvature when some concepts, as those of convexity, are not applicable. Finally, the fourth part is an article written in collaboration with professor Alexandre Ananin and professor Nikolai Goussevskii. In this article, new series of examples of complex hyperbolic manifolds are constructed, solving some problems in the area
Doutorado
Geometria
Doutor em Matemática
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Lannin, John K. Langrall Cynthia Willey. "Developing middle school students' understanding of recursive and explicit reasoning." Normal, Ill. Illinois State University, 2001. http://wwwlib.umi.com/cr/ilstu/fullcit?p3006621.
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Thesis (Ph. D.)--Illinois State University, 2001.Title from title page screen, viewed April 25, 2006. Dissertation Committee: Cynthia W. Langrall (Chair), Graham A. Jones, Tami S. Martin, Patricia H. Klass. Includes bibliographical references (leaves 138-146) and abstract. Also available in print.
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Offergeld, Andrea [Verfasser], Aloys [Verfasser] Krieg, and Sebastian [Verfasser] Walcher. "Rekonstruktion von 3D-Punkten aus Kamerabildern : eine anwendungsgeleitete Lernumgebung an der Schnittstelle von analytischer Geometrie der gymnasialen Oberstufe und elementaren Ideen der linearen Algebra / Andrea Offergeld, Aloys Krieg, Sebastian Walcher." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/1128598043/34.
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Santos, Sueli dos Prazeres 1981. "Erros e dificuldades de alunos em álgebra elementar : uma metanálise qualitativa de dissertações brasileiras de mestrado." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/250822.
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Orientador: Dario FiorentiniDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação
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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
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Ramos, Mageri Rosa. "Uma investigação sobre a produção de tarefas algébricas para o 6º ano do ensino fundamental." Universidade Federal de Juiz de Fora (UFJF), 2011. https://repositorio.ufjf.br/jspui/handle/ufjf/3249.
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Esta produção científica tem como ponto de partida a análise de diferentes concepções de álgebra, pensamento algébrico e atividade algébrica. Essas informações influenciaram nossa tomada de decisão sobre a concepção adotada como referência neste trabalho, ajudando a verificar de que maneira diferentes concepções afetam o processo de ensino e de aprendizagem de elementos da álgebra escolar. A investigação se caracteriza por uma abordagem qualitativa e adota como base teórica o Modelo dos Campos Semânticos (MCS). Um dos objetivos desta pesquisa foi a produção de tarefas, com características específicas e referenciadas teoricamente, que auxiliassem no desenvolvimento do pensamento algébrico discente. As tarefas que elaboramos foram aplicadas a um grupo de alunos do 6º ano do Ensino Fundamental, e os significados que eles produziram para estas tarefas foram analisados sob os aportes do MCS. A pesquisa também teve como finalidade a confecção de um produto educacional que consiste no conjunto de tarefas aplicadas no trabalho de campo e em orientações que auxiliem o professor a utilizá-las em sala de aula.
This scientific work begins with the analysis of different concepts for algebra, algebraic thinking and algebraic activity. Those informations guide the decision making about the concept adopted as reference in this work, helping to verify how different concepts affect the teaching and learning processes of algebraic elements. This investigation is based on a qualitative approach and uses the Model of Semantic Fields (MSF) as the theoretical base. One objective of this research was the production of tasks with specific characteristics based on theoretical references aiming at aiding the development of the students’ algebraic thinking. The tasks we have developed have been applied to a group of students from the 6th grade of the elementary school, and the meanings they produced for these tasks were analyzed from the contributions of the MSF. The present research also targets at producing an educational product that consists of a set of tasks applied in the field work and in advisories that aids the teachers to use them in the classes.
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Aquino, Lucimeire Omoti de. "Os alunos de 5ª série/6º ano frente a atividades sobre abservação e generalização de padrões." Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11309.
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Previous issue date: 2008-05-20Secretaria da Educação do Estado de São Paulo
This work reports a research which aim was to investigate whether and how 5th series/ 6th year of elementary school students are sensitized by and create strategies to solve situations involving the perception and generalization of patterns. Mason (1996), Vale & Pimentel (2005), Radford, Bardini & Sabena (2007) and Machado (2006) works gave the main base for the research. For the investigation it was created and applied a didactic sequence, inspired by stages of the methodology of Didactic Engineering as reported by Machado (2002). The a posteriori analysis was a multidimensional: analysis of the protocols, audio and video. The experiments involved 33 students from a public school in the suburb of Sao Paulo. It was concluded that pupils were sensitized by the subject, and had appropriate of the considered problems. So, pupils showed capacity of to observe, to analyze, to recognize and to express a sequence pattern, in addition to express the generality symbolically, in explicit or implicit way, either by verbal or written speech, by actions, by gestures, by signs or by rhythms
Esta dissertação relata uma investigação cujo objetivo foi investigar se e como alunos de uma 5ª série/6º ano do Ensino Fundamental são sensibilizados e criam estratégias para resolver situações que envolvem a percepção e generalização de padrões em seqüências. Os trabalhos de: Mason (1996) Vale e Pimentel (2005), Machado (2006) e Radford, Bardini e Sabena (2007) constituíram a principal fonte das escolhas teóricas feitas. Para a coleta de dados elaborou-se e aplicou-se uma seqüência didática, inspirada nas fases da Engenharia Didática, conforme Machado (2002), sendo que a análise a posteriori foi multidimensional, pois englobou: análise dos protocolos, de áudio e de vídeo. As atividades da seqüência foram propostas a 33 alunos de uma escola pública da periferia de São Paulo. Concluiu-se que os alunos da 5ª série/6º ano foram sensibilizados, pois se apropriaram dos problemas propostos. Essa apropriação possibilitou aos alunos observar, analisar, reconhecer e expressar de modo explícito ou implícito, seja pelo discurso oral ou escrito, pelas ações, pelos gestos, pelos sinais ou pelos ritmos, a regularidade de seqüências que apresentavam um padrão
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Santos, Jonas Borsetti Silva. "Argumantação e prova: análise de argumentos algébricos de alunos da educação básica." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11491.
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Secretaria da Educação do Estado de São Paulo
The present work focuses questions presented in the questionnaire of Algebra of the AProvaME project (Argumentation and Proof in the School Mathematics), of the PUC-SP. One of the goals of the project is to raise a map on the conceptions of argument and proof of the Brazilian pupils, more necessarily of the pupils of the State of São Paulo. Two questionnaires, one of Algebra and one of Geometry, had been elaborated for this survey, applied for a composed sample of 1998 pupils in the band of 14 the 16 years, registered in 8th series of Basic School and 1° year of Average School. After descriptive analysis of the collected data, we could verify that the creation of argumentation and proof for the pupils is defective, since many of them had never seen any type of argumentation or proof in its school life. Made the descriptive analysis, we carry through a multidimensional analysis, with the aid of the software C.H.I.C. that also assisted us in the choice of the pupils who would be interviewed. Still, for one better analysis, we carry through interviews with some teachers, concerning the questions that are object of our study, as also on the use of argumentations and proofs in classroom. The same ones are little used in their classes. In general, our analyses, in such a way quantitative how much qualitative, they suggest that the processes of argumentation and proofs are not being contemplated with these pupils. The pupils who had answered to the questions had presented, in the majority of the times, empirical arguments. The ones that had tried to evidence some property or some structure for the argumentations and proofs had used many times the narrative form. Moreover, the use of the algebraic language is little spread out in the schools, fact evidenced for the arguments presented for the pupils
O presente trabalho trata de questões apresentadas no questionário de álgebra do projeto AprovaME (Argumentação e Prova na Matemática Escolar), da PUC-SP. Uma das metas do projeto é levantar um mapa sobre as concepções de argumentação e prova dos alunos brasileiros, mais precisamente dos alunos do Estado de São Paulo. Foram elaborados dois questionários, um de Álgebra e um de Geometria para esse levantamento, aplicados para uma amostra composta de 1998 alunos na faixa de 14 a 16 anos, matriculados na 8ª série do Ensino Fundamental e 1º ano do Ensino Médio. Após a análise descritiva dos dados coletados, pudemos verificar que a criação de argumentação e prova pelos alunos é falho, visto que muitos deles sequer viram qualquer tipo de argumentação ou prova em sua vida estudantil. Feita a análise descritiva, realizamos uma análise multidimensional, com o auxílio do software C.H.I.C. que também nos auxiliou na escolha dos alunos que seriam entrevistados. Ainda, para uma melhor análise, realizamos entrevistas com alguns professores acerca das questões que são objeto de nosso estudo, como também sobre o uso de argumentações e provas em sala de aula. Os mesmos valem-se muito pouco desse recurso. Em geral, nossas análises, tanto quantitativas quanto qualitativas, sugerem que os processos de argumentação e provas não estão sendo contemplados com esses alunos. Os alunos que responderam às questões apresentaram, na maioria das vezes, argumentos empíricos. Os que tentaram evidenciar alguma propriedade ou alguma estrutura para a argumentação e prova valeram-se muitas vezes da língua materna. Além disso, o uso da linguagem algébrica é pouco difundida nas escolas, fato evidenciado pelas argumentações apresentadas pelos alunos
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Wang, Yu, and 王煜. "The Performance of Mathematics gifted Elementary Students on solving Algebra Word Problems." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/2gnxqv.
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碩士國立臺北教育大學
數學暨資訊教育學系(含數學教育碩士班)
98
The purpose of the research is to investigate the performance of solving algebraic word problems in mathematics-gifted students. The research method is content analysis and the research samples are 40 mathematics-gifted fifth graders. The data consisted of 40 questions, sampling from in-class practices, homework assignments and one winter vacation assignment. The scorer reliability is 0.91. There are two parts of the results: A. Problems with low correct responses and their relationships between the concept of mathematics content and incorrect problem-solving strategies: 1. Comparing to other types of problems, the problems on intensive quality and ratio are more difficult for students. 2. There are several major incorrect problem-solving strategies: misunderstanding on the meaning of the problem, using the comparative data as the actual data in calculation, failing to determine the reference quantity, confusing the relationship between the reference quantity and comparative quantity, incapable of formulating and/or solving the inequality, and unable to solve simultaneous equations. B. The relationship between the application of problem-solving strategies and the problems: 1. When the description of the problems is self-declarative, students prefer to use the strategy of “finding relation”. 2. When the description of the problem is relationship-declarative, students prefer to use the strategy of “formulating equation”. 3. When the information provided in the problem matches with the information needed on mathematics principle, definition and formula, students prefer to use the strategy of “retrieving relevant mathematics knowledge”. 4. When the information provided in the problem suggests “the number of possible answer is limited” or the problem has the characteristic of consisting many repetitive statements (similar sentence meaning with a little variation on data), students prefer to use the strategy of “reasoning”.
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Tseng, YuJiue, and 曾于珏. "Analyzing the problems types of algebra in the elementary mathematics textbook of Taiwan, Finland and Singapore." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/56525432367715471702.
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碩士國立屏東教育大學
應用數學系
101
The purpose of this study is to compare and analyze the problems types of algebra in most popular textbooks used in three countries: Kang-Hsuan mathematics in Taiwan, Laskutaito in English in Finland and My Pals are Here! Maths in Singapore. Content analysis was used as method and mathematics problem was as unit to analyze the similarities and differences among them. The analytic categories were followed the classification of Stein, Remilliard and Simth (2000) that classified problems base on cognitive demand when problem solving, the design of the contexts by Lesh and Lemon (1992), and the types of representations by Zhu and Fan (2006). The finding of this study indicated the percentages of question in three versions is different, Kang-Hsuan has 13.17%、Laskutaito has 7.21% and My Pals are Here!Maths has 10.17%. Kang-Hsuan and My Pals are Here!Maths presented a complete problem-solving process for each example task, Laskutaito only offers a brief question narrative for each example and exercise. Three versions of textbooks all emphasize tasks in low cognitive demand, especially using processes without connections as the most. The percentage of task in processes with connections in Kang-Hsuan is twice than Laskutaito and My Pals are Here!Maths. The number of exercise/example in Laskutaito is about 30.38, it is the highest in three country. Kang Hsuan is about 2.48 and My Pals are Here!Maths is about 1.53. Considering the dimensions of task contexts, Considering the approach to present questions, Kang-Hsuan use verbal attribute, Laskutaito and My Pals are Here!Maths hold representational types of question mostly in the mathematical attribute.
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Lee, Ching-Lin, and 李青霖. "The Content Analysis of the Elementary School Mathematics Textbooks from Taiwan's Three Periods—Taking Algebra for Example." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/b469s7.
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碩士國立臺北教育大學
課程與教學研究所
106
The purpose of the study is to investigate the changes of the problem posing in elementary math textbooks and of the curriculum standards/ guidelines in algebra across three time periods in Taiwan. Based on the analytic categories from previous literature, this study applied content analysis to the elementary math textbooks in three time periods, including 1975, 1993, and 2003. The study included topics of curriculum standards/guidelines, algebraic content knowledge, types of representation in problems, and types of cognitive demand in problem solving. The main results are in the following statements: 1. The statements of curriculum standards/guidelines in the three time periods of Taiwan were changed from general to specific. Moreover, the content in algebra was beyond the area of general arithmetic. Furthermore, the descriptions of the curriculum standards/guidelines in the three time periods of Taiwan were changed from general to concrete and the math content knowledge became more diverse, which could help students solve math problems. 2. In the algebra from the elementary math textbooks of the three time periods, the percentages of problems about operational rules of math and formula expressions (such as ”transitive law”, ”commutative law”, ”associative law”, ”distribution law”, ”regular pattern of expression”) either declined or maintained at a low level compared to percentages of other subcategories. 3. As for the type of representation in problems, the verbal type was the main type of representation in the problems from the elementary math textbooks; meanwhile, the symbol type was decreasing in the problems from the textbooks. 4. As for the cognitive demand of problem solving in problem posing, “procedure without connections” was becoming the main type of cognitive demand in the problems from elementary math textbooks across the three time periods According to the above results, suggestions for future references were provided.
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Beatty, Ruth. "Pattern Rules, Patterns, and Graphs: Analyzing Grade 6 Students' Learning of Linear Functions through the Processes of Webbing, Situated Abstractions, and Convergent Conceptual Change." Thesis, 2010. http://hdl.handle.net/1807/26347.
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The purpose of this study, based on the third year of a three-year research study, was to examine Grade 6 students’ previously developed abilities to integrate their understanding of geometric growing patterns with graphic representations as a means of further developing their conception of linear relationships. In addition, I included an investigation to determine whether the students’ understanding of linear relationships of positive values could be extended to support their understanding of negative numbers. The theoretical approach to the microgenetic analyses I conducted is based on Noss & Hoyles’ notion of situated abstractions, which can be defined as the development of successive approximation of formal mathematical knowledge in individuals. I also looked to Roschelle’s work on collaborative conceptual change, which allowed me to examine and document successive mathematical abstractions at a whole-class level. I documented in detail the development of ten grade 6 students’ understanding of linear relationships as they engaged in seven experimental lessons. The results show that these learners were all able to grasp the connections among multiple representations of linear relationships. The students were also able to use their grasp of pattern sequences, graphs and tables of value to work out how to operate with negative numbers, both as the multiplier and as the additive constant. As a contribution to research methodology, the use of two analytical frameworks provides a model of how frameworks can be used to make sense of data and in particular to pinpoint the interplay between individual and collective actions and understanding.
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"Young Children’s Algebraic Reasoning Abilities." Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.40807.
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abstract: The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children.
The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem presents sequences of figures of geometric shapes that differ in complexity and can be represented by the function, y = mf +b: in Type 1 problems (1 - 4), m = 1, and in Type 2 problems (5 - 8), m = 2. The two questions in each problem require participants to first, name the number of shapes in the pattern in a near position, and then to identify the number of shapes in a far position. To clarify reasoning methods, participants were asked how they solved the problems.
The GPFA was administered, one-on-one, to 60 students in Grades 1, 2, and 3 with an equal number of males and females from the same elementary school. Problem solution scores without and with assistance, along with reasoning method(s) employed, were tabulated.
Results of data analyses showed that when no assistance was required, scores varied significantly by problem, problem type, and question, but not grade level or gender. With assistance, problem scores varied significantly by problem, problem type, question, and grade level, but not gender.Dissertation/Thesis
Doctoral Dissertation Curriculum and Instruction 2016
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Ofori-Kusi, Daniel. "An investigation into the use of problem-solving heuristics to improve the teaching and learning of mathematics." Thesis, 2017. http://hdl.handle.net/10500/23305.
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The aim of this study was to explore the effects of a problem-solving heuristic instructional method on Grade 6 learners’ achievements in algebra. Two main theories inspired the design of this teaching method, namely the modelling and modelling perspective, and action, process, object, schema (APOS) theory. Modelling and modelling perspectives guided the development of modelling-eliciting activities used in the teaching method and the APOS theory guided the sequence of activities used to develop Grade 6 learners’ conceptions in algebra.
The impact of the problem-solving heuristic instructional method was investigated with 198 Grade 6 learners from four different primary schools in the Zululand district of Kwazulu-Natal that were conveniently sampled. A mixed-method approach was used in this study and a hypothesis was formulated to investigate the effects of the teaching method on the learners’ achievements in algebra. The qualitative component consisted of a pre-intervention class observation of mathematics lessons of all four mathematics educators in the schools used for this study. The design and implementation of the problem-solving heuristic instructional method and the quantitative component employed non-equivalent control group design with pre-test and post-test measure.
The main instruments for data collection were an observation schedule to document sequence of events in the classroom during the class observation, a standardized achievement test in algebra used to measure effects of the problem-solving heuristic instructional method and modelling-eliciting activities used as a medium of interaction between learners and the researcher during the implementation of the problem-solving heuristic instructional method.
Findings from the class observation indicated all four schools made use of comparable traditional methods of instruction. The implementation of the problem-solving instructional method gave insights into how a problem-solving heuristic instructional method can be developed and used in Grade 6 algebra lessons, and the factors that could influence learners’ conceptual development in algebra. The findings from the quantitative component supported the initial hypothesis that improved scores in algebra are achieved through participation in the problem-solving heuristic instructional method. Quantitative data was analysed using the t-test, analysis of covariance, Johnson-Neyman (J-N) technique and the effect size.Mathematics Education
D. Phil. (Mathematics Education)
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Tseng, Jui-Yi, and 曾瑞怡. "Reasoning-and-proving opportunities in elementary mathematics textbooks : Algebraic." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/gp8kfg.
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碩士國立清華大學
數理教育研究所碩士在職專班
107
This study is Reasoning-and-proving opportunities in elementary mathematics textbooks : Algebraic.It is mainly to discuss how many questions of Reasoning-and-proving opportunities for students in K , N , H editions. Our research object are elementary mathematics textbooks which were adopted in 2008 curriculum guidelines.This research method mainly adopted the“content analysis method”.The research units are analyzed and compared by the major problems in elementary mathematics activities, and class with Reasoning-and-proving opportunities, purpose of Reasoning-and-proving problem, type of argument elictited. The results show the number of Reasoning-and-proving opportunities in Algebraic：the K edition has the most number of Reasoning-and-proving opportunities, the second is the H edition, the lastest is the N edition. The results show the purpose of Reasoning-and-proving problems in three editions：they all have the highest proportion of the "making claims" category, followed by the " making claims & justifying claims" category, and the " justifying claims " has the lowest proportion. The results show the type of argument elicited in three editions：they all have the highest proportion of the "generic example" and " rationale " category, followed by the "demonstration" category, and the " empirical " has the lowest proportion. We do hope that the findings of this study can be used as a reference for fufure textbook development and revision.
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CHANG, YA-WEN, and 張雅雯. "The Content Analysis of Algebra Material in the Elementary Mathematic Textbooks of Taiwan and Finland." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/98575172121949237642.
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碩士國立屏東教育大學
數理教育研究所
102
The research study is to compare and contrast the math textbook content of the Kang Hsuan edition in Taiwan and that of the WSOY edition in Finland. The study, using “questions” as analysis unit, adopts content analysis to analyze the way both textbooks present their content with regard to algebra, and to explore their respective characteristics. The results, in terms of algebra material, indicate (1) that the teaching objective accounts for higher percentage in Taiwan’s textbook than in Finland’s; (2) that the majority of questions are found in the basic concept in both textbooks while questions on “algebraic equation” are relatively few; and (3) that the content layouts of both textbooks have seen questions getting more difficult though the arrangements of unit titles vary. While algebra-related unit titles can be seen in the fifth and sixth grades of Taiwan’s edition, there seems to be none observable from the first to the sixth grades in Finland’s. However, the concept layout in Finland’s edition has more varieties.
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Hsu, Hsiao-Hui, and 徐曉慧. "A comparative study of the algebra material content analysis of elementary mathematic textbooks in Taiwan and China." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/nwj6a8.
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碩士國立臺北教育大學
數學暨資訊教育學系(含數學教育碩士班)
98
This study discusses the differences and specialties of algebra material in elementary school textbooks between Taiwan and China. This thesis adopted the way of comparative and content analysis. The main categories are summarized into algebra of enlightenment, symbolic algebra, and algebraic equation from literature of researches. This thesis analyzes two different types of mathematic materials, one is published by Kang Hsuan Educational Publishing Group of Taiwan and the other is published by Beijing Normal University Publishing Group in China. It is analyzed from the Dimensions of teaching goals, material proportion, test content, and concept organization. The results are summarized in the following. 1.The teaching goals presented in algebra material of both textbooks base on Mathematics Curriculum Guidelines. 2.The proportion of algebra material published by Kang Hsuan Educational Publishing Group of Taiwan increases steadily. The proportion of algebra material published by Beijing Normal University Publishing Group in China decreases steadily at two stages. 3.In the category of test content, the algebra material published by Kang Hsuan Educational Publishing Group of Taiwan focuses primary algebra, which is entering the stage of symbolic algebra, and algebraic equation. The one published by Beijing Normal University Publishing Group in China put emphasis on the practice of algebra of enlightenment. 4.In the category of concept organization, the symbolic fillings published by Kang Hsuan Educational Publishing Group of Taiwan owns specialties, and “exploring routinely” published by Beijing Normal University Publishing Group in China play an important role in presenting concept organization. 5.Both are lack of test content of transitive experiences. This study promotes practical suggestions based on the results as the reference of adjusting the material in the future, also looks forward to contributing in teaching and future researches.
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Schwebinghaus, Ulrich [Verfasser]. "Grundlagen der elementaren Algebra eigenverantwortlich erlernen : Entwicklung und Erprobung einer multimedialen Lernumgebung / Ulrich Schwebinghaus." 2008. http://d-nb.info/989870421/34.
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Yi-Chun, Chen, and 陳怡君. "Comparison of elementary mathematically gifted students' algebra promblem solving and mathematical attitude before and after training--participate in APMOPS 2007 for example." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/9r6tn7.
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碩士國立臺北教育大學
數學暨資訊教育學系(含數學教育碩士班)
96
This study explored elementary gifted students’ changes in mathematical attitude, problem solving strategies, and communication ability before and after training to compete Asia Pacific Mathematical Olympiad for Primary Schools in 2007(APMOPS). The subjects of this study from participating in APMOPS.This study conducted questionnaire survey, paper-pencil test, and semi-structure interview to collect data. The results of the study were showed as follows: (1)There were significantly different in mathematical attitude before and after the first-stage training; and mathematical attitude of the 10 contestants for representing Taiwan were improved mostly after the second stage of Training Curriculum. (2)In problem solving strategies, elementary gifted students usually used the quickest and simplest ways to solve the problems according to their experiences, therefore there was no difference before and after the training; but as they encountered questions with higher difficulties they would use more diversified problem solving strategies to solve them. (3)In the writing, most elementary gifted students were more able to write out the thoughts of solving problems clearly, explain the origin of the equation and the reason of listing equations. In addition, some of them nade agreat progress in writing down multiple solutions to the question at this time. Finally, some suggestions for teachers and future research were recommended.
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Ley, Allison F. "A cross-sectional investigation of elementary school students' ability to work with linear generalizing patterns : the impact of format and age on accuracy and strategy choice /." 2005. http://link.library.utoronto.ca/eir/EIRdetail.cfm?Resources__ID=370268&T=F.
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