The purpose of this dissertation was to study how teachers and school leaders perceived a specific set of classroom math innovations, and how those innovations impacted instruction in relation to the Georgia Vision Project (GVP) standards and recommendations. This was a qualitative study conducted in two GVP districts. The participants in the study were five elementary teachers, two school administrators, and two district leaders. The participants were interviewed to gain an understanding of their perceptions of recent math innovations. The innovations included (a) math instruction using manipulatives (such as counting objects and puzzles) that utilize the Concrete Representational Abstract (CRA) model, which engages students to conceive from the concrete to the abstract; (b) differentiation through flexible student grouping; (c) information about how different subgroups of students learn mathematics; and (d) math professional learning. Previous research had focused on these innovations separately. However, no research study had grouped these innovations together to see how teachers perceived them within the context of a math classroom, and how teachers implemented them in their classrooms in order to increase student achievement. This qualitative case study included schoolteacher and educational leader interviews, observations, and artifacts. The two districts in the study were high performing in the area of mathematics. The results indicated that schoolteachers and educational leaders could not directly relate the math innovations to student success and, moreover, to the GVP standards and recommendations. During the study all GVP standards were analyzed at varying levels. The study primarily focused on the teaching and learning standard, which was a significant initiative for both districts. Both districts had varying levels of implementation concerning the innovations in the study: (a) use of manipulatives, (b) differentiation in classrooms, and (c) professional learning. All participants referenced the innovations as a part of their instruction, but could not directly relate the innovations beneficial to the success of the students.

Teaching algebra-based concepts to students with learning disabilities: The effects of preteaching using a gradual instructional sequence by Sarah Jean Watt An Abstract of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Teaching and Learning Special Education) in the Graduate College of The University of Iowa May 2013 Thesis Supervisor: Associate Professor William J. Therrien Research to identify validated instructional approaches to teach math to students with LD and those at-risk for failure in both core and supplemental instructional settings is necessary to assist teachers in closing the achievement gaps that exist across the country. The concrete-to-representational-to-abstract instructional sequence (CRA) has been identified through the literature as a promising approach to teaching students with and without math difficulties (Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Cass, Cates, Smith, & Jackson (e.g. CSA), 2003; Flores, 2010). The CRA sequence transitions students from the use of concrete manipulatives to abstract symbols through the use of explicit instruction to increase computational and conceptual understanding. The main purpose of this study was to assess the effects of preteaching essential pre-algebra skills on the overall algebra achievement scores for students with disabilities and those at-risk for failure in math. Specifically the study examined the following research questions: (1) What are the effects of preteaching math units using the CRA instructional sequence on the algebra achievement of students with LD and those at risk for math failure? (2) What are the effects of preteaching math units using the CRA instructional sequence on the transfer of algebra-based skills of students with LD and those at risk for math failure to the general education setting? (3) What are the effects of preteaching math units using the CRA instructional sequence on the maintenance of algebra-based skills for students with LD and those at risk for math failure? Summary of Study Design and Findings Thirty-two students enrolled in one of four 6th grade classrooms across two elementary schools participated in this study. Sixth grade students who currently receive tier 2 or tier 3 supplemental and intensive instruction in math; and those identified as having a math learning disability will be participants. A treatment and control, pre/post experimental design was used to examine the effect of the intervention on students' math achievement. The intervention was replicated across two math units related to teaching algebra-based concepts: Solving Equations and Fractions. The treatment condition consisted of a combination of preteaching and the use of the CRA instructional sequence. Prior to each unit, Solving Equations and Fractions, researchers pretaught students 3 essential prerequisite skills necessary for success in the upcoming unit, at the concrete, representational, and abstract levels of learning. Each preteaching session lasted for ten days, 30 minutes each day. Immediate, delayed, and follow-up measures were used to support the examination of the research questions and hypotheses. Overall findings indicate that the combination of preteaching using the CRA gradual sequence is effective at improving the overall algebra performance for students with disabilities.

No description available.

Approximately 5 to 14% of school age children are affected by mathematics learning disabilities. With the implementation of inclusion, many of these children are now being educated in the regular education class- room setting and may require additional support to be successful in algebra. Therefore, teachers need to know what interventions are available to them to facilitate the algebraic learning of students with mathemat- ics learning disabilities. This systematic literature review aims to identify, and critically analyze, interventions that could be used when teaching algebra to these students. The five included articles focused on interven- tions that can be used in algebra, specifically when solving equations. In the analysis of the five studies two types of interventions emerged: the concrete-representational-abstract model and graphic organizers. The concrete-representational-abstract model seems to show it can be used successfully in a variety of scenarios involving solving equations. The use of graphic organizers also seems to be helpful when teaching higher- level algebra content that may be difficult to represent concretely. This review discovered many practical implications for teachers. Namely, that the concrete-representational-abstract model of intervention is easy to implement, effective over short periods of time and appears to positively influence the achievement of all students in an inclusive classroom setting. The graphic organizer showed similar results in that it is easy to implement and appears to improve all students’ learning. This review provided a good starting point for teachers to identify interventions that could be useful in algebra; however, more research still needs to be done. Future research is suggested in inclusive classroom settings where the general education teacher is the instructor and also on higher-level algebra concepts.

Submitted by Márcio Maia (marciokjmaia@gmail.com) on 2016-08-23T18:10:38Z No. of bitstreams: 1 arquivototal.pdf: 2357164 bytes, checksum: 62541a818674108c505d79d5aeb493a6 (MD5) / Made available in DSpace on 2016-08-23T18:10:38Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2357164 bytes, checksum: 62541a818674108c505d79d5aeb493a6 (MD5) Previous issue date: 2015-12-09 / Although this research discusses the specificity of Mathematics objects of study, focusing on the concepts of concrete and abstract, it is not characterized as an ontological study, but a predominantly epistemological one. We have analyzed how the concrete and the abstract are conceived and how they relate to the mathematics teaching-learning process. Therefore, we have considered theoretical elements from the fields of Philosophy, Education and the History of Mathematics. In the field of mathematics education, we have adopted a constructivist perspective and our research has a theoretical dimension, although we approach the consequences of the thesis that advocate for the teaching and learning of mathematics. Aiming to expand the understanding of our object of study and settle our arguments, we take as an additional source of information, in addition to theoretical studies conducted on the subject, the views, beliefs and practices of teaching. We seek to identify possible connections between them and the conceptual aspects of the concrete and the abstract, in the mathematical objects and in the process of teaching and learning. As a tool, we used semi-structured interviews conducted with a group of seven teachers at work in Basic Education, under which were evidenced conceptions of the concrete and abstract concepts, close to common sense, with no evidence of promoting a dialectical relationship between them in the teaching of Mathematics. Most respondents said that most mathematical objects studied in Basic Education is concretely representable and that they should be associated with manipulated objects materially. We argue, however, that the concreteness of a mathematical object is not related to sensitive issues, to the materiality, but that it depends on a specific set of elements and on the performing of an educational process that needs to be based on a dialectical relationship between the concrete (whether material or cognitive) and the abstract. Only when they reach the condition of cognitive concrete objects and become susceptible to mental manipulation, they form a group of prior knowledge that will support the learning of new mathematical objects associated with them. / A presente pesquisa, embora discuta a especificidade dos objetos de estudo da Matemática, tendo como foco os conceitos de concreto e de abstrato, não se caracteriza como um estudo ontológico, mas predominantemente epistemológico. Nela analisamos como o concreto e o abstrato são concebidos e se relacionam no processo de ensino-aprendizagem de Matemática. Para isso, consideramos elementos teóricos dos campos da Filosofia; da Educação e da História da Matemática. No âmbito da Educação Matemática, adotamos uma perspectiva construtivista e nossa investigação tem uma dimensão teórica, embora tratemos dos desdobramentos da tese que defendemos para o ensino e aprendizagem de Matemática. Visando ampliar a compreensão de nosso objeto de estudo, bem como sedimentar nossas argumentações, tomamos como fonte complementar de informações, além dos estudos teóricos já realizados sobre a temática, as concepções, crenças e práticas docentes. Procuramos identificar possíveis conexões entre elas e os aspectos conceituais relativos ao concreto e ao abstrato, nos objetos matemáticos e no processo de ensino e aprendizagem. Como instrumento, utilizamos entrevistas semiestruturadas, realizadas com um grupo de sete professores em atuação na Educação Básica, com base nas quais ficaram evidenciadas concepções sobre os conceitos de concreto e de abstrato, próximas do senso comum, sem evidências de promoção de uma relação dialética entre eles, no ensino de Matemática. A maior parte dos entrevistados afirma que a maioria dos objetos matemáticos estudados na Educação Básica é representável concretamente e que estes devem ser associados a objetos manipuláveis materialmente. Defendemos, entretanto, que a concretude de um objeto matemático não está relacionada aos aspectos sensitivos, à materialidade, mas depende de um conjunto específico de elementos e da realização de um processo de ensino que precisa ser pautado em uma relação dialética entre o concreto (seja material ou cognitivo) e o abstrato. Apenas quando atingem a condição de objetos concretos cognitivos e passam a ser passíveis de manipulação mental, constituem um conjunto de saberes prévios que servirão de apoio para a aprendizagem de novos objetos matemáticos a eles associados.

Orientador: Geraldo Antonio Bergamo / Banca: Maria Aparecida Mello / Banca: Washington Luiz Pacheco de Carvalho / Resumo: Esta pesquisa é um trabalho que tem como objetivo explorar a potencialidade do modelo da atividade de estudo articulado com a teoria do conhecimento e constituir uma modelagem inicial para o Ensino de Geometria Eucliadiana Plana, segundo o modelo da atividade de estudo. Fundamenta-se na Teoria do Conhecimento Marxista, na Psicologia Sócio-Histórica e no Experimento Formativo (EF) que ocorreu na União Soviética, sob coordenação de Daniíl B. Elkonin e Vasili V. Davidov. Parte da análise de uma Iniciação Científica na qual se apresenta um experimento didático piloto baseado no modelo da atividade de estudo, para conteúdos de Geometria Plana e número real. Apresenta um estudo a respeito da teoria do conhecimento como forma de justificar e evidenciar algumas das escolhas, tanto de organização, quanto de conteúdos que foram abordados. Aborda a teoria da atividade no seu sentido mais geral apresentando a hipótese que o ponto de partida de seu estudo teórico é o conceito de modelo de atividade. Apresenta um estudo da teoria da atividade, nos seus aspectos psicológicos gerais (Leontiev) e da teoria da atividade de estudo formulada no EF. Finalizando a dissertação, são formulados alguns apontamentos para o ensino de Geometria Euclidiana Plana a partir dos pressupostos teóricos abordados, com ênfase no significado do método de ascensão de ascensão do abstrato ao concreto para a assimilação do sistema no significado do método de ascensão do abstrato ao concreto para assimilação do sistema de conceitos desse conteúdo de Matemática. A metodologia foi a reflexão sobre o modelo de atividade de estudo subordinando o modelo lógico-dedutivo da Geometria Euclidiana Plana, de forma a obter-se uma modelagem inicial desse conteúdo segundo a atividade de estudo. Propõe, em termos de hipótese, a relação geneticamente inicial (célula) para o estudo teórico da Geometria ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This research is a theorical study that has a goal to explore the potentiality of the model of the study articulated activity with the theory of the knowledge and to build an initial molding for the study activity. It's based on the Theory of the Marxist Knowledge, in the Socio Historical Psychology and in the Formative Experiment (FE) that occurred in the Soviet Union, coordinated by Daniel B. Elkonin and Vasili V. Davidov. A part of the analyses of a Scientific Study in Which is shown that a didatic experiment based on the model of the study activity, for the content of the Plan Geometry and the real number. It presents a study regarding the knowledge theory as a way of justifying and substantiating some of the choices, as much organization as contents that there used in the study. It broaches the activity theory on its sense more general presenting the hypothesis that the foothold of its theoretical study is the conception of the activity model. It presents a study of the activity theory, on its general psychological aspects (Leontieve) and on the theory of the study activity formulated on the FE. Concluding the dissertation, some notes are made for the teaching of Plan Euclidean Geometry from the prerequisite theoretical report, with emphasis in the meaning of the method of the ascension from the abstract to the concrete for the assimilation of the concepts system of this content of the Mathematics. The Methodology was the reflexion about the model of the study activity, subordinating the model logical deductive of the Plan Euclidean Geometry, to obtain an initial molding of this second content the study activity. It proposes, in hypothesis terms, the genetically initial relation (cell) for the theorical study of the Plan Euclidean Geometry: ... (Complete abstract click electronic access below) / Mestre

A partir de um levantamento do conceito de conceito na filosofia e da polissemia da noção de generalização em várias áreas do conhecimento, chegamos à conclusão de que a última questão não se encontra problematizada na literatura consultada. Tal fato pode ser reflexo de considerações do senso comum sobre o processo de generalização, fazendo com que não haja \"razão aparente\" para discuti-lo. A grande maioria dos trabalhos tem por generalização o processo indutivo em si ou a conclusão a partir dele. Outros trabalhos, particularmente referentes às obras de Vigotski, associam generalização à descontextualização. Segundo nossa reflexão, tais modos de ver a generalização podem ser encontrados em trabalhos de fundamentação da Teoria do Perfil Conceitual (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). A partir de referenciais teóricos ligados ao materialismo dialético, à psicologia histórico-cultural e à complexidade, discutimos as limitações do modelo de perfil e propomos de que maneira a noção de generalização entendida sob uma abordagem dialético-complexa de ensinoaprendizagem é capaz de trazer nova luz à dinâmica das zonas do perfil e à relação sujeito-objeto. / From an investigation about the concept of concept in philosophy and the polysemy of generalization in several knowledge areas, we have reached the conclusion that the last topic is not problematized in the literature studied. Such a fact may be a reflex of common sense consideration concerning the process of generalization, making people conclude that there is no \"appearant reason\" to discuss it. The vast majority of the works investigated understand generalization as the inductive process per se or the conclusion obtained from it. Other works, particularly referring to Vigotski´s ideas, associate generalization to decontextualization. According to our reflections, such ways to consider generalization have been found in works basing the Conceptual Profile Theory (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). From theoretical frameworks related to dialectic materialism, cultural-historical psychology and complexity, we discuss the limitations of the conceptual profile model and we talk about the way in which generalization, seen under a dialectic-complex approach of the teaching-learning process, is able to shed some light to the dynamics of the conceptual profile zones and to the subject-object relation.

A partir de um levantamento do conceito de conceito na filosofia e da polissemia da noção de generalização em várias áreas do conhecimento, chegamos à conclusão de que a última questão não se encontra problematizada na literatura consultada. Tal fato pode ser reflexo de considerações do senso comum sobre o processo de generalização, fazendo com que não haja \"razão aparente\" para discuti-lo. A grande maioria dos trabalhos tem por generalização o processo indutivo em si ou a conclusão a partir dele. Outros trabalhos, particularmente referentes às obras de Vigotski, associam generalização à descontextualização. Segundo nossa reflexão, tais modos de ver a generalização podem ser encontrados em trabalhos de fundamentação da Teoria do Perfil Conceitual (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). A partir de referenciais teóricos ligados ao materialismo dialético, à psicologia histórico-cultural e à complexidade, discutimos as limitações do modelo de perfil e propomos de que maneira a noção de generalização entendida sob uma abordagem dialético-complexa de ensinoaprendizagem é capaz de trazer nova luz à dinâmica das zonas do perfil e à relação sujeito-objeto. / From an investigation about the concept of concept in philosophy and the polysemy of generalization in several knowledge areas, we have reached the conclusion that the last topic is not problematized in the literature studied. Such a fact may be a reflex of common sense consideration concerning the process of generalization, making people conclude that there is no \"appearant reason\" to discuss it. The vast majority of the works investigated understand generalization as the inductive process per se or the conclusion obtained from it. Other works, particularly referring to Vigotski´s ideas, associate generalization to decontextualization. According to our reflections, such ways to consider generalization have been found in works basing the Conceptual Profile Theory (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). From theoretical frameworks related to dialectic materialism, cultural-historical psychology and complexity, we discuss the limitations of the conceptual profile model and we talk about the way in which generalization, seen under a dialectic-complex approach of the teaching-learning process, is able to shed some light to the dynamics of the conceptual profile zones and to the subject-object relation.

Made available in DSpace on 2014-06-11T19:24:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-04-29Bitstream added on 2014-06-13T20:52:36Z : No. of bitstreams: 1 scarpim_s_me_bauru.pdf: 1757017 bytes, checksum: 43e19c67a1730df49c3dc742da1383a3 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Esta pesquisa é um trabalho que tem como objetivo explorar a potencialidade do modelo da atividade de estudo articulado com a teoria do conhecimento e constituir uma modelagem inicial para o Ensino de Geometria Eucliadiana Plana, segundo o modelo da atividade de estudo. Fundamenta-se na Teoria do Conhecimento Marxista, na Psicologia Sócio-Histórica e no Experimento Formativo (EF) que ocorreu na União Soviética, sob coordenação de Daniíl B. Elkonin e Vasili V. Davidov. Parte da análise de uma Iniciação Científica na qual se apresenta um experimento didático piloto baseado no modelo da atividade de estudo, para conteúdos de Geometria Plana e número real. Apresenta um estudo a respeito da teoria do conhecimento como forma de justificar e evidenciar algumas das escolhas, tanto de organização, quanto de conteúdos que foram abordados. Aborda a teoria da atividade no seu sentido mais geral apresentando a hipótese que o ponto de partida de seu estudo teórico é o conceito de modelo de atividade. Apresenta um estudo da teoria da atividade, nos seus aspectos psicológicos gerais (Leontiev) e da teoria da atividade de estudo formulada no EF. Finalizando a dissertação, são formulados alguns apontamentos para o ensino de Geometria Euclidiana Plana a partir dos pressupostos teóricos abordados, com ênfase no significado do método de ascensão de ascensão do abstrato ao concreto para a assimilação do sistema no significado do método de ascensão do abstrato ao concreto para assimilação do sistema de conceitos desse conteúdo de Matemática. A metodologia foi a reflexão sobre o modelo de atividade de estudo subordinando o modelo lógico-dedutivo da Geometria Euclidiana Plana, de forma a obter-se uma modelagem inicial desse conteúdo segundo a atividade de estudo. Propõe, em termos de hipótese, a relação geneticamente inicial (célula) para o estudo teórico da Geometria... / This research is a theorical study that has a goal to explore the potentiality of the model of the study articulated activity with the theory of the knowledge and to build an initial molding for the study activity. It's based on the Theory of the Marxist Knowledge, in the Socio Historical Psychology and in the Formative Experiment (FE) that occurred in the Soviet Union, coordinated by Daniel B. Elkonin and Vasili V. Davidov. A part of the analyses of a Scientific Study in Which is shown that a didatic experiment based on the model of the study activity, for the content of the Plan Geometry and the real number. It presents a study regarding the knowledge theory as a way of justifying and substantiating some of the choices, as much organization as contents that there used in the study. It broaches the activity theory on its sense more general presenting the hypothesis that the foothold of its theoretical study is the conception of the activity model. It presents a study of the activity theory, on its general psychological aspects (Leontieve) and on the theory of the study activity formulated on the FE. Concluding the dissertation, some notes are made for the teaching of Plan Euclidean Geometry from the prerequisite theoretical report, with emphasis in the meaning of the method of the ascension from the abstract to the concrete for the assimilation of the concepts system of this content of the Mathematics. The Methodology was the reflexion about the model of the study activity, subordinating the model logical deductive of the Plan Euclidean Geometry, to obtain an initial molding of this second content the study activity. It proposes, in hypothesis terms, the genetically initial relation (cell) for the theorical study of the Plan Euclidean Geometry: ... (Complete abstract click electronic access below)

Recent developments in educational research raise important questions about the design of learning environments—questions that suggest the value of rethinking what is taught, how it is taught, and how is it assessed. During the past few decades, STEM disciplines began formally recognizing and integrating discipline-based education research (DBER) into their research programs to improve STEM education. One of the less literature-affluent areas of DBER addresses curriculum order and design appertaining to concept types and the order in which we teach those concepts. As educational researchers, we pose the question: does content order matter? In this project we designed, implemented and analyzed a concrete-to-abstract curriculum as a way of teaching and learning that not only builds off what students already know but how their intellect develops throughout the learning process. This semester-long curriculum design is scientifically supported and provides a learning environment aimed to not only building a student’s declarative knowledge of the subject but procedural knowledge as well and a way of developing scientific reasoning skills. This design also aimed at enhancing a student’s ability to make connections between biological concepts despite being classified as different biological concept types (e.g. descriptive, hypothetical, and theoretical concepts) as described by Lawson et al (2000). The reasoning behind and development of this project was based from Jean Piaget’s proposed stages of intellectual development, which supports the concrete-to-abstract theory. We found that, when compared to a traditional biology course (abstract-to-concrete in terms of content order), a concrete-to-abstract order of content resulted in significantly higher biological declarative knowledge and ability to make concept connections. While we failed to detect a significant difference between the two courses in terms of how quickly scientific reasoning skills are developed or how students’ scores on scientific reasoning skill assessments, the concrete-to-abstract course did show significantly higher gains in reasoning between the start and end of the semester. In addition to this project, a significant amount of time was also allocated to the design and evaluation of a health promotion and education program in Samoa. We developed a program which centered on a principal-run caregiver meeting as a means to expand health promotion and prevention efforts concerning Rheumatic Heart Disease, which is a significant cause of child morbidity and mortality in Samoa. We found that training principals on how to inform their student’s caregivers was an effective way to increase RHD awareness and disseminate correct health information including what to do if their child presents with a sore throat.