O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.

O uso de procedimentos imaturos de contagem e a permanência de lentidão para recuperar fatos aditivos básicos da memória de longo prazo têm sido apontados pelas pesquisas como sendo habilidades pouco desenvolvidas nas crianças com dificuldades na matemática. Em vista disso, nesta pesquisa foi desenvolvida uma prática pedagógica em alunos do 4° ano do ensino fundamental com dificuldades de aprendizagem na matemática tendo como objetivo o aumento no uso de recuperação de fatos aditivos básicos. O estudo foi dividido em três etapas. Na primeira etapa, foi realizada uma avaliação com 7 4 alunos com idades entre 9 e ll anos de três escolas públicas de Porto Alegre. Para avaliar o desempenho aritmético foi utilizada a Prova de Aritmética de Capovilla, Montiel e Capovilla (2007). Para avaliar as estratégias e procedimentos de contagem e recuperação de fatos aditivos da memória, foram utilizadas duas tarefas adaptadas de Siegler e Shrager (1984) e Geary, Hamson e Hoard (2000). Após a avaliação, os resultados passaram por uma análise estatística, e os escores totais da Prova de Aritmética, além de avaliar o desempenho aritmético, serviram de base para separar os grupos em graves e moderadas dificuldades. Na segunda etapa, dos 74 alunos 19 foram selecionados para participar da intervenção pedagógica, sendo que 12 deles apresentaram graves dificuldades e 7 moderadas dificuldades em matemática. Durante o desenvolvimento da intervenção, foi utilizada uma combinação de ensino direto e ensino de estratégia de Swanson e Sachse-Lee (2000). As intervenções foram realizadas em grupos de 4 e 5 alunos, perfazendo um total de 12 encontros. Na terceira etapa, foi realizada avaliação utilizando os mesmos instrumentos da primeira etapa. Após a quantificação dos dados, os resultados revelaram que a diferença de pontuação entre o pré-teste e pós-teste foi estatisticamente significativa nos dois grupos de alunos. Os resultados indicaram que os alunos com graves e moderadas dificuldades na aprendizagem da matemática se beneficiaram com a prática pedagógica, pois, na resolução de fatos aditivos básicos, houve progressos do uso de estratégias e procedimentos de contagem para processos apoiados na memória. A combinação de abordagens de ensino direto e ensino de estratégias mostrou que é possível estimular a aprendizagem dos alunos indicando progressos no mesmo período escolar. / The use of immature counting procedures and the slow retrieval of basic addition facts of long-term memory has been suggested by research as being deficit developed abilities in children with difficulties in mathematics. Therefore, in this study a pedagogical practice was developed with 4th grade elementary school students who presented difficulties in mathematics learning aiming at enhancing the use of retrieval of basic addition facts. The study was divided into three phases. In the first phase, an evaluation was performed with 74 students aging from 9-11 years-old from three public schools in Porto Alegre. In order to evaluate their arithmetic performance, the Arithmetic Test by Capovilla, Montiel, & Capovilla (2007) was applied. To evaluate procedures and strategies counting and retrieval of addition facts from memory, two adapted tasks from Siegler & Shrager (1984) and Geary, Hamson & Hoard (2000) were used. After the evaluation, the results were statistically analyzed, and the total scores of the Arithmetic Test, besides being used to evaluate the arithmetic performance, were used as a base to divide the group into a severe anda moderate difficulties. In the second phase, 19 of the 74 students were selected to participate of the pedagogical intervention, with 12 presenting with severe difficulties and 7 with moderate difficulties in mathematics. During the intervention development process, a combination of direct teaching and strategy teaching by Swanson and SachseLee (2000) was used. Interventions were performed in groups of 4 and 5 students, with a total of 12 meetings. In the third phase, an evaluation was performed with the same tools used in the first phase. After data quantification, results revealed that the difference between the pre-test and post-test scores was statistically significative in the two groups of students. Results indicated that students with severe and moderate difficulties in mathematics learning would benefit from the pedagogical practice, because, while solving the basic addition facts, there was progress in using counting strategies and procedures to memory-based processes. A combination of direct teaching and strategy teaching approaches showed to be possible to stimulate learning while indicating progress during the same school term.

The aim of this study was to investigate the effectiveness of a game-based app (Motion Math: Fraction) to help students with Mathematics Learning Disabilities (MLD) to gain fraction skills including comparison, estimation, and word problem solving in an after school program. The researcher used multiple baseline design by extending with follow-up phase to determine whether students retained the knowledge they learned while engaging with the app. Even though six students participated to the study, the researcher withdrew two of them and analyzed data came from four students. The result o the study showed that all of the students improved their fractions skills after engaging with Motion Math: Fraction and maintained the knowledge after no longer playing. The researcher presented recommendations for further studies, for implementation into classroom, and recommend for app developers to increase app efficiency for students who have different learning profiles, and needs variety learning materials while learning the content matters.

Made available in DSpace on 2016-07-18T17:54:26Z (GMT). No. of bitstreams: 1 Susimara Santade - UNOESTE_Dissertacao.pdf: 3499544 bytes, checksum: aa3051abc5b384968e0bbec0f5fdd118 (MD5) Previous issue date: 2015-08-20 / This research is linked to line 2 - Formation and Pedagogical Practice of Teacher Professional, of Master Program in Education from University of Oeste Paulista (Unoeste - Presidente Prudente - SP). It is a documentary research whose purpose was to analyze the activities of treatment of information contained in the materials that permeate the curriculum of Secretaria da Educação do Estado de São Paulo, confronting them with the questions of Educational Performance Evaluation System of São Paulo State (Saresp) inside the same thematic area, checking if the curriculum corresponds with the questions of external evaluation. The analysis focused on mathematics learning both evaluated series- fifth year and in subsequent series the sixth year, because the curriculum focuses on spiral learning . In the course of research was possible to check, in the context of paulista education, the potentialities (if the curriculum questions are associated with Saresp questions) and weaknesses (presentation of thematic area Treatment of Information only the last two months in both materials analyzed). It was also observed that the students have shown low school performance in external evaluation. / A presente pesquisa está vinculada à linha 2 Formação e Prática Pedagógica do Profissional Docente, do Programa Mestrado em Educação da Universidade do Oeste Paulista (Unoeste Presidente Prudente - SP). Trata-se de uma pesquisa documental cujo objetivo foi analisar as atividades de tratamento da informação contidas nos materiais que permeiam o currículo da Secretaria da Educação do Estado de São Paulo, confrontando-as com as questões do Sistema de Avaliação do Rendimento Escolar do Estado de São Paulo (Saresp) dentro do mesmo eixo temático, verificando, assim, se o currículo está condizente com as questões da avaliação externa. A análise centrou-se na aprendizagem matemática tanto na série avaliada externamente quinto ano quanto na série posterior sexto ano , pois o currículo foca a aprendizagem em espiral. No transcorrer da pesquisa, foi possível verificar, no contexto da educação paulista, as potencialidades esperadas (se as questões do currículo estão associadas às questões do Saresp) e as fragilidades (a apresentação do eixo temático Tratamento da Informação, apenas no último bimestre, em ambos os materiais analisados). Observou-se, também, que os discentes têm apresentado baixo rendimento escolar na avaliação externa.

Syftet med denna systematiska litteraturstudie är att undersöka hur digitala verktyg stödjer elevers lärande inom taluppfattning, och målet är således att bidra med mer kunskap om varför och hur verktygen stödjer eleverna. I uppsatsen presenteras de missuppfattningar och svårigheter som elever har med taluppfattning bland annat inom multiplikation och division, samt hur dessa problem kan lösas med digitala verktyg. Digitala verktyg är ett relativt nytt område inom skolvärlden, därav kan det vara komplext att veta hur verktygen ska användas och positioneras i klassrummet.Resultatet som presenteras visar på att forskning stödjer användning av digitala verktyg inom taluppfattning, vilket har identifierats genom fyra centrala aspekter. Dessa aspekter är motivationshöjning, individuella anpassningar, lärares beredskap samt kognitiva processer. Genom dessa kategorier stödjer digitala verktyg elevers lärande av taluppfattning på olikasätt. I analysen av detta arbete användes den kvalitativa innehållsanalysen. / The aim of this systematic literature study is to investigate how digital tools support pupils’ development of number sense. The goal is to contribute with more knowledge of why and how digital tools support pupils learning of number sense. The study presents themisconceptions and difficulties that pupils have in number sense for instance in multiplication and division, and how these problems can be solved with digital tools. Digital tools are a relatively new area within the school world, which is why the tools usefulness may be complex and how they should be positioned. The Results presented in this study show that research support the use of digital tools in mathematics and number sense, which has been identified through four central aspects. These aspects are motivational increase, individual adaptions, teachers’ readiness and cognitive processes. Through these categories the digital tools support pupils learning of number sense in different ways.In the analysis of this work, the qualitative content analysis was used.

Arbetet som presenteras i rapporten omfattar en undersökning av dimensioner och strategier som främjar flerspråkiga elever inom låg-, mellan- och högstadiet. Samt att se vilka likheter och skillnader som framkommer i de olika stadierna. I studien betonas vikten av att undervisningsspråket, språkkompetenser samt att inkluderande arbetssätt och språkinriktad undervisning är avgörande faktorer för matematiklärandet och språkutveckling hos andraspråkselever. Framöver anses kodväxling där eleverna växlar mellan olika språk som resurs. Denna studie är baserad på vetenskapliga forskningar och erfarenheter från verksamhetsförlagd utbildning (VFU). Forskningen visar att det finns en koppling mellan matematikinlärning och språkkunskaper och betonar vikten av språkutvecklande arbetssätt där eleverna skall inkluderas och får anpassat stöd utifrån deras språkbehov. Detta examensarbete baseras på en kvalitativ studie som bygger på ljudinspelningar från lektioner i matematik på låg-, mellan- och högstadiet. Datainsamlingen är baserad på lärarnas mobiltelefoner för att spela in ljud från lektionerna och därefter transkriberades alla ljudinspelningar, för att möjliggöra en detaljerad analys av samtalet och interaktioner i klassrummet. Olika dimensioner såsom matematisk diskurs, klassarumsdiskurs i alla stadier samt explicit (tydlig och strukturerad undervisning) och implicit (självupptäckt och utforskning) undervisning, användes i studien. Dock fanns det en begränsning av användandet av flerspråkiga resurser. Slutsatsen pekar på att andraspråkselever gynnas av matematikundervisning när eleverna inkluderas i matematiska diskussioner på olika språk. / This thesis presents an investigation into the dimensions and strategies that promote the academic success of multilingual students in primary, middle, and high school levels. The study aims to identify similarities and differences across these stages while emphasizing the crucial role of language skills, inclusive practices, and language-focused teaching in fostering mathematics learning and language development among second language learners. Code-switching, which refers to students switching between different languages, is recognized as a valuable resource for their educational experience.The research is grounded in scientific studies and field-based education (FBE) experiences. The findings demonstrate a clear connection between mathematics learning and language skills, underscoring the importance of language development approaches that provide tailored support based on students' language needs. This thesis is based on a qualitative study employing audio recordings from mathematics lessons in primary, middle, and high school. Data collection involved teachers using their mobile phones to record audio during lessons, which were later transcribed to facilitate a detailed analysis of classroom discussions and interactions. Various dimensions were considered in the study, including mathematical discourse, classroom discourse across all educational levels, as well as explicit and implicit teaching. However, there were limitations in utilizing multilingual resources. In conclusion, this study highlights that second language learners benefit from mathematics education when they actively engage in mathematical discussions conducted in different languages.

Dagens samhälle är väldigt digitaliserat och i skolans styrdokument framgår det tydligt hur viktigt det är att elever får möjlighet att arbete med digitala verktyg. Även tidigare forskning visar att informations- och kommunikationsteknik behöver integreras i utbildningssituationer för att bilda samhällsmedborgare som kan leva och verka i ett globaliserat informationssamhälle. Syftet med denna studie är att bidra med mer vetskap om digitala verktyg i matematikundervisningen. Studien kan ge fördjupad kunskap om hur, i vilken omfattning, med vilket syfte lärare använder digitala verktyg samt beskrivning av lärares uppfattningar om de digitala verktygens påverkan på elevernas kunskapsutveckling. För att undersöka detta har en kvalitativ metod i form av intervjuer använts. Fem lärare från fem olika skolor har intervjuats där resultatet visar att individanpassning är det främsta syftet med att använda digitala verktyg i matematikundervisningen. Vidare framgår det att samtliga lärare anser att elevernas kunskapsutveckling kan gynnas om de i matematikundervisningen får använda digitala verktyg. En skillnad som upptäcktes var i vilken utsträckning de intervjuade lärarna använde digitala verktyg. Fyra av fem lärare använde digitala verktyg ett till tre matematikpass i veckan medan en lärare uppgav att de väldigt sällan använde digitala verktyg. Däremot var samtliga lärare överens om att den digitala undervisningen inte bör ersätta den traditionella, utan en variation mellan traditionella läromedel och digitala verktyg var det bästa både för elevernas motivation och kunskapsutveckling. Det empiriska materialet har analyserats med hjälp av pragmatismen samt det sociokulturella perspektivet och därefter diskuteras resultatet i jämförelse med tidigare forskning. Slutsatserna som framkommit är att digitala verktyg i matematikundervisningen kan underlätta elevernas inlärningsförmåga samt att det är ett enkelt sätt att individanpassa undervisningen. Även elevernas motivation och kunskapsutveckling kan påverkas positivt om de i matematikundervisningen får använda digitala verktyg.

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.

Orientador: Miriam Godoy Penteado / Banca: João Pedro Mendes da Ponte / Banca: Marcelo de Carvalho Borba / Banca: Maria Elizabeth Bianconcini Trindade Morato Pinto de Almeida / Banca: Vani Moreira Kenski / Resumo: A presente pesquisa analisa a natureza da aprendizagem matemática em um curso online de formação continuada de professores, denominado Geometria com Geometricks. Nele, alunos-professores de uma mesma rede de escolas, situadas em diferentes localidades do país, desenvolveram atividades de Geometria utilizando-se do software Geometricks, e se encontravam para discuti-las. Esses encontros aconteceram a distância, em tempo real, por chat ou videoconferência. Nessa proposta pedagógica, a telepresença condicionou a comunicação e oportunizou o estar-junto-virtual-com-mídias. De modo singular, os recursos da videoconferência permitiram que construções geométricas fossem compartilhadas visualmente e realizadas por todos os envolvidos, fomentando a interação e a participação ativa, constituindo, por meio do diálogo, uma comunidade virtual de aprendizagem. Os resultados levam a inferir que, nesse contexto, a aprendizagem matemática teve natureza colaborativa, na virtualidade das discussões, tecidas a partir das contribuições de todos os participantes; coletiva, na medida em que a produção matemática era condicionada pelo coletivo pensante de seres-humanos-com-mídias; e argumentativa, uma vez que conjecturas e justificativas matemáticas se desenvolveram intensamente do decorrer do processo, contando para isso com as tecnologias presentes na interação ocorrida de forma constante e colaborativa. / Abstract: This study was conducted to analyze the nature of mathematical learning in an online continuing education course for teachers entitled Geometry with Geometricks. Teachers employed in a nation-wide network of privately-supported schools developed geometry activities using the software Geometricks and discussed them in virtual meetings, in real time, via chat or video-conference. In this pedagogical proposal, tele-presence conditioned the communication and provided the opportunity for virtual-togetherness-with-media. In a unique way, the resources of the videoconference made it possible for everyone to participate in and visually share geometrical constructions, encouraging interaction and active participation and constituting a virtual learning community through dialogue. The results indicate that, in this context, mathematical learning nature was characterized by: collaboration, in the virtual discussions that were woven from the contributions of all the participants; collectivity, to the degree to which mathematical production was conditioned by the humans-with-media thinking collective; and argumentation, as the development of mathematical conjectures and justifications was intense throughout the process, aided by the technologies that were present in the constant, collaborative interaction. / Doutor

In this investigation, two schools - a control school and an experimental school – were compared in terms of learner performance in two traditional grade 11 mathematics tests, namely the pre-intervention test and the post-intervention test. Both schools completed the two tests simultaneously. Educators saw both tests before intervention. In the experimental school, four grade 11 mathematics classes were studied. The four classes were given worksheets that complied with an open-ended approach (OEA) to mathematics teaching and learning for learners to work independently on, with the teacher only facilitating. The learner-centredness expressed in the OEA complied with learner-centredness as envisaged by the National Curriculum Statement (NCS), and was predominantly constructivist in character. Throughout the five-month intervention, the author observed proceedings in two of the four classes in the experimental school, ensuring that questions the teacher asked complied with the OEA. The two classes would be referred to as monitored classes. The other two classes at the experimental school worked on the worksheet, with the teacher having been briefed about what was expected of the learners using the worksheet -basically that the learners would have to take own initiatives in solving the mathematics problems with minimal teacher intervention. The two grade 11 mathematics classes were monitored, but not as frequently as the monitored classes. The classes will be referred to as unmonitored classes. At the control school the educators followed their usual (traditional) teaching approach. Both the experimental and control schools followed the same grade 11 mathematics work schedule. The educators in the control school taught without any interference from the author, but the classes at the control school were occasionally observed by the author. In addition to the intervention comparison, the author also gathered qualitative information about participating educators' and learners' experiences and opinions about the OEA at the experimental school by using interviews. The results of the pre-intervention test showed no statistical difference between the experimental and control school performance, meaning that the learners from both schools were of comparable pre-requisite knowledge. In the post-intervention test, learners from the two monitored classes meaningfully outperformed those from the two unmonitored experimental classes and those from the control school. However, there was no significant difference in performance between learners from the two unmonitored classes and those from control school, The study concludes that the appropriate OEA intervention was responsible for the good results of the monitored classes., and then uses the gathered qualitative information to design a model for the successful implementation of' OEA in mathematics classes. / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2010.