Most of people have fatal attitude to Mathematics: some of them are capable to learn it form nature, but the others are not. So is their fate – to suffer from it for the whole of life… But it is a rude though natural mistake, as it results from means of mathematical education and its content. Most of parents and teachers are directed on these aspects both in kindergarten and at primary school. Of course, parents are different. Nevertheless so many parents can’t possibly but speak about achievements of their children. Some start making their own children learn better by the example of success of the others. They make their children learn long chains of figures with no understanding. It is even more sad to see how a mom asks her 4-year old son: “How much is two plus three?..’ But he replies just because he learned the answer but not calculated. Not only parents but also kindergarten tutors don’t want to understand that drilling for arithmetic has no sense. For a specialist it would take two days only…But teach him how to think logically – is a goal demanding from him, reached by different means.

Orientador: Marcia Regina Ferreira de Brito / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-04T03:33:49Z (GMT). No. of bitstreams: 1 Alves_EricaValeria_D.pdf: 1163734 bytes, checksum: 3e1d15f522b3121acf5d9aedf463b9cb (MD5) Previous issue date: 2005 / Resumo: O presente estudo teve o objetivo de compreender e analisar as relações entre a memória, os conhecimentos declarativo e de procedimento e o desempenho na solução de problemas matemáticos. Para tanto, 177 estudantes do primeiro e último ano do ciclo II do Ensino Fundamental e último ano do Ensino Médio provenientes de uma escola pública e uma escola privada foram solicitados a responder um questionário informativo, uma prova matemática para avaliar o domínio dos conhecimentos declarativo e de procedimento e o desempenho na solução de problemas matemáticos, e uma prova para avaliar a memória matemática. A partir do desempenho obtido nesses instrumentos trinta e dois sujeitos foram selecionados e submetidos ao teste de Cópia e Reprodução de Figuras Complexas de Rey. Os resultados indicaram que a memória matemática está intimamente relacionada com o desempenho na solução de problemas e que a capacidade de perceber os elementos de forma analítica e sintética favorecem a representação do problema influenciando o desempenho na solução. Também foi verificado que a percepção desempenha um papel fundamental nos processos cognitivos superiores, uma vez que constitui a mais imediata das reações humanas diante de uma situação inédita, pois, antes de representar, reter, ou recuperar uma informação na memória, o sujeito a percebe / Abstract: The objective of this investigation was to understand and to analyze the relationship between memory, performance and procedural and declarative knowledge memory in problem solving. Subjects were 177 elementary and high school students from two private and public schools. Instruments were a questionnaire, a mathematical test to evaluate procedural and declarative knowledge and a mathematical memory test. After this, 32 subjects was selected and submitted to Rey Complex Figures Test. The results indicated that were relationships between mathematical memory and problem solving performance, and synthetic and analytic problem perception improves representation and problem solving performance. It was found, also, that perception performs a primordial role in the higher cognitive processes therefore constitutes the most immediate of the human reactions in front of an uncommon situation, because before recall, retention or representation an information, the person perceives that / Doutorado / Educação Matematica / Doutor em Educação

This study is a quantitative study that has examined 29 students in grade 8 who have not received a pass grade in mathematics. The focus of this study is in two areas: first, which mathematical abilities do the students have the greatest difficulties in, and second, on the relationship between mathematics difficulties and reading and writing difficulties. Mathematical abilities have been studied using knowledge matrices from the national tests in mathematics. Reading and writing difficulties has been investigated using test results from diagnostic material in the area. The results show that conceptual and problem-solving skills are the most difficult abilities in which previous research also indicates. Procedural ability is the ability where most students show competency, which also is consistent with previous research. The study indicates that there are links between mathematics difficulties and reading and writing difficulties, although it is not possible to show strong correlations in this small study.

Denna studie syftar till att undersöka vilka matematiska förmågor som förekommer inom vanliga kursläromedel i matematik på gymnasienivå. Hur dessa är fördelade i förhållande till varandra inom respektive matematikläromedel samt hur de är fördelade i jämförelse över dessa läromedel. Det är en innehållsanalys baserat på ett etablerat ramverk som utgår ifrån att först konstatera vad som är matematiskt kunnande, och därefter implementera ett analysverktyg som kan koda tryckta uppgifter ifrån matematikläromedlen till någon matematisk förmåga. Verktyget bygger på att indentifiera kompetensrelaterade aktiviteter ifrån läromedlen för att bestämma vilken matematisk kompetens det motsvarar, även kallade förmågor. Dessa förmågor är definierade i Skolverkets aktuella läroplan för gymnasieämnet Matematik. De är procedur, begrepp, problemlösning, modellering, resonemang och kommunikation. Resultatet visar att olika förlag med olika författare till de analyserade läromedlen har valt att premiera olikartad över hur fördelningen utav förmågorna ska se ut, inom det undersökta specifika avsnittet. Men generellt sett så konstaterar denna studie, med stöd ifrån resultatet, att procedurs- och begreppsförmågan är överrepresenterade bland uppgifterna som ska träna elever i matematiska förmågor. Historiskt sett är inte resultatet helt märkvärdigt eftersom procedurer, eller algoritmer, alltid har på ett eller sätt varit ett stort fokusområde för inlärningen utav matematisk kunskap inom skolväsendet. För vidare studier på universitet och högskola är det oftast mer väsentligt att basala algoritmiska procedurer sitter hos eleverna. Men då denna studie enbart har fokuserat på läromedlen så kan nästa steg vara att undersöka lärarens pedagogik och möjlighet till påverkning utav vilka matematiska förmågor som eleverna tränas på, både under och utanför lektionstiden. Samtliga matematiska förmågor som innebär matematiskt kunnande bör ges utrymme till att tränas på av eleverna. / This study aims at investigating which mathematical abilities appear in regular math textbooks aimed towards secondary education. How these abilities are proportioned to each other within respective textbook as well as how they are proportioned in comparison over several textbooks. This is a content analysis based on an established framework which proceeds from first determining what is mathematical knowing and thereafter implementing a tool of analysis which can code printed textbook exercises to some mathematical ability, or competency. The tool identifies competence related activities from the textbooks in order to determine which mathematical competency it corresponds to. The mathematical abilities are defined in current Swedish national school curriculum for mathematics in secondary education. They are procedure, concept, problem solving, modelling, reasoning and communication. Results show that different publishers with various authors of the analyzed textbooks have divergent proportions of mathematical abilities represented, within a specific subchapter. In general this study can state that the abilities procedure and concept are overrepresented among all the abilities which students are meant to practice. Historically seen, this result is not that surprising as procedures, or algorithms, have always in one way or another been a primary focus for attaining mathematical knowledge in school. For further studies at college or university it is important that students are already familiar with basic algorithmic procedures. Although this study has mainly focused on mathematics textbooks, next step could be to study the teacher’s role and pedagogy in affecting which abilities students get to practice, both in and outside class time. All mathematical abilities should be given enough time for students to practice and improve in

Darbe atlikta teorinė specialiųjų poreikių mokinių integracijos į bendrojo lavinimo mokyklas situacijos bei mokinių matematinių gebėjimų analizė. Iškelta hipotezė, kad specialiosiose mokyklose besimokančių 10 klasės nežymiai protiškai atsilikusių mokinių matematiniai gebėjimai baigiant pagrindinę mokyklą yra panašūs kaip ir toje pačioje klasėje bendrojo lavinimo mokyklose besimokančių nežymiai protiškai atsilikusių mokinių, pasitvirtino. Anketinės apklausos metodu buvo atliktas tyrimas, kurio tikslas - įvertinti ir palyginti 10 klasės nežymiai protiškai atsilikusių mokinių, besimokančių skirtingo tipo ugdymo įstaigose, matematikos gebėjimus baigiant pagrindinę mokyklą. Atlikta kiekybinė duomenų analizė. Tyrime dalyvavo šešiasdešimt 10 klasės mokinių, besimokančių įvairiose Lietuvos mokyklose (30 bendrojo lavinimo mokyklos mokinių ir 30 specialiosios mokyklos mokinių), be to buvo apklausti 20 bendrojo lavinimo mokyklos mokytojų, dirbančių su nežymiai protiškai atsilikusiais mokiniais. Empirinėje dalyje nagrinėjami nežymiai protiškai atsilikusių mokinių, besimokančių specialiosiose mokyklose ir integruotai, matematikos programos įsisavinimo lygis. Svarbiausios empirinio tyrimo išvados: 1. Palyginus nežymiai protiškai atsilikusių mokinių matematinius gebėjimus pagal specialiosios mokyklos programą galima teigti, kad abiejų grupių mokinių programinės medžiagos įsisavinimo lygis beveik nesiskiria, o esantis skirtumas yra toks nežymus ir parodo, kad abiejų tipų mokyklų mokinių... [toliau žr. visą tekstą] / The work presents a theoretical analysis of the situation of SEN children’s integration into comprehensive schools and their mathematical abilities. The hypothesis raised in this work, i.e. that the mathematical abilities of slightly mentally deficient 10th formers at special and comprehensive schools are very much similar, has been approved. An investigation has been carried out in a survey method with a purpose to evaluate the mathematical abilities at the period of graduating from the basic school of slightly mentally deficient 10th formers’ at different educational institutions. A quantitative data analysis has been made. Sixty 10th formers from different schools in Lithuania (30 children from comprehensive schools, and 30 from special education schools) have been investigated, as well as 20 teachers from comprehensive schools, that work with slightly mentally deficient children, have been interviewed. The empiric part of the work deals with slightly mentally deficient children’s from special education schools and those who are integrated in the comprehensive schools level of mathematical knowledge. The following are the main conclusions drawn from the empiric investigation: 1. After comparing slightly mentally deficient children’s from both groups abilities to absorb the information at maths, it turned out that these abilities are rather equal, and the difference, if any, is so little, that it only supports the idea that children’s from the special education... [to full text]

Orientador: Marcia Regina Ferreira de Brito / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Educação / Made available in DSpace on 2018-08-05T04:06:21Z (GMT). No. of bitstreams: 1 Viana_OdaleaAparecida_D.pdf: 13457630 bytes, checksum: cf0ae91ebe117f9120972fbd9fc97dc2 (MD5) Previous issue date: 2005 / Resumo: Considerando a influência de fatores cognitivos e afetivos no desempenho escolar em geometria, este trabalho teve como objetivos analisar o componente espacial da habilidade matemática e verificar a existência de relações entre este componente, o raciocínio espacial, as atitudes em relação à matemática e à geometria e o desempenho escolar. Foram sujeitos 177 alunos de ensino médio de uma escola particular, tendo sido aplicadas duas provas tipo lápis e papel, um teste psicológico de raciocínio espacial e duas escalas de atitudes em relação à matemática e geometria. A análise fatorial das operações do componente espacial da habilidade matemática (contagem de cubos, formação e identificação de polígonos no espaço, secção, planificação, projeção e revolução) indicou a existência de um único fator, o que comprova que a prova avaliou a habilidade geral dos sujeitos em lidar com conceitos geométricos espaciais trabalhados no ensino médio, com base nas tarefas propostas. As atitudes em relação à matemática estavam relacionadas com as atitudes em relação à geometria. O desempenho em geometria estava relacionado com o raciocínio espacial, com o componente espacial da habilidade matemática e com as atitudes em relação à geometria. O trabalho faz referência aos processos de formação, inspeção e transformação de imagens mentais evidenciados nas fases de obtenção e de processamento da informação geométrica de problemas. As representações pictóricas externas demonstradas na solução de problemas geométricos com estrutura espacial foram classificadas de acordo com a funcionalidade, coerência e detalhamento, sendo que os dados mostraram que sujeitos mais habilidosos elaboram representações parciais e coerentes e não as utilizavam com a função de assistência perceptual.Psicologia da educação matemática; ensino de geometria; habilidade matemática; raciocínio espacial; habilidade visual / Abstract: In considering the influence of cognitive and affective factors in academic achievement of geometry, the objectives of this work were to analyze the spatial component of mathematical ability and to verify the existence of relations among this component, the spatial sense, the attitudes toward Mathematics and Geometry and the academic performance. The subjects of this research were 177 students, from three grades of a particular school from Mogi das Cruzes ¿ SP. Two questionnaires with pencil and paper, one spatial sense test and two attitudes scales toward mathematics and geometry were applied. The factorial analysis of spatial component operations of mathematics ability (counting of cubes, formation and identification of polygon in space, section, planning, projection and rotation) indicated the existence of one factor. It proved that the test evaluated the general ability to deal with geometric concepts that are taught in the secondary school, taking into account the proposed tasks. The attitudes toward Mathematics were related to the attitudes toward geometry. The geometry performance was related to the spatial sense, to the spatial component of mathematical ability and to the attitudes toward mathematics and geometry. This work made reference to the formation, inspection and transformation of visual mental images, whose processes were evidenced in the phases of acquisition and processing of problems geometrical information. The external graphical representations that were evidenced in the solution of geometry problems with the spatial structure were classified according to the function, coherence and detailing, and the dates indicated that the most talented students made partial and coherent representations and did not utilize them as perceptual assistance.Psychology of Mathematics Education; geometry teaching; mathematical abilities; spatial sense / Doutorado / Educação Matematica / Doutor em Educação

Most of people have fatal attitude to Mathematics: some of them are capable to learn it form nature, but the others are not. So is their fate – to suffer from it for the whole of life… But it is a rude though natural mistake, as it results from means of mathematical education and its content. Most of parents and teachers are directed on these aspects both in kindergarten and at primary school. Of course, parents are different. Nevertheless so many parents can’t possibly but speak about achievements of their children. Some start making their own children learn better by the example of success of the others. They make their children learn long chains of figures with no understanding. It is even more sad to see how a mom asks her 4-year old son: “How much is two plus three?..’ But he replies just because he learned the answer but not calculated. Not only parents but also kindergarten tutors don’t want to understand that drilling for arithmetic has no sense. For a specialist it would take two days only…But teach him how to think logically – is a goal demanding from him, reached by different means.

Vid arbete med matematiska textuppgifter krävs det en god läsförmåga, läsförståelse och ett bra arbetsminne. Om en elev har brister såväl i läsningen som i arbetsminnet resulterar det i stora svårigheter när arbete med matematiska textuppgifter sker. Det finns ett flertal förklaringar till varför elever har svårigheter vid arbete med matematiska textuppgifter, dessa förklaringar belyses i den här studien. Den här systematiska litteraturstudien har som syfte att beskriva de underliggande faktorerna till svårigheter vid arbete i matematiken med textuppgifter samt hur lärare arbetar för att underlätta lärande i ämnet matematik för elever med svårigheter inom matematiska textuppgifter. Metoden som används för att besvara studiens frågeställningar är en innehållsanalys av tio vetenskapliga artiklar som har sökts fram på ett systematiskt och strukturerat sätt. Resultatet utgår från de tio vetenskapliga artiklar som analyserades genom innehållsanalys. I artiklarna identifieras följande teoretiska ramverk, (1) sociokulturellt perspektiv, (2) diskursanalys och (3) Kintschs teori om textförståelse. Flera artiklar förklarar svårigheter med matematiska textuppgifter som en konsekvens av antingen kognitiva nedsättningar eller överflödig information. Båda dessa försvårar för eleverna. Ett antal av artiklarna lyfter även metoder som lärare kan använda sig av när de ska stötta samt utmana elever när det gäller matematiska textuppgifter.

Today's Swedish mathematics education is largely textbook-bound. At the same time, the textbooks are not reviewed, quality assured or checked by the curriculum in mathematics. The purpose of this study was to investigate the prevalence of open assignments and what abilities these helped the students develop. As a teacher, it is important to be aware of what tasks students encounter as well as what abilities these will train. Previous research shows that open-ended assignments are very helpful for the development of mathematical abilities for students. As an analytical starting point, Sullivan and Lilburn’s (2002) criteria for open-ended questions and MCRF's framework (Lithner et. al, 2010) for mathematical abilities were used. The analysis revealed that there was little data that fell under the criteria for open-ended questions. In the available tasks, they get to develop several mathematical abilities. “Favorit matematik” was the textbook that offered the greatest variety of tasks for developing mathematical abilities in the open-ended assignments that existed.

I dagens skola ur en global kontext pekar forskning på att undervisningen i matematiken är väldigt bokbunden. Forskningen visar samtidigt att läroböckerna behandlar rutinuppgifter i stor utsträckning och liten variation av problemlösningsuppgifter som elever får möta i undervisningen. Detta ger inte samma möjlighet till utmaning av alla de matematiska förmågorna hos eleverna. Syftet med undersökningen var att ta reda på vilka möjligheter läroböckerna gav eleverna att möta problemlösning som kunde stödja deras utveckling inom matematiken.  För att få svar på vårt syfte genomfördes en läromedelsanalys av två olika läroboksserier som innehöll sex böcker totalt. Resultatet pekade på att olika läroböcker presenterade problemlösning på olika sätt, vilket gav eleverna olika möjligheter till problemlösning. Studiens resultat visade också på att det fanns en övervägande mängd rutinuppgifter som hindrar eleverna att tillägna sig matematik. Läraren kommer därför vara en viktig funktion för elevernas utveckling av problemlösning, då de har en avgörande roll att frambringa de matematiska problemens fullständiga potential i elevernas utövande kring de matematiska förmågorna. Lärarens val av läroböcker kan vara avgörande för elevernas möjligheter att möta problemlösning, då läraren måste vara medveten om lärobokens begränsningar och potential för att stödja elevernas utveckling inom matematik. / In today's educational context, research indicates that mathematics instruction is heavily reliant on textbooks. At the same time, studies show that textbooks focus on routine exercises and offer limited variation in the problem-solving tasks students encounter in class. This lack of diversity does not adequately challenge all students' mathematical abilities. The aim of this study was to investigate the extent to which textbooks provide opportunities for students to engage in problem-solving tasks that support their mathematical development. To address this aim, a textbook analysis was conducted on two different textbook series comprising a total of six books. The results indicated that different textbooks presented problem-solving in varying ways, thereby affording students different opportunities for engaging in problem-solving activities. The study also revealed that there is a predominance of routine tasks, which impedes students' ability to fully acquire mathematical skills. Therefore, the role of the teacher is crucial in enhancing students' problem-solving capabilities, as they are instrumental in unlocking the full potential of mathematical problems in the context of developing students' mathematical competencies. Teachers' choice of textbooks can significantly impact students' exposure to problem-solving, as educators must be aware of both the limitations and potential of textbooks in supporting students' mathematical development.