I Sverige är vart fjärde barn flerspråkig på grund av utländsk bakgrund. Studier har visat att flerspråkiga elever har sämre skolresultat än enspråkiga elever. Denna kunskapsöversikt fokuserar på de faktorer som utgör svårigheter för flerspråkiga elever i matematikämnet i Sverige. Vidare uppmärksammas även de olika svårigheter. Sökningen efter kunskap gjordes systematiskt i tre olika databaser, SwePub, ERC och ERIC samt i Google och Malmö universitets hemsida. Sökorden, antal träffar och ett första urval dokumenterades. Sammanfattningarna för artiklarna lästes och ytterligare några artiklar valdes bort. De kvarvarande artiklarna användes för att besvara frågeställningarna. Flerspråkiga elever möter större utmaningar i matematikundervisningen och har därmed svårare att utveckla matematiska förmågor. Elevernas språkliga bakgrund är således en anledning till deras försämrade skolresultat. De svårigheter som uppstår för en elev som ännu inte behärskar undervisningsspråket väl, är främst i samband med textuppgifter i matematik och beror på elevens ordförråd i det ämnesspecifika språket. Denna kunskapsöversikt ger en djupare förståelse av anledningarna till att flerspråkiga elever möter svårigheter i matematikämnet och vilka dessa svårigheter är. Nyckelord: Matematikförmågor, språkfärdigheter, anledningar, svårigheter, flerspråkighet

SOUSA, Eryvelton Alves. A matemática nos truques, adivinhações e enigmas. 2014. 73 f. Dissertação (Mestrado em Matemática em Rede Nacional) – Centro de Ciências, Universidade Federal do Ceará, Juazeiro do Norte, 2014 / Submitted by Rocilda Sales (rocilda@ufc.br) on 2016-04-22T12:50:42Z No. of bitstreams: 1 2014_dis_easousa.pdf: 1269050 bytes, checksum: 7bd7f3447dcc4e4235eb3a100b5cccfb (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-04-22T12:53:55Z (GMT) No. of bitstreams: 1 2014_dis_easousa.pdf: 1269050 bytes, checksum: 7bd7f3447dcc4e4235eb3a100b5cccfb (MD5) / Made available in DSpace on 2016-04-22T12:53:55Z (GMT). No. of bitstreams: 1 2014_dis_easousa.pdf: 1269050 bytes, checksum: 7bd7f3447dcc4e4235eb3a100b5cccfb (MD5) Previous issue date: 2014 / This paper discusses mathematical problems known as tricks, riddles or puzzles, in order to show the teachers and students with the beauty that can be found in mathematics. It is through less routine situations we seek to foster in students a mathematician. We also present a brief pedagogical foundation based on the needs of the teacher teaching mathematics to know how to approach situations and problems during a course, and not a theoretical axiomatic exposition of content but so that they can ensure the correct interpretation of the problems listados.O goal was to gather a list of issues to support and motivate students to become more interested in mathematics using a subtle side that is often neglected in the teaching of mathematics in elementary and middle school. / Esta dissertação aborda problemas matemticos conhecidos como truques, adivinhações ou enigmas, com o intuito de mostrar a professores e alunos a beleza com que pode ser encontrada a matemática. É através de situações menos rotineiras que buscamos um despertar matemático nos estudantes. Apresentamos também um breve embasamento pedagógico fundamentado nas necessidades do professor conhecer o ensino da matemática e como abordar situações problemas durante um curso, e uma exposição teórica de conteúdos de forma não axiomática mas que possam garantir a boa interpretação dos problemas listados.O objetivo foi reunir uma lista de problemas sobre álgebra para fundamentar e motivar os alunos a se interessarem mais pela matemática usando um lado sutil que muitas vezes é deixado de lado no ensino da matemática do ensino fundamental e médio.

Made available in DSpace on 2015-03-26T14:00:04Z (GMT). No. of bitstreams: 1 texto completo.pdf: 3121918 bytes, checksum: 6f872883d570dfc6b725f9158a25be1a (MD5) Previous issue date: 2013-03-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this dissertation we developed a proposal for an educational activity involving math competitions. The work consists of a literature review, presenting a route of the history of the Mathematics Olympics in Brazil and around the world, we make this through the reading and study of regulations, the electronic pages of competitions and such other documents. In this context, we present activities that can be used as diffusion, preparation and stimulation of participation and engagement with the competition or even that may be used in the classroom. We concluded by preparing a primer, A Primer for the Olympiad Mathematics , a backing material and support to those interested in implementing a competition of this kind in a school or even in a broader context. / Nesta dissertação elaboramos uma proposta de atividade educacional que envolve competições matemáticas. O trabalho consta de revisão bibliográfica, apresentando um histórico das Olimpíadas de Matemática no Brasil e no Mundo e dando subsídios, através da leitura e estudo de regulamentos, páginas eletrônicas de competições dessa natureza e outros documentos para elaboração da atividade. Neste contexto, apresentamos atividades que podem ser utilizadas como divulgação, preparação e estímulo à participação e envolvimento com a competição ou até mesmo que possam ser utilizadas apenas na sala de aula. Concluímos elaborando uma cartilha, A Cartilha da Olimpíada de Matemática , um material de suporte e apoio aos interessados em implantar uma competição desse tipo, em uma escola ou até mesmo em contexto mais amplo.

Submitted by MARCOS LEANDRO TEIXEIRA DE OLIVEIRA (marcosteixeira@ufv.br) on 2018-09-13T13:43:08Z No. of bitstreams: 2 texto completo.pdf: 3563880 bytes, checksum: d9fabbe1e5d5e321f110a6eef8ec0d8e (MD5) texto completo.pdf: 3563880 bytes, checksum: d9fabbe1e5d5e321f110a6eef8ec0d8e (MD5) / Made available in DSpace on 2018-09-13T13:43:08Z (GMT). No. of bitstreams: 2 texto completo.pdf: 3563880 bytes, checksum: d9fabbe1e5d5e321f110a6eef8ec0d8e (MD5) texto completo.pdf: 3563880 bytes, checksum: d9fabbe1e5d5e321f110a6eef8ec0d8e (MD5) Previous issue date: 2018-02-23 / São analisados contextos reais - combustı́veis, consumo de água e energia elétrica, sistema eleitoral brasileiro e finanças pessoais -, bem como o reconhecimento e o desenvolvimento de modelos matemáticos associados a cada contexto. A partir dos princı́pios norteadores dos Parâmetros Curriculares Nacionais e da Base Nacional Comum Curricular, que reforçam a relevância da Matemática para a formação de cidadãos, estabelece-se uma proposta pedagógica que alinha o rigor dos conceitos matemáticos às suas aplicabilidades práticas. Para isso, são apresentadas sequências de atividades investigativas em ambientes colaborativos, que promovem o debate argumentativo entre os pares para a resolução de problemas e privilegia o uso de tecnologias digitais de informação e comunicação. / Real contexts are analyzed - water and electricity consumption, fuels, Brazilian electoral system and personal finance -, as well as the recognition and development of mathematical models associated to each context. Based on the guiding principles of the National Curricular Parameters and the National Curricular Common Base, which reinforce the relevance of Mathematics for the formation of citizens, a pedagogical proposal is established, that aligns the rigor of mathematical concepts with their practical applicability. To do this, sequences of investigative activities are presented in collaborative environments, which promote argumentative debate among peers to solve problems and favor the use of digital and communication technologies.

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-04-05T16:56:00Z No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-06T11:04:20Z (GMT) No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-04-06T11:04:20Z (GMT). No. of bitstreams: 2 Dissertação - Adriano Rodrigues Teixeira - 2015.pdf: 12601586 bytes, checksum: 7d86470df655890876bcda71442e2d53 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-07 / The essay brings the main concepts of financial mathematics, looking to directly connect it to the events in our surroundings. As such, we descant about interest, discounting, periodic cycles and amortization systems. We will also apply Newtons method in order to determine the interest rates on payment series. / O trabalho traz os principais conceitos da matemática financeira, buscando sempre fazer uma ligação imediata com os acontecimentos ao nosso redor. A saber, discorremos sobre juros, descontos, séries periódicas e sistemas de amortizações. Além disso, aplicaremos o método de Newton para determinar da taxa de juros de séries de pagamentos.

Orientador: Vera Lucia Xavier Figueiredo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-24T01:52:45Z (GMT). No. of bitstreams: 1 Santos_LaudoClaumir_M.pdf: 2046963 bytes, checksum: 7e5846cd5860b61687378860b26a038b (MD5) Previous issue date: 1998 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática

Thesis (PhD)--Stellenbosch Universityh, 1995. / ENGLISH ABSTRACT: This study investigates the influence of readability of mathematics examination questions on achievement. The aim of any mathematics examination is to assess whether the aims of a specific mathematics programme have been realized. Readability factors that unnecessarily prevent a clear understanding of questions could jeopardize this aim. The important issue is, therefore, whether there are indeed readability factors in mathematics examination questions that cause comprehension problems for students and, if there are, do they hav~ any effect on test scores? The issue of readability is of even greater importance for second language readers. In the South Mrican context, the reading problems of second language readers are of particular importance as most students at school are second language learners. An important question would therefore be: What readability factors cause comprehension difficulties for second language students, especially those whose mother tongue is not kindred to English? Furthermore, what is the influence of cultural factors on readability? This study provides answers to these and other related questions for mathematics text at senior secondary school level. Protocol analysis was used to ascertain what readability problems are experienced by students when reading examination questions in mathematics. Three different language groups, comprising 17 -18-year-old students, were used in the study: English First Language students and two groups who had English as a second language. One second language group had Mrikaans as first language while the other group comprised Mrican students whose mother tongue is unrelated to English. A framework was developed to analyse the protocols and it comprised five categories: unfamiliar vocabulary structural problems obscure information visualization difficulties non-verbal factors Mter the protocol study, students were asked to adapt the examination questions to a more comprehensible form. Students' adaptations addressed lexical, syntactical, discourse and non-verbal factors. Most of the readability problems identified in the literature study were verified in the empirical study. However, the empirical study generated additional readability problems that are mainly restricted to mathematics text and relate to nonverbal factors like mathematical expressions. During the last phase of the empirical study a composite test was used to test the hypothesis that improved readability of the common language used in mathematics examination questions' will improve achievement. Nine socalled "word problems" from previous examination papers were set in three different versions: original, adapted and non-verbal. The hypothesis was confirmed in a number of important cases. A significant finding of the study was, therefore, that readability factors not only influence the comprehension of mathematics examination questions, but also have a marked influence on students' achievement levels. The results of the empirical study are reported quantitatively as well as qualitatively. Other results include the following: Not only second language students, but also first language students experienced a variety of readability problems. All three language groups demonstrated the same level of competency on the non-verbal versions. When comparing test scores of the verbal versions, differences in achievement levels between the different language groups were often caused by linguistic and cultural factors. Cultural thought patterns, typical of a mother tongue but absent in a second language, were often a source of comprehension difficulties for second language readers. This study has led to certain conclusions for teaching and examination practice. For example, factors influencing the readability of ordinary English should be considered with other factors when writing mathematics examination questions. Furthermore, the distinctly different reading needs of second language students suggest that examination papers be set, so that the language needs of second language learners are accommodated. Guidelines for writing more readable examination questions were developed and are presented as a readability checklist. Suggestions for further research include the investigation of the influence of readability on achievement in authentic examination conditions. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die invloed van leesbaarheid van wiskunde eksamenvrae op prestasie. Die doel van enige wiskunde eksamen is om vas te stel of die doelwitte van 'n spesifieke wiskunde program bereik is. Leesbaarheidsfaktore wat die volledige begryp van vraestelle onnodig belemmer, kan die bereiking van hierdie doel verhinder. Dit is dus belangrik om vas te stel of daar wel leesbaarheidsfaktore in wiskunde eksamenvrae bestaan wat vir leerlinge begripsprobleme veroorsaak en, indien wel, of hulle enige effek op toetspunte het. Vir tweedetaallesers is die kwessie van leesbaarheid van nog groter belang. In die SuidAfrikaanse opset is die leesprobleme van tweedetaal lesers 'n uiters aktuele saak aangesien die meeste skoolleerlinge tweedetaal leerders is. Belangrike vrae is dus: Watter faktore veroorsaak leesbaarheidsprobleme vir tweedetaalleerlinge, veral diegene met 'n nie-verwante moedertaal en, watter invloed het kultuur op leesbaarheid? Hierdie ondersoek bied antwoorde op hierdie en ander verwante vrae ten opsigte van wiskunde eksamenvrae op senior sekondere vlak. Protokol analise is gebruik om vas te stel watter leesbaarheidsprobleme ondervind word wanneer leerlinge wiskunde eksamenvrae lees. Drie verskillende taalgroepe, bestaande uit 17 -18-jarige leerlinge, het aan die ondersoek deelgeneem: Engels Eerstetaalleerlinge en twee groepe wat Engels as tweede taal gehad het. Een van die tweedetaal groepe het Afrikaans as eerste taal gehad terwyl die ander groep bestaan het uit Afrikane wie se moedertaal nie aan Engels verwant is nie. 'n Raamwerk is ontwikkel om die protokolle te analiseer en het uit die volgende vyf kategoriee bestaan: onbekende woordeskat strukturele probleme onduidelike inligting visualiseringsprobleme nie-verbale probleme Gedurende die tweede fase van die ondersoek is leerlinge gevra om die vrae tot 'n meer verstaanbare vorm aan te pas. Leerlinge se aanpassings het leksikale, sintaktiese, diskoers en nie-verbale faktore aangespreek. Sommige leesbaarheidsprobleme wat in die literatuurstudie gei'dentifiseer is, is in die empiriese ondersoek geverifieer. Die empiriese ondersoek het egter addisionele leesbaarheidsprobleme uitgelig wat meerendeels wiskundig van aard is en verband hou met nie-verbale faktore soos wiskunde uitdrukkings. Gedurende die laaste deel van die empiriese ondersoek is 'n samegestelde toets gebruik om die volgende hipotese te toets: Verbeterde leesbaarheid van die gewone taal wat in wiskunde eksamenvrae gebruik word, sal die prestasie van leerlinge verb et er. N ege sogenaamde woordsomme is op verskillende maniere gestel: oorspronklik, aangepas en nie-verbaal. Die hipotese is in 'n hele aantal belangrike gevalle bevestig. Een van die bevindinge van die ondersoek was dus dat leesbaarheidsfaktore nie slegs be grip ten opsigte van wiskunde eksamenvrae bei:nvloed nie, maar ook 'n beduidende invloed op prestasie het. Die resultate van die empiriese ondersoek word kwalitatief sowel as kwantitatief weergegee. Ander resultate sluit die volgende in: Nie slegs tweedetaal leerlinge nie, maar ook eerstetaal leerlinge het 'n verskeidenhied van leesbaarheidsprobleme ondervind Al drie taalgroepe het op die nie-verbale weergawe dieselfde bekwaamheidsvlak getoon. Verskille in die prestasievlakke tussen die verskillende taalgroepe op die verbale weergawes is baiekeer deur taalkundige en kulturele faktore veroorsaak Kulturele denkpatrone wat tipies is van 'n leerling se moedertaal, maar nie in die tweedetaal voorkom nie, het dikwels tot begripsprobleme by tweedetaal lesers gelei. Hierdie ondersoek het sekere gevolgtrekkings v1r o~derrig- en eksamenpraktyk. Byvoorbeeld, faktore wat die leesbaarheid van gewone Engels bei:nvloed, behoort saam met ander faktore in ag geneem te word wanneer wiskunde eksamenvraestelle opgestel word. Verder is daar duidelike aanduidings dat aparte vraestelle vir eerste- en tweedetaal leerlinge opgestel moet word sodat die taalbehoeftes van tweedetaal leerlinge in ag geneem kan word. Riglyne vir die skryf van meer leesbare eksamenvrae is saamgestel en as 'n oorsiglys aangebied. Voorstelle vir verdere navorsing sluit in die ondersoek na die invloed van leesbaarheid op prestasie in ware eksamen omstandighede.

Diplomová práce s názvem "Poruchy učení v matematice a jejich reedukace na základní škole" je zaměřena na studium obtíží v matematice, které se objevují u žáků prvních až devátých ročníků. Práce je rozdělena do tří hlavních kapitol, které jsou pak ještě dále děleny na dílčí podkapitoly. První část tvoří teoretický základ o specifických vývojových poruchách obecně. Ten je nutný pro další studium poruch učení v matematice a zasazuje tak poruchy učení v matematice do širšího kontextu specifických vývojových poruch. Druhá kapitola je zaměřena konkrétně na poruchy a narušení matematických funkcí. Celý tento úsek tvoří teorie nezbytná pro pochopení této problematiky v praxi. Poslední, tedy třetí kapitola je orientována právě na praxi. Její podkapitoly se zabývají statistikou na Základní škole v Heřmanově Městci, výukovými programy na PC a mojí spoluprací s integrovaným chlapcem. Cílem mé práce bylo obohatit si teoretické znalosti, poznat práci s integrovanými žáky na základní škole a zkusit s nimi pracovat.

本研究旨在探討小學生在數學基本運算的歷程中，所產生的錯誤類型，由文獻中尋找出特定的錯誤類型加以驗證，並利用與受試晤談的方式來了解兒童的思考歷程，試圖找出這些錯誤類型發生的原因，同時探討不同性別在這些錯誤類型上是否有差異存在。 　　本研究以國小二、三及四年級的學生為取樣對象，有效樣本為1782人（男926，女856人）。研究工具為自編之「加法運算能力測驗」、「減法運算能力測驗」、「乘法運算能力測驗」及「除法運算能力測驗」：資料分析則以信度考驗、次數分配、皮爾遜積差相關及單因子多變量變異數分析來進行。 　　本研究的主要結果如下： 　　（一）在加法的基本運算中，學生最常犯的錯誤為「相加時未加上進位數」，但此類型錯誤多為隨機產生的。在與學生晤談過程中，即可發現是因學生對進位概念不夠深刻而導致不小心犯錯。比較具有系統性規則可循的錯誤類型為「個位數未進位至十位」及「不對稱相加」二種，這二種錯誤的產生與學生誤用對齊相加的概念有關。這四種錯誤類型彼此之間具有顯著的正相關存在。 　　（二）在減法的基本運算中，最明顯也具有系統性的錯誤類型為「大數減小數」及「０減任何數為０」，這二種類型錯誤可能原因與兒童自行建構錯誤算則及對０的概念不清楚有關，由學生的晤談中可加以佐證；其他的類型（由左而右運算及未退位相減）的系統性偏低，是屬於隨機性發生的，這四種錯誤類型之間具有顯著的正相關存在。 　　（三）在乘法的基本運算中，「進位數直接與十位相乘」、「個位數直接相乘，十位往左乘」及「未乘十位數」等三個錯誤類型具有系統性規則可循，而且這三種錯誤的產生與進位數位置干擾有關；其餘二個類型錯誤（進位數重複相加及未加進位數）則屬於隨機發生的錯誤，此五類型之間亦具有顯著正相關存在。 　　（四）在除法運算中「商數未補０」及「商數多加０」二種錯誤類型是系統性較強的錯誤，這二種錯誤與學生的位值概念不清楚有關；而「單獨相除」及「倒置商數」二個類型錯誤則多為隨機性產生的，此四種類型間具有顯著正相關存在。 　　根據研究結果加以討論，並提出若干建議，以供教學輔導之參考。

Studentų pažangą geriausiai nusako jų studijų dalykų bei bakalauro darbo vertinimai. Šiaulių universitete Matematikos ir informatikos fakultete Matematikos bei Matematikos ir informatikos bakalauro studijų programose pagrindiniai studijų dalykai yra: Matematinė analizė, Algebra, Fizika, Geometrija, Kompiuterinės matematikos sistemos ir Programavimo pagrindai. Bakalauro darbe analizuojame Šiaulių universiteto Matematikos ir informatikos fakulteto Matematikos bei Matematikos ir informatikos bakalauro studijų programų studentų įstojusių 2004–2008 pasiekimus. Šio darbo tikslas yra nustatyti, kuris iš pagrindinių studijų dalykų vertinimų labiausiai susijęs su baigiamojo bakalauro darbo vertinimu. Šiam ryšiui nustatyti naudojame koreliacinę analizę bei tiesinę regresiją. / Students’ advancement is described by their evaluation of study subjects and Bachelor's work. Basic subjects in Bachelor's degree program at Siauliai University, Faculty of Mathematics and Informatics are: Mathematical analysis, Algebra, Geometry, Physics, Computer mathematics system and Programming fundamentals. In Bachelor's work, we investigate a relation between 6 study subjects and Bachelor's work evaluations of students who entranced in 2004–2008. To describe this relation we use correlation analysis and linear regression.