Det verkar finnas en allmän uppfattning om att matematiska texter är så speciella att man måste få lära sig en särskild typ av läsförmåga för att förstå sådana texter. Denna uppfattning verkar dock inte vara baserad på forskningsresultat eftersom det visar sig inte finnas mycket forskning genomförd som behandlar läsförståelse inom matematik. Huvudsyftet med denna avhandling är att undersöka om det krävs speciella kunskaper eller förmågor för att läsa matematiska texter. Fokus ligger på studerandes läsning av olika typer av texter som behandlar matematik från grundläggande universitetsnivå. Detta studeras utifrån två olika perspektiv, dels ett kognitivt, där läsförmågor och ämneskunskaper studeras i relation till läsförståelse, och dels ett metakognitivt, vilket innefattar uppfattningar och hur man som läsare avgör om man förstått en text. I avhandlingen ingår tre empiriska studier samt teoretiska diskussioner som bland annat utgår från två litteraturstudier, den ena om egenskaper hos matematiska texter och den andra om läsning i relation till problemlösning. I de empiriska studierna jämförs dels läsning av matematiska texter med läsning av texter med annat ämnesinnehåll och dels läsning av olika typer av matematiska texter, där speciellt symbolanvändningen och om innehållet berör begrepp eller procedurer studeras. Dessutom undersöks hur studerande uppfattar sin egen läsförståelse samt läsning och texter i allmänhet inom matematik, och huruvida variationer i dessa uppfattningar kan kopplas till läsförståelsen. Resultat från studierna i denna avhandling visar att de studerande verkar använda en speciell sorts läsförmåga för matematiska texter; att fokusera på symboler i en text. För matematiska texter utan symboler utnyttjas en mer generell läsförmåga, det vill säga en läsförmåga som används också för texter med annat ämnesinnehåll. Men när symboler finns i texten läses alltså texten på ett särskilt sätt, vilket påverkar läsförståelsen på olika sätt för olika typer av texter (avseende om de berör begrepp eller procedurer). Jämfört med när den generella läsförmågan utnyttjas, skapas sämre läsförståelse när den speciella läsförmågan används. Det verkar finnas ett behov av att fokusera på läsning och läsförståelse inom matematikutbildning eftersom resultat visar att kurser på gymnasiet (kurs E) och på universitetet (inom algebra och analys) inte påverkar den speciella läsförmågan. De nämnda resultaten påvisar dock att det primärt inte nödvändigtvis handlar om att lära sig att läsa matematiska texter på något särskilt sätt utan att utnyttja en befintlig generell läsförmåga också för matematiska texter. Resultat från det metakognitiva perspektivet påvisar en skillnad mellan medvetna aspekter, såsom avseende uppfattningar och reflektion kring förståelse, samt omedvetna aspekter, såsom de mer automatiska processer som gör att man förstår en text när den läses, där också metakognitiva processer finns aktiva. Speciellt visar det sig att uppfattningar, som undersökts med hjälp av en enkät, inte har någon tydlig och oberoende effekt på läsförståelse. Utifrån de texter som använts och de studerande som deltagit verkar det som helhet inte finnas någon anledning att betrakta läsning av matematiska texter som en speciell sorts process som kräver särskilda läsförmågor. Studerandes utveckling av speciella läsförmågor kan istället handla om att de inte upplevt något behov av (eller krav på) att läsa olika typer av matematiska texter där likheter med läsning i allmänhet kan uppmärksammas och utnyttjas. / There seems to exist a general belief that one needs to learn specifically how to read mathematical texts, that is, a need to develop a special kind of reading ability for such texts. However, this belief does not seem to be based on research results since it does not exist much research that focus on reading comprehension in mathematics. The main purpose of this dissertation is to examine whether a reader needs special types of knowledge or abilities in order to read mathematical texts. Focus is on students’ reading of different kinds of texts that contain mathematics from introductory university level. The reading of mathematical texts is studied from two different perspectives, on the one hand a cognitive perspective, where reading abilities and content knowledge are studied in relation to reading comprehension, and on the other a metacognitive perspective, where focus is on beliefs and how a reader determines whether a text has been understood or not. Three empirical studies together with theoretical discussions, partly based on two literature surveys, are included in this dissertation. The literature surveys deal with properties of mathematical texts and reading in relation to problem solving. The empirical studies compare the reading of different types of texts, partly mathematical texts with texts with content from another domain and partly different types of mathematical texts, where focus is on the use of symbols and texts focusing on conceptual or procedural knowledge. Furthermore, students’ beliefs about their own reading comprehension and about texts and reading in general in mathematics are studied, in particular whether these beliefs are connected to reading comprehension. The results from the studies in this dissertation show that the students seem to use a special type of reading ability for mathematical texts; to focus on symbols in a text. For mathematical texts without symbols, a more general reading ability is used, that is, a type of ability also used for texts with content from another domain. The special type of reading ability used for texts including symbols affects the reading comprehension differently depending on whether the text focuses on conceptual or procedural knowledge. Compared to the use of the more general reading ability, the use of the special reading ability creates a worse reading comprehension. There seems to exist a need to focus on reading and reading comprehension in mathematics education since results in this dissertation show that courses at the upper secondary level (course E) and at the university level (in algebra and analysis) do not affect the special reading ability. However, the mentioned results show that this focus on reading does not necessarily need to be about learning to read mathematical texts in a special manner but to use an existing, more general, reading ability also for mathematical texts. Results from the metacognitive perspective show a difference between conscious aspects, such as regarding beliefs and reflections about comprehension, and unconscious aspects, such as the more automatic processes that make a reader understand a text, where also metacognitive processes are active. In particular, beliefs, which have been examined through a questionnaire, do not have a clear and independent effect on reading comprehension. From the texts used in these studies and the participating students, there seems not do be a general need to view the reading of mathematical texts as a special kind of process that demands special types of reading abilities. Instead, the development of a special type of reading ability among students could be caused by a lack of experiences regarding a need to read different types of mathematical texts where similarities with reading in general can be highlighted and used.

Made available in DSpace on 2016-06-02T19:44:01Z (GMT). No. of bitstreams: 1 TeseGRSM.pdf: 4427126 bytes, checksum: 24de1763ffa95aca870f571e61dd695e (MD5) Previous issue date: 2007-05-22 / The comprehension of written texts continues being one of the most difficult academic practices for students of Basic Education. If comprehending a written material in linguistic terms brings out difficulties for some students, a text written in mathematical language can be even more difficult, because besides the mother language understanding, mathematical concepts are also needed. A lot of research has been done to try to find better ways to help children understand what was asked in mathematical problem-questions. However, there is a lot to be done to understand the difficulties and processes of problem resolution and about basic conceptual comprehension present in mathematical problems instructions. In this sense, the purpose of the present study was to elaborate, apply and evaluate an intervention program performed with children in the fourth year of Elementary School who showed difficulties comprehending and solving mathematical problems, and maximize their cognitive capacity. The methodology chosen was the experimental delineation of comparison between groups, an experimental and a control group. The study consisted of a pretest, an intervention program, a post-test and a delayed post-test. The pretest evaluated the children s performance in resolving arithmetical problems. Next, the teaching program was used with students who showed performance under 40% right in problems. This aimed to develop, in the students, enough knowledge to increase their resolution capacity of mathematical problems. That program sought to teach students to read mathematical problems instructions and find the most appropriate mathematical representation to solve the question. For this, it was necessary to teach the arithmetical operations concepts, since one of the children s difficulties was connected with understanding the meaning of each operation (addition, subtraction, multiplication and division) and its symbolic representation. The post-test and delayed posttest results for the experimental group were superior to the pretest results for the experimental and control groups, indicating an improvement in performance for the students who took part in the program. Those data showed that the intervention utilized was efficient, increasing the cognitive capacity necessary to the task of resolving arithmetical problems, which basically consists of comprehending written instructions and representing them mathematically. / A compreensão de textos escritos mantém-se, atualmente, como uma das práticas acadêmicas mais difíceis para estudantes da Educação Básica. Se compreender um material escrito em termos linguísticos traz dificuldades para alguns alunos, um texto escrito em linguagem matemática pode ser mais difícil, porque, além do entendimento da língua materna, faz-se necessário ter conceitos matemáticos para compreendê-lo. Muitas pesquisas tentaram encontrar formas melhores para ajudar as crianças a entender o que era solicitado em situações-problema de matemática, entretanto, ainda há muito que fazer para se entender os processos e dificuldades envolvidos na resolução de problemas pelos escolares e para se levá-los a compreender os conceitos básicos contidos nos enunciados matemáticos. Nesse sentido, o presente estudo teve como objetivos elaborar, aplicar e avaliar um programa de intervenção com crianças de 4ª série do Ensino Fundamental que apresentavam dificuldades na compreensão e resolução de problemas matemáticos e maximizar as capacidades cognitivas destas crianças. A metodologia escolhida foi o delineamento experimental de comparação entre grupos, um grupo experimental e um grupo controle. O estudo consistiu de um pré-teste, um programa de intervenção, um pós-teste e um pós-teste postergado. O pré-teste avaliou o desempenho das crianças na tarefa de resolução de problemas aritméticos. Em seguida, foi aplicado o programa de ensino nos estudantes que apresentaram um desempenho inferior a 40% de acertos nos problemas propostos. O objetivo foi desenvolver nos alunos o repertório necessário para aumentar a capacidade de resolução de problemas matemáticos. Este programa procurou ensinar os estudantes a lerem os enunciados dos problemas e encontrarem a representação matemática mais apropriada para resolver a questão. Para tanto, foi necessário ensinar os conceitos das operações aritméticas, visto que uma das dificuldades das crianças estava no campo do entendimento do significado de cada operação (adição, subtração, multiplicação e divisão) e sua representação simbólica. Os resultados dos pós-teste e pós-teste postergado do grupo experimental foram superiores aos resultados dos pré-teste do grupo experimental e do grupo controle, indicando melhora no desempenho dos estudantes que participaram do programa. Demonstrou-se, com estes dados, que a intervenção utilizada foi eficiente, desenvolvendo as capacidades cognitivas necessárias à tarefa de resolução de problemas aritméticos, que consiste basicamente, em compreender o enunciado escrito e representá-lo matematicamente.