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Kognitiva och metakognitiva perspektiv på läsförståelse inom matematik
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2006 (Swedish)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Cognitive and metacognitive perspectives on reading comprehension in mathematics (English)
Abstract [sv]

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.

Abstract [en]

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.

Place, publisher, year, edition, pages
Matematiska institutionen , 2006.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1057
Keyword [en]
mathematical texts, metacognition, reading comprehension, self-regulation, university, upper secondary level, beliefs, cognition
Keyword [sv]
gymnasium, kognition, läsförståelse, matematiska texter, metakognition, självreglering, universitet, uppfattningar
National Category
Didactics
Identifiers
URN: urn:nbn:se:liu:diva-7674ISBN: 91-85643-45-9 (print)OAI: oai:DiVA.org:liu-7674DiVA: diva2:22667
Public defence
2006-12-08, C3, Hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2006-11-10 Created: 2006-11-10 Last updated: 2016-11-30
List of papers
1. A reading comprehension perspective on problem solving
Open this publication in new window or tab >>A reading comprehension perspective on problem solving
2006 (English)In: Developing and researching quality in mathematics teaching and learning : proceedings of MADIF 5 : the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006 / [ed] Christer Bergsten and Barbro Grevholm, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2006, 136-145 p.Conference paper, Published paper (Refereed)
Abstract [en]

The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can affect and become an integral part of problem solving, and how it can be affected by the mathematical text content or by the mathematical situation when the text is read. Based on theories of reading comprehension and a literature review it is found that the relationship under study is complex and that the reading process can affect as well as act as an integral part of the problem solving process but also that not much research has focused on this relationship.

Place, publisher, year, edition, pages
Linköping: Svensk förening för matematikdidaktisk forskning (SMDF), 2006
Series
Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 5
National Category
Other Mathematics Didactics
Identifiers
urn:nbn:se:liu:diva-14116 (URN)91-973934-4-4 (ISBN)
Conference
MADIF 5, the 5th Swedish mathematics education research seminar, January 24-25, Malmö, Sweden
Available from: 2012-04-18 Created: 2006-11-10 Last updated: 2012-04-18Bibliographically approved
2. Characterizing reading comprehension of mathematical texts
Open this publication in new window or tab >>Characterizing reading comprehension of mathematical texts
2006 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 63, no 3, 325-346 p.Article in journal (Refereed) Published
Abstract [en]

This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.

Keyword
literacy, mathematical texts, mental representation, reading comprehension, symbols, university, upper secondary level
National Category
Other Mathematics Didactics
Identifiers
urn:nbn:se:liu:diva-14117 (URN)10.1007/s10649-005-9016-y (DOI)
Available from: 2006-11-10 Created: 2006-11-10 Last updated: 2012-03-21
3. Metacognition and reading - criteria for comprehension of mathematics texts
Open this publication in new window or tab >>Metacognition and reading - criteria for comprehension of mathematics texts
2006 (English)In: Proceedings of the 30th conference of the International group for the psychology of mathematics education / [ed] J. Novotná, H. Moraová, M. Krátká and N. Stehlíková, Prague: The International Group for the Psychology of Mathematics Education , 2006, Vol. 4, 289-296 p.Conference paper, Published paper (Other academic)
Abstract [en]

This study uses categories of comprehension criteria to examine students’ reasons for stating that they do, or do not, understand a given mathematics text. Nine student teachers were individually interviewed, where they read a text and commented on their comprehension, in particular, why they felt they did, or did not, understand the text. The students had some difficulties commenting on their comprehension in this manner, something that can be due to that much of comprehension monitoring, when criteria for comprehension are used, might be operating at an unconscious cognitive level. Some specific aspects of mathematics texts are examined, such as the symbolic language and conceptual and procedural understanding.

Place, publisher, year, edition, pages
Prague: The International Group for the Psychology of Mathematics Education, 2006
Series
PME Conference Proceedings, ISSN 0771-100X
National Category
Other Mathematics Didactics
Identifiers
urn:nbn:se:liu:diva-14118 (URN)000281571400037 ()
Conference
Conference of the International Group for the Psychology of Mathematics Education, 16 – 21 July, Prague, Czech Republic
Available from: 2010-02-16 Created: 2009-03-18 Last updated: 2012-08-16Bibliographically approved
4. A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
Open this publication in new window or tab >>A metacognitive perspective on reading mathe-matical texts: Students’ beliefs and criteria for comprehension
2006 (English)Manuscript (preprint) (Other academic)
National Category
Didactics Other Mathematics
Identifiers
urn:nbn:se:liu:diva-52953 (URN)
Available from: 2010-01-14 Created: 2010-01-14 Last updated: 2010-02-24

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