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Difficult to read or difficult to solve?: The role of natural language and other semiotic resources in mathematics tasks
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC). Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Språk och kommunikation)
2016 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Svårt att läsa eller svårt att lösa? : Aspekter av svårighet i relation till naturligt språk och andra semiotiska resurser i matematikuppgifter (Swedish)
Abstract [en]

When students solve mathematics tasks, the tasks are commonly given as written text, usually consisting of natural language, mathematical notation and different types of images. This is one reason why reading and interpreting such texts are important parts of being mathematically proficient, at least within the school context. The ability utilized when dealing with aspects of mathematical text is denoted in this thesis as a mathematical reading ability; this ability is useful when reading mathematical language, for example, in task text. There is, however, a lack of knowledge of what characterizes this mathematical language, what students need to learn regarding the mathematical language, and exactly which mathematical language that tests should preferably assess. Therefore, the purpose of this thesis is to contribute to the knowledge of aspects of difficulty related to textual features in mathematics tasks. In particular, one aim is to distinguish between a difficulty that has to do with a mathematical ability and another that has not. Different types of text analyses are utilized to capture textural features that might be demanding for the students when reading and solving mathematics tasks. Aspects regarding vocabulary are investigated both in a literature review and in a study where corpora are used to analyse word commonness. Other textual analyses focus on textual features that concern mathematical notation and images, besides natural language. Statistical methods are used to analyse potential relations between the textual features of interest and both task difficulty and task demand on reading ability. The results from the research review are sparse regarding difficult vocabulary, since few of the reviewed studies analyses word aspects separately. Several of the analysed textual features are related to aspects of difficulty. The results show that tasks with more words that are uncommon both in a mathematical context and in an everyday context, may favour students with good reading ability rather than students with good mathematical ability. Another textual feature that is likely to be demanding for students, is if the task texts contains many meaning relations, for example, when several words refer to the same or similar object. These results have implications for the school practice both regarding textual features that are important from an educational perspective and regarding the construction of tests. The research does also contribute to an understanding of what characterizes a mathematical language.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2016. , 74 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 58/16
Keyword [en]
mathematics education, multisemiotics, task text, difficulty, mathematical reading ability
National Category
Didactics Mathematics Languages and Literature Educational Sciences
Research subject
didactics of mathematics
Identifiers
URN: urn:nbn:se:umu:diva-126016ISBN: 978-91-7601-554-4 (print)OAI: oai:DiVA.org:umu-126016DiVA: diva2:974406
Public defence
2016-10-21, MA 121, MIT-huset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2016-09-30 Created: 2016-09-26 Last updated: 2016-10-11Bibliographically approved
List of papers
1. The study of difficult vocabulary in mathematics tasks: a framework and a literature review
Open this publication in new window or tab >>The study of difficult vocabulary in mathematics tasks: a framework and a literature review
(English)Manuscript (preprint) (Other academic)
Abstract [en]

The purpose of this study is to contribute to the methodology of research on difficult vocabulary in mathematics tasks. The contribution consists of a framework for the study of difficult vocabulary in mathematics tasks and a literature review of empirical research in the area. The framework includes five main aspects of word difficulty that have been examined in empirical studies and discuss these in the light of theories on reading comprehension. In addition, methodological issues are presented in relation to each main aspect. The literature review examines both methodological aspects of 36 reviewed articles, and synthesizes results on difficult vocabulary. The literature review shows that a commonly used method—to study several word aspects together—is very unfortunate from the perspective of building accumulative knowledge about difficult vocabulary in mathematics tasks. The only well-supported conclusion possible to draw from the synthesis of results from the empirical studies, is that some word aspects are not related to task difficulty.

Keyword
Review, vocabulary, difficult, task text
National Category
Didactics Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-126011 (URN)
Available from: 2016-09-26 Created: 2016-09-26 Last updated: 2016-09-29
2. Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency
Open this publication in new window or tab >>Uncommon vocabulary in mathematical tasks in relation to demand of reading ability and solution frequency
2015 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 20, no 1, 5-31 p.Article in journal (Refereed) Published
Abstract [en]

This study reports on the relation between commonness of the vocabulary used in mathematics tasks and aspects of students’ reading and solving of the tasks. The vocabulary in PISA tasks is analyzed according to how common the words are in a mathematical and an everyday context. The study examines correlations between different aspects of task difficulty and the presence of different types of uncommon vocabulary. The results show that the amount of words that are uncommon in both contexts are most important in relation to the reading and solving of the tasks. These words are not connected to the solution frequency of the task but to the demand of reading ability when solving the task.

Place, publisher, year, edition, pages
NMC Nationellt centrum för matematikutbildning, 2015
National Category
Didactics Other Mathematics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-91340 (URN)
Available from: 2014-07-30 Created: 2014-07-30 Last updated: 2017-12-05Bibliographically approved
3. The role of semiotic resources when reading and solving mathematics tasks
Open this publication in new window or tab >>The role of semiotic resources when reading and solving mathematics tasks
2016 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 21, no 3, 51-72 p.Article in journal (Refereed) Published
Abstract [en]

One part of being proficient in mathematics is to be able to read and solve mathematics tasks where mathematics is represented using different semiotic resources (i.e. natural language, mathematical notation, and different types of images). In the current study, statistical methods are used to investigate the potential meaning that the presence and co-occurrences of semiotic resources have for how demanding a mathematical task is to read and solve. The results reveal that the number of different semiotic resources in a mathematical task is not related to difficulty, but that difficulty is related to the particular combinations of semiotic resources where pictorial images are one of the resources. The results also indicate that the difficulty related to these semiotic characteristics is not related to an unnecessary reading demand.

Place, publisher, year, edition, pages
Gothenburg: Nationellt centrum för matematikutbildning (NCM), 2016
Keyword
language, semiotics, task text
National Category
Mathematics Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-125993 (URN)
Available from: 2016-09-26 Created: 2016-09-26 Last updated: 2017-11-21Bibliographically approved
4. Relations between various semiotic resources in mathematics tasks: a possible source of students’ difficulties
Open this publication in new window or tab >>Relations between various semiotic resources in mathematics tasks: a possible source of students’ difficulties
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Reading and solving mathematics tasks often involves reading and interpreting different semiotic resources such as natural language, mathematical notation and images. In the current study the purpose is to enhance the knowledge about how meaning relations (cohesive ties) between and within different semiotic resources are related to how difficult mathematics tasks are to read and solve. Statistical analyses are conducted of relations between the presence of different types of cohesive ties in relation to quantitative measures for how difficult the tasks are to read and solve. The results reveal a difficulty aspect related to the extent to which a task has cohesive ties, of any kind, but that a non-mathematics specific reading demand is not part of this difficulty aspect. For cohesive ties between different semiotic resources there is only a week relation between presence of such ties and task difficulty.

Keyword
Semiotics, language, task text, cohesion, mathematics
National Category
Mathematics Didactics
Research subject
didactics of mathematics
Identifiers
urn:nbn:se:umu:diva-126002 (URN)
Available from: 2016-09-26 Created: 2016-09-26 Last updated: 2016-09-29

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