# Magnus ÖsterholmUmeå University | UMU · Department of Science and Mathematics Education

Magnus Österholm

PhD

## About

33

Publications

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Introduction

## Publications

Publications (33)

The purpose of this study is to deepen the understanding of the relation between the language used in mathematics tasks and the difficulty in reading and solving the tasks. We examine issues of language both through linguistic features of tasks (word length, sentence length, task length, and information density) and through different natural langua...

The purpose of this study was to characterize students’ self-assessments when reading mathematical texts, in particular regarding what students use as a basis for evaluations of their own reading comprehension. A total of 91 students read two mathematical texts, and for each text they performed a self-assessment of their comprehension and completed...

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 diffi...

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 diffi...

This volume contains the proceedings of MADIF 9, the Ninth Swedish Mathe- matics Education Research Seminar, held in Umeå, February 4-2, 2014. The MADIF seminars are organised by the Swedish Society for Research in Mathematics Education (SMDF). MADIF aims to enhance the opportunities for discussion of research and exchange of perspectives, amongst...

Det språk vi använder oss av i matematikklassrummet kan fokuseras på många olika sätt. Språket är också nödvändigt att förhålla sig till vid utvecklingen av sitt matematiska tänkande. Författarna diskuterar här relationer mellan språk och lärande.

This study surveys claims in research articles regarding linguistic properties of mathematical texts, focusing on claims supported by empirical or logical arguments. It also performs a linguistic analysis to determine whether some of these claims are valid for school textbooks in mathematics and history. The result of the survey shows many and vary...

The study presented in this paper is a contribution to the scientific discussion about the role and use of theory in mathematics education research. In particular, focus is here on the use of and comparison between different types of theories and frameworks, which is discussed primarily through the example of an empirical study examining what types...

This paper focuses on relationships between vocabulary in mathematical tasks and
aspects of reading and solving these tasks. The paper contains a framework that
highlights a number of different aspects of word difficulty as well as many issues to
consider when planning and implementing empirical studies concerning vocabulary
in tasks, where the asp...

In this study we utilize results from Swedish students in PISA 2003 and 2006 to examine what types of task properties predict the demand of reading ability of a task. In particular, readability properties (sentence length, word length, common words, and information density) and task type properties (content, competence, and format) are examined. Th...

In this paper we examine four statistical methods used for characterizing mathematical test items regarding their demands of reading ability. These methods rely on data of students’ performance on test items regarding mathematics and reading and include the use of regression analysis, principal component analysis, and different uses of correlation...

In this study we analyse the communication competence included in two different frameworks of mathematical knowledge. The main purpose is to find out if mathematical communication is primarily described as communication of or about mathematics or if it is (also) described as a special type of communication. The results show that aspects of mathemat...

This study focuses on a distinction between process- and object-oriented discourses when characterising the discourse of university students’ summaries of lectures and examining connections between students’ discourse and the discourse of lectures. Results show that students’ discourse in general tends to be process-oriented, by their use of active...

The discursive use of 'belief' in research articles are analyzed as a contribution to the reflexive activity in belief-research, in particular regarding theoretical aspects of the notion of belief. The purpose of this paper is to create an explicitly described procedure for such an analysis, from the selection of data to categorizations of the smal...

University students' evaluations of mathematical presentations are examined in this paper, which reports on part of a pilot study about different types of presentations, regarding different topics, formats (oral or written), and discourses (process-or object-oriented). In this paper focus is on different formats; oral lectures and written texts. St...

A common problem in belief research seems to be a missing link between aspects of theory and empirical analyses and results. This issue highlights a question of how dependent empirical studies about beliefs actually are on the theoretical perspective described in the study. In this paper, I examine relationships between two different perspectives....

In this paper we suggest a theoretical model of the connection between the pro-cess of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship be-tween reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguis...

In this paper, I investigate what types of epistemologies are conveyed through properties of mathematical discourse in two lectures. A main purpose is to develop and explore methods for a type of analysis for this investigation. The analysis focuses on the types of statements and types of argumentations used in explicit argumentations in the lectur...

In order to refine existing theories of beliefs, attention is given to the ontology of beliefs, in particular how a belief can be seen as a mental object or a mental process. The analysis focuses on some central aspects of beliefs; unconsciousness, context-ualization, and creation and change of beliefs, but also relates to research metho-dology. Th...

In this paper I analyze different existing definitions of the term beliefs, focusing on relations between beliefs and knowledge. Through this analysis I note several problems with different types of definitions. In particular, when defining beliefs through a distinction between belief and knowledge systems, this creates an idealized view of knowled...

In this chapter I examine what roles different types of prior knowledge have in the comprehension process when reading mathematical texts. Through theoretical analyses, three central aspects are highlighted; cognitive structure, cognitive process, and metacognition. For all these three aspects, questions arise regarding relationships between genera...

In order to develop more detailed knowledge about possible effects of beliefs in mathematics education, it is suggested that we look more in-depth at more general types of theories. In particular, the study of relations between epistemological beliefs and communication is put forward as a good starting point in this endeavor. Theories of the constr...

För uppgifter som man använder i undervisning eller prov i matematik så vill man i första hand utveckla eller testa kunskaper i matematik och inte elevernas läsförmåga. Om undervisning i matematik bygger mycket på läsning så verkar det finnas större risk att elever som har svårigheter med läsning också kommer få svårigheter med matematikämnet. En t...

Denna artikel beskriver undersökningar kring hur universitetsstudenter och skolelever läser olika typer av texter. Frågor jag vill besvara är hur man bör förhålla sig till läsning inom matematikutbildning och om man behöver behandla läsförståelse som en del av undervisning inom matematik. I artikeln behandlar jag undersökningar kring läsning av upp...

The main question discussed in this paper is whether students need to learn how to read mathematical texts. I describe and analyze the results from different types of studies about mathematical texts; studies about properties of mathematical texts, about the reading of mathematical tasks, and about the reading of mathematical expository texts. Thes...

The purpose of this paper is to discuss the bi-directional relationship between reading comprehension and problem solving, i.e. how reading comprehension can af fect 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 o...

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 mathema...

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 stud...

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...

There is a need to distinguish between understanding a text and learning from a text, something that can be done by looking at different levels of mental representations created when reading. This study is focusing on the mental representations created in two types of situations, where different kinds of cognitive processes are dominant, either a m...