Journal Articles by Magnus Österholm
Nordic Studies in Mathematics Education, 2015
This study reports on the relation between commonness of the vocabulary used in mathematics tasks... more 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.
Reading Psychology
The purpose of this study was to characterize students’ self-assessments when reading mathematica... more 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 a test of reading comprehension. Students’ self-assessments were to a less degree based on their comprehension of the specific text read, but more based on prior experiences. However, the study also produced different results for different types of texts and when focusing on different aspects of reading comprehension.
ZDM - The International Journal on Mathematics Education, 2013
This study surveys claims in research articles regarding linguistic properties of mathematical te... more 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 varying claims that mainly describe mathematical texts as highly compact, precise, complex, and containing technical vocabulary. However, very few studies present empirical support for their claims, and the few empirical studies that do exist contradict the most common, and unsupported, claims, since no empirical study has shown mathematical texts to be more complex than texts from other subjects, and any significant differences rather indicate the opposite. The linguistic analysis in this study is in line with previous empirical studies and stands in contrast to the more common opinion in the unsupported claims. For example, the mathematics textbooks have significantly shorter sentences than the history textbooks.
Educational Studies in Mathematics, 2006
This study compares reading comprehension of three different texts: two mathematical texts and on... more 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.
Nordic Studies in Mathematics Education, 2012
This is an accepted version of a paper published in Nordisk matematikkdidaktikk.
Nordic Studies in Mathematics Education, 2008
This is an accepted version of a paper published in Nordisk matematikkdidaktikk.
The Mathematics Enthusiast, 2012
The study presented in this paper is a contribution to the scientific discussion about the role a... more 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 of messages about mathematics are conveyed in lectures.
Nordic Studies in Mathematics Education, 2011
This is an accepted version of a paper published in Nordisk matematikkdidaktikk.
Conference Papers by Magnus Österholm
Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (PME), 2012
Proceedings of MADIF 8, The Eighth Mathematics Education Research Seminar, Umeå, January 24-25, 2012, 2013
This paper focuses on relationships between vocabulary in mathematical tasks and aspects of readi... more 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 aspect of common/uncommon words is one important part. The paper also presents an empirical method where corpora are used to investigate issues of vocabulary in mathematical tasks. The results from the empirical study show that there are connections between different types of vocabulary and task difficulty, but that they seem to be mainly an effect of the total number of words in a task.
Proceedings of MADIF 7, The Seventh Mathematics Education Research Seminar, Stockholm, January 26-27, 2010, 2010
In this paper we suggest a theoretical model of the connection between the process of reading and... more In this paper we suggest a theoretical model of the connection between the process of reading and the process of solving mathematical tasks. The model takes into consideration different types of previous research about the relationship between reading and solving mathematical tasks, including research about traits of mathematical tasks (a linguistic perspective), about the reading process (a psychological perspective), and about behavior and reasoning when solving tasks (a mathematics education perspective). In contrast to other models, our model is not linear but cyclic, and considers behavior such as re-reading the task.
Proceedings of Norma 11, The Sixth Nordic Conference on Mathematics Education in Reykjavík, May 11-14, 2011, 2012
Sllf{~)! ll'e fltilize lest reslIlts ./i·om Sl{'eC/isb sl ut/ellis ill PISA 2003 tllId 2006 10 (!... more Sllf{~)! ll'e fltilize lest reslIlts ./i·om Sl{'eC/isb sl ut/ellis ill PISA 2003 tllId 2006 10 (!:rClmill(! wbal ZJ1J(!S qf lask properties predict tbe del1lCflld qf reading abiliZI I qf a lIlath e m a lica/lasl.~.ll1parliclfICII ; readabilizl' properties (selllel1 ce {eng /b, wo rd length, COIl/iJ/OJI ll'ords, ami il!/url1ltlliol/ dellsiqJ ) tlnd Itlsk Zl1Je properties (coJ/ lelll, cOllljJetence, tllldJ(Jl"Il1at) are e.'J,:am illed. "/1J(! reslflts show fbat il is jJril1l ari~)1 reaclabiliz)l properties qfa (tis!..! fh a l jJredict tbe task's demalld q/readillg ability, ill particlllar word {euglb (,f lll/io some ex/elll i l !/orl1ltllioll dellsily (measured Ibrollgb the /lOll II-verb quotient).
Proceedings of MADIF 5, the 5th Swedish Mathematics Education Research Seminar, Malmö, January 24-25, 2006, 2007
The purpose of this paper is to discuss the bi-directional relationship between reading comprehen... more 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 proceh but also that not much research has focused on this relationship.
Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), 2012
This study focuses on a distinction between process-and object-oriented discourses when character... more 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 verbs and little use of nominalisations. Students' summaries of process-oriented lectures also tend to be more process-oriented, but the differences between individual students are larger than differences caused by variations of the discourse in the lectures.
Proceedings of the AAMT–MERGA conference held in Alice Springs, 3–7 July 2011, 2011
University students' evaluations of mathematical presentations are examined in this paper, which ... more 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. Students' written comments about what is good or bad about given presentations are analysed in order to examine what students focus on when evaluating the quality of presentations. In addition, evaluations given about written and oral presentations are compared in order to examine if/how format affects students' evaluations regarding quality.
Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, 2011
Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education (PME), 2006
This study uses categories of comprehension criteria to examine students' reasons for stating tha... more 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.
Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education, January 28th - February 1st 2009, Lyon, France, 2010
In this paper I analyze different existing definitions of the term beliefs, focusing on relations... more 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 knowledge, seen as something more pure (less affective, less episodic, and more logical). In addition, attention is generally not given to from what point of perspective a definition is made; if the distinction between beliefs and knowledge is seen as being either individual/psychological or social. These two perspectives are also sometimes mixed, which results in a messy construct. Based on the performed analysis, a conceptualization of beliefs is suggested.
Proceedings of the conference MAVI-15: Ongoing research on beliefs in mathematics education, September 8-11, 2009, Genoa, Italy, 2010
In order to refine existing theories of beliefs, attention is given to the ontology of beliefs, i... more 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, contextualization, and creation and change of beliefs, but also relates to research methodology. Through the analysis, the creation of belief is highlighted as a central aspect for more in-depth theories of beliefs. The outline of a theoretical framework is describeda framework that has the benefit of creating a coherent integration of all different aspects discussed, and which can also be used as a framework when designing and analyzing methods for empirical research.
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Journal Articles by Magnus Österholm
Conference Papers by Magnus Österholm