Computer-based assessment in mathematics

Computer-based assessments is becoming more and more common in mathematics education, and because the digital media entails other demands than paper-based tests, potential threats against validity must be considered. In this study we investigate how preparatory instructions and digital familiarity, may be of importance for test validity. 77 lower secondary students participated in the study and were divided into two groups that received different instructions about five different types of dynamic and/or interactive functions in digital mathematics items. One group received a verbal and visual instruction, whereas the other group also got the opportunity to try using the functions themselves. The students were monitored using eye-tracking equipment during their work with mathematics items with the five types of functions. The result revealed differences in how the students undertook the dynamic functions due to the students’ preparatory instructions. One conclusion is that students need to be very familiar with dynamic and interactive functions in tests, if validity is to be ensured. The validity also depends on the type of dynamic function used

Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS

The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language. Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language. The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS). In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language. The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic. The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.

Matematikängslan ur elevens perspektiv

Flera undersökningar visar att ett stort antal elever upplever obehag och oro i samband med matematik och därför får svårt att tillgodogöra sig skolans matematikundervisning på bästa sätt. Denna studie syftar till att belysa några elevers upplevelser av matematikängslan. Genom att lyfta fram elevernas tankar och erfarenheter kan studien förhoppningsvis bidra till en fördjupad dialog mellan lärare och elever kring matematikängslan. Kanske kan elevernas erfarenheter tas tillvara och användas när det gäller att utforma både den fysiska och den undervisningsmässiga skolmiljön.   Undersökningen är en hermeneutisk studie som baseras på intervjuer med sju elever i den svenska grund- och gymnasieskolan. Alla sju informanter har upplevt eller upplever någon form av matematikängslan.   Enligt denna studie är oron för att känna skam i sociala situationer och inför andra människor den kanske mest betydande orsaken till matematikängslan. Att blotta svårigheter innebär en risk att hamna i generande situationer. Istället avstår flera av informanterna från att ställa frågor både under gemensamma genomgångar och under eget arbete, trots att de inte förstår. Följden blir att de får problem med matematikämnet, problem som kan bli ihållande. Tidigare forskning förefaller i första hand vara inriktad på orsaker som vilka specifika moment som ger upphov till ängslan, hur brister i arbetsminne påverkar, om intelligens eller verbal förmåga inverkar på upplevelsen av matematikängslan och betonar inte betydelsen av elevernas egna tankar, känslor och upplevelser av undervisningen.   De första åren under mellanstadiet förefaller vara särskilt känsliga för att matematikängslan ska uppstå. Orsaken skulle kunna vara den så kallade nioårskrisen då många barn börjar jämföra sig med varandra och blir medvetna om sina eventuella brister.   Andra möjliga förklaringar till att matematikängslan uppstår skulle kunna vara att abstrakta begrepp införs utan att betydelsen blir tydlig för eleverna eller att det saknas en tydlig progressionslinje genom grundskolan vilket medför att ett glapp uppstår mellan skolår tre och fyra

Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS

The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language. Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language. The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS). In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language. The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic. The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.

Bokstavligt, bildligt och symboliskt i skolans matematik : – en studie om ämnesspråk i TIMSS

The overall aim of this thesis is to deepen the understanding of mathematical subject language regarding three semiotic resources, written language, images and mathematical symbols. The theses also investigates high- and low-performingstudents encounter with mathematical subject language. Based on previous research on language and from a theoretical foundation based on systemic functional linguistics (SFL) and social semiotics, four meaning dimensions – packing, precision, personification and presentation – were identified as central in academic language in general and in mathematical subject language. A didactically based reception theoretical perspective has been used for an analysis of high and low achieving students' encounter with the mathematical subject language. The thesis comprises three studies each examining the mathematical subject language in TIMSS 2011 from various angles. The analyzes were conducted on four content areas algebra, statistics, geometry and arithmetic in the Swedish version of the international study Trends in International Mathematics and Science Study 2011 (TIMSS). In a summary, the results showed that the mathematical subject language was used in different ways in the four content areas in TIMSS where colloquial and subject-specific forms of languages had different roles and were expressed in varying degrees by the written language, images and mathematical symbols. Thus each content area was expressed by its own register which means that is not sufficient to talk about mathematical subject language as one single language. The result shows that two forms of language, subject specific and everyday language were used parallel in the TIMSS material. The subject specific forms were most salient in algebra and geometry and the more everyday forms of language were more common in statistics and arithmetic. The results from the correlation analyses indicated that fewer students managed the encounter with tasks in algebra and geometry when they were expressed by subject specific language. In contrast, the results indicated that students were able handle the encounter with the more colloquial expressions of the content areas statistics and arithmetic.

Using heat maps from eye tracking in stimulated recall interviews

This presentation discusses students’ interpretations of heat maps from eye tracking. Heat maps are often referred to as ‘just’ eye candy because of their appealing nature and the somewhat ‘hidden’ data. Undoubtedly, there is valuable information in these visualisations and if attention is paid when conclusions are drawn, the data is a useful complement to quantitative measures. We explore pros and cons when using heat maps in stimulated recall interviews and contrast this method to stimulated recall using videos or the use of think aloud protocols. A conclusion is that the heat map can attract attention to what actually happened and thereby evoke valuable references to thought processes, but at the same time it may draw attention to actions instead of to reasoning and thoughts because the image represents the reader’s activity (“I looked at…”).Digitala läromedel i matematik: Aspekter av betydelse för för elevers interaktion med den multimodala texte

The Subject Language Use In Year 8 TIMSS-Test Questions : A Comparison Of Language Uses In Science And Mathematics

In this study we want to make a contribution by making a comparison between the subject languages in mathematics and science based on linguistic theories about language and language function. Through this theoretical foundation in this present study we also have the opportunity to analyze the language function and thus we can also discuss the language's role in teaching. The aim of this study is to compare and thus gain more knowledge of grammatical features in subject language in science and mathematics and how these grammatical features are used to express meaning. To fulfil this purpose, science and mathematics items from Trends in International Mathematics and Science Study (TIMSS) 2011, grade eight, have been analysed from a functional perspective on language. Empirical studies that compare language use in different subjects are sparsely present (Österholm & Bergqvist, 2013) but there are studies pointing out that how language are used to express meaning varies between different school subjects (e.g. Fang & Schleppegrell, 2008; Schleppegrell, 2004). These linguistic differences have been highlighted as arguments for a more differentiated language-based teaching of subjects, leaning on disciplinary literacy (Shanahan & Shanahan, 2008). In order to conduct such a language-based teaching of subjects, an awareness of the different functions in the language used in various school subject is of great importance. One example of a comparative language study is the corpus study conducted by Ribeck (2015) where the language in Swedish teaching materials in science is analyzed, and compared with teaching materials in social science and with textbooks in mathematics. However, Ribeck does not make a direct analysis of mathematical subject language, her focus is rather on the language used in natural science compared to social science. There are also studies that focuses on the language use within subjects. Here it appears that the subject language is used differently and has different functions in different content areas within school mathematics (e.g. Bergvall, 2016) as well as within the different school science subjects, e.g. biology, physics, chemistry and earth science (e.g. Persson, 2016).   This study draws on a social semiotic perspective and systemic functional linguistics (SFL) (Halliday & Matthiessen, 2004). A point of departure is the perspective that different registers of language are used in different social contexts, which in this study is defined as the two school subjects science and mathematics. Grounded in SFL and the three meta-functions ideational, interpersonal and textual function the meaning dimension model of analysis was developed in a previous research project (Bergvall et al., 2016; Persson et al., 2016). Four central meaning dimensions, packing, precision, personification and presentation, were condensed from previous research regarding academic language and language use in the school subjects science and mathematics. The meaning dimensions can be used as measures of how grammatical features are used in various types of texts in order to express meaning. Packing and precision are regarded as aspects of the ideational meta-function. Packing is a measure of the information density in a text and precision is a measure of how and to what extent the given information in the text is specified. Personification, as an aspect of the interpersonal meta-function, is a measure of how personal relations between the reader and the text are expressed. The last meaning dimension, presentation, concerns how the information is structured in the text and is regarded as an aspect of the textual meta-function. In the present study, the four meaning dimensions are used to describe and compare the language and its function in science and mathematics items in TIMSS 2011. Method By the use of a quantitative method all items in mathematics and science from the Swedish version of TIMSS 2011, grade eight were analyzed. This material consists of 197 items in science and 217 items in mathematics. The language in these items have been analyzed for word class, word length and number of words per items by a computer based automatic parsing. For this parsing Extensible Markup Language (XML) was used. Some other linguistic features, i.e. passive forms and subordinate clauses, were identified manually. Since the meaning dimensions are used as a base for the linguistic analysis, the results will possibly be generally applicable also for other European languages, although the analysis was conducted on the Swedish version of TIMSS items. Packing was measured by calculating the number of nouns and the number of long words (>6 characters). Precision in the items were provided by words such as adjectives, adverbs, participles and counting words specifying different attributes in the items. Personification was here measured by the number of personal pronouns and proper names and presentation was measured by the presence of subordinate clauses and passive forms. In order to compensate for the varying length of different items, the number of the different linguistic features were divided by the number of words in the particular item. To enable the adding of different features, each feature is normalized by calculating its z-score. An index was then calculated for each meaning dimension based on the linguistic information on each item. From these indices a comparison between the language uses in the two subjects was possible. In the next step of the analysis each subject were separated into content domains: Algebra, Data & chance, Geometry and Numbers for mathematics items and Biology, Chemistry, Earth science and Physics for science items. This enabled variations of language use within the subjects also to be analyzed. The results were compiled in box-plots diagrams which visualized the distribution of the expressions of the four meaning dimensions in the various content domains. Expected Outcomes Preliminary results show that central traits of the academic language as measured by the four meaning dimensions are used in similar ways in both science and mathematics. The levels of packing, precision and presentation are fairly similar when looking at differences between the subjects. Personification shows the largest differences between the subjects, where mathematics as a whole makes more use of personal pronouns and proper names in the items. When separating the subjects into content domains, Statistics shows the highest level of personification. In this domain it can therefore be concluded that human participants are essential, thus emphasizing that this is a domain that this is an area of relevance for people in general or for the student him/herself. This can be interpreted as signaling the possibility to actively participate and interact in similar situations as described by the items context. On the other hand, in domains such as Algebra, Geometry and Earth science where the content is expressed with a low level of personification, the interpretation is that the content of these domains –at least as expressed in TIMSS items- are more separated from peoples’ everyday lives and thus the students’ own reality. Another result that emerges from the analysis relates to the meaning dimension presentation where we see that the written texts, especially in Algebra, but also in Geometry, Numbers and Earth science, mainly contains short sentences without subordinate clauses. In written academic language, subordinate clauses are a common tool for creating information flow and link different parts of the text (Fang, 2006; Schleppegrell, 2004; Veel, 1997). The lack of subordinate clauses in tasks in certain content areas of TIMSS indicates a subject-specific linguistic form that may require a familiarity with this specific form of language use. References Bergvall, I. (2016). Bokstavligt, bildligt och symboliskt i skolans matematik – en studie om ämnesspråk i TIMSS. [Diss.] Uppsala: Acta Universitatis Upsaliensis. Bergvall, I., Wiksten Folkeryd, J., & Liberg, C. (2016). Linguistic features and their function in different mathematical content areas in TIMSS 2011. Nordic Studies in Mathematics Education, 21(2), 45-68. Fang, Z. (2006). The Language Demands of Science Reading in Middle School, International Journal of Science Education, 28(5) 491-520. Fang, Z., & Schleppegrell, M. J. (2008). Reading in secondary content areas: A language-based pedagogy. Ann Arbor: University of Michigan Press. Halliday, M. A. K., & Matthiessen, C. M. I. M. (2004). An introduction to functional grammar (3.th ed.). London: Arnold. Persson, Tomas (2016). De naturvetenskapliga ämnesspråken. De naturvetenskapliga uppgifterna i och elevers resultat från TIMSS 2011 år 8. [Diss.] Uppsala: Acta Universitatis Upsaliensis. Persson, T., af Geijerstam, Å., & Liberg, C. (2016). Features and functions of scientific language(s) in TIMSS 2011. Nordic Studies in Science Education, 12(2), 176-196. Ribeck, Judy (2015). Steg för steg. Naturvetenskapligt ämnesspråk som räknas. [Diss.] Data linguistica. No. 28, Institutionen för svenska språket, Göteborgs universitet. Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy. Harvard Educational Review, 78(1), 40–59. Schleppegrell, M. J. (2004). The language of schooling; a functional linguistics perspective. London: Lawrence Erlbaum Associates. Veel, R. (1997). Learning How to Mean-Scientifically Speaking: Apprenticeship into Scientific Discourse in the Secondary School. In. Christie Frances & Jim R. Martin (Eds.), Genre and Institutions: Social Processes in the Workplace and School, s. 161-195. London: Cassell. Österholm, M. & Bergqvist, E. (2013). What is so special about mathematical texts? Analyses of common claims in research literature and of properties of textbooks. ZDM Mathematics education, 45(5) 751-763

Designing tasks with self-explanation prompts

This paper presents some results from an ongoing review on self-explanation prompts. An emphasis is laid on design principles based on empirical research. The review is grounded in scaffolding theory, which means that the self-explanation prompts are seen as a temporary support that the student shall learn to manage without. Three themes identified in the review are described and discussed in relation to design and implementation of tasks with self-explanation prompts: prompts with different purposes, the necessity to adapt prompt to students’ prior knowledge, and factors of importance for students’ engagement in the prompts. Examples of tasks with prompts for which these design aspects have been taken into account are given in the paper