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- Bergvall, Ida, 1975-, et al.
(författare)
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Multi-semiotic progression in school mathematics
- 2019
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Ingår i: NERA 2019. ; , s. 270-271
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In mathematical school language, both everyday and technical expressions are commonly used (Barwell, 2013). This means that two discourses, an everyday and a technical discourse, are used together and that students must handle these two discourses simultaneously. In this study, we investigate how images and natural language are used to express these two discourses in Swedish national tests for grade three, six and nine. The aim is to learn more about progression in multisemiotic demands in mathematical subject language.The theoetical base for this study is social semiotics (e.g. Kress & van Leeuwen, 2006), which also forms the framework for the analysis. In a first step of the analysis, the coding orientation (ibid.) in the images was examined, i.e. whether the images express the mathematical content in a naturalistic coding orientation, with a connection to everyday situations, or in a technical coding orientation implicating a subject specific and technical focus in the mathematical content. In the next step, cohesion regarding coding orientation between image and text will be studied, i.e. how participants, processes and circumstances are expressed by an everyday or technically oriented in written natural language and in images and how cohesion is expressed between these two semiotic resources.The analysed materials are the latest released Swedish national tests in mathematics for grade three, six and nine. This means that for grade three and six, the test from 2015 have been studied, while the test for grade nine was from 2013.Preliminary results from the first step of the analysis, show that for a clear majority of the images inthe test for year three and six, the coding-orientation is naturalistic. The images are to a very high degree drawings of people, naturalistic objects or environments. In year nine, the opposite applies and a technical coding orientation is the most common. Exceptions can be found in the problemsolving tasks, with a relatively comprehensive contextual description. In these problem solving tasks, images with a naturalistic coding orientation are used even in grade nine.A tentative conclusion is that there is a rather significant progression towards a more technical language in the multi-semiotic language used in this sample of the Swedish national tests. The results indicate a need to highlight the function of the various multi-semiotic resources used inschool mathematics, in order to support the students’ development of the subject language. These results are relevant for a Swedish, as well as for a Nordic school context and literacy research, since there are great similarities between the school systems in the Nordic countries.
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| 3. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Exploring teaching traditions in mathematics
- 2019
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Konferensbidrag (refereegranskat)abstract
- The background to the actions that take place in classrooms are formed during a long time period. This kind of content formation is sometimes referred to as the emergence of teaching traditions, which can bedefined as “regular patterns of choices of content which have been developed over time within a specific subject” (Almqvist et al., 2008). Content patterns form a certain education culture which constitutes whatis considered as adequate teaching and relevant content. Exploring teaching traditions can provide knowledge with respect to what values a specific educational culture holds.Within the Swedish field of science education, there has been much research on teaching traditions during the past decade. The results reveal three established teaching traditions in science education: an‘academic tradition’, an ‘applied tradition’, and a ‘moral tradition’ (Marty et al., 2018). In mathematics education, the focus of this study, such typology of teaching traditions has not yet been formed.Considering mathematics as an academic discpline within the STEM field, it is reasonable to assume similar, but not identical, teaching traditions as in science. During the last decades, there has been aheavy emphasis on comptencies within mathematics education, which has affected teachers’everyday practice. In addition, the focus on mathematical literacy has the potential to impact teaching traditions in mathematics. The aim of this study is to identify teaching traditions in the Swedish mathemaics curriculum and contrast these traditions with those developed within science. The study is embedded in Chevallard’s theory of transposition of knowledge, where the curriculum is regarded as thestep between the transposition from scholarly knowledge to the taught knowledge in the classroom.This study is a first step towards a more comprehensive conceptualization of teaching traditions inmathematics. The mathematics curricula with commentary materials for primary and upper secondary school will be analyzed, which allows comparisons between compulsory courses and courses thatprepare for university studies. The analytical tool is based on Roberts (1982) curriculum emphases andon the teaching traditions developed within science (Marty et al., 2018). A broader view will however beadopted to ensure that traditions unique for mathematics are also included. One such example is the analysis of emphases on literacy.Our preliminary analysis indicates a pronounced emphasis on abilities in mathematics whereas inscience knowledge is emphasized. The final results will consist of a conceptualization of teaching traditions in the Swedish curricular materials in mathematics. These results provide a means to evaluate mathematical practices with a more comprehensive scope than mathematical competencies. This is relevant for all Nordic countries considering their structural similarities of policy documents.
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| 4. |
- Dyrvold, Anneli, 1970-, et al.
(författare)
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Meeting the needs of today’s society – developing collaborative problem solving skills
- 2019
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Ingår i: NERA 2019 Programme. ; , s. 501-502
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Konferensbidrag (refereegranskat)abstract
- In a globalized world, the ability to collaborate in problem solving is essential. Increasingly high demands are placed on the ability to collaborate with people with different perspectives and cultural background, and our educational systems plays an eminent role in the development of such an ability. On the other hand, both private and professionally, aspects of individualism and expectations to compete are very common. Accordingly, it may not be a clear-cutdecision for individuals to prioritize the development of collaborative problem solving skills. The PISA survey has been investigating problem solving skills since 2003 and in PISA 2015 collaborative problem solving was tested for the first time (OECD, 2017). The results show good individual problem solvers are not necessarily successful in collaborative problem solving.The aim of the study is to contribute knowledge about how a designed milieu can contribute to collaboration in problem solving and to development of collaborative problem solving skills. In particular, it is stressed how different features of the milieu become important throughout the collaborative work. Theoretically the study is framed by Brouesseau’s theory of didactical situations, the concept of milieu and three types of situations: situations of situations of action, situations of formulation, and situations of validation (Brousseau, 2006). Data is collected from collaborative problem solving in mathematics, where a designed tool-box with requests to interact is included in the milieu toencourage and support the collaborative work. The negotiation of meaning and the extent to which real collaboration come into being is analyzed in the three types of situations. A detailed analysis ofthe extent to which the students’ milieu is shared and the role the tool-box has for the milieu will contribute in-depth knowledge about how the development of collaborative problem solving skills can be supported.Preliminary analyses reveal students’ interactions with the design element of the milieu, the toolbox, do largely influence which types of situations the students engage in and how the collaboration proceeds. Unexpectedly, the collaboration resulting from the use of the tool-box was not only fruitful. In some cases, it was used in arather mechanical manner, distorting the collaboration from the problem solving. Social conventions also seem to hinder the validation to proceed, because of a strive for agreement.The study is relevant in a modern society where collaboration skills are essential. In addition, collaborative problem solving seems to be an equality issue in the Nordic countries. In all nordic countries except Norway the percentage of top performers in collaborative problem solving among top performers in science, reading and mathematics is higher than the OECD average (OECD,2017). This may indicate it is mainly the top performers that are given support in development of collaborative problem solving skills, something that needs to be considered in education.
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| 5. |
- Ribeck, Judy, 1982-, et al.
(författare)
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Subject Language in mathematics textbooks : Verbal text fragments supplemented by other semiotic resources
- 2019
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Ingår i: ECER 2019 Conference Programme.
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Konferensbidrag (refereegranskat)abstract
- Different subjects have developed their own ways to construe meaning. To be able to convey the message, specific linguistic means are used in particular ways depending on the subject. The subject language in mathematics is characterized by the utilization of verbal language together with the semiotic resources mathematical notation and images. Each semiotic resource contribute to different functions of language and one resource can modulate the meaning made by another resource. Thus, adding one semiotic resource enhances the affordances of the other, a phenomenon referred to as meaning multiplication(e.g., Lemke, 1998). The intricacy of how the semiotic resources can be used together is indeed an asset, but at the same time this intricacy increases the demand on the reader. There are several reasons why students of mathematics must appropriate the subject language and learn to read mathematics. For example, language not only determines what is possible to communicate within a subject, but also modulates the way we think (e.g., Pederson, Danziger, Wilkins, Levinson, Kita, & Senft, 1998). In addition, texts with multiple semiotic resources are an important means to enhance students’ conceptual knowledge (e.g., Kilpatrick, Swafford, & Findell, 2001). Important contributions have been made to characterize the subject language in mathematics (e.g., Morgan & Tang, 2016; O'Halloran, 2005), but much is still unknown or needs further analysis. There are also features about the subject language in mathematics that are taken for true, but for which the empirical evidence is weak (Österholm, & Bergqvist, 2013). Since knowledge about the particular features of a subject language is a prerequisite for teaching the subject, there is a need to develop our understanding about how we communicate in mathematics to solidify the basis on which language-conscious mathematics teaching must be built. One distinguishing feature of printed mathematics texts is the mixture of mathematical notation and words, even in short fragments of text (Ribeck, 2015). In this study, we aim at characterizing the subject language in mathematics by linguistically analysing such verbal text fragments(hereafter referred to as VTFs), sorting out how the totality of semiotic resources interact to make the message complete. The categories taken into account in the analysis concern information structure (i.e. Theme and Rheme) and semantic roles (i.e. Participant, Process and Circumstance). In line with this focus, the following research questions are posed: RQ 1) What characterizes VTFsin mathematics textbooks regarding their linguistic content?RQ 2) What role do VTFs and the semiotic resources mathematical notationand imagestake in relation to each other to make the message complete?The analysis of relations between the different semiotic resources is based on a functional perspective on language, with a particular focus on means that are used to create a mental representation of reality. Royce’s (2007) framework for intersemiotic complementarity between the semantic categories Process, Participantand Circumstance is used. Intersemiotic complementarity is a concept that catches how the means of different semiotic resources in a text interact to provide a coherent message. Since mathematical notation is an important resource in mathematics texts the framework is modified to include also mathematical notation (cf. Dyrvold, 2016). In addition, we use the notion of Theme and Rheme (Halliday 1994), which is seen as crucial to the organisation and construal of meaning from a reader’s perspective.MethodThe data used in this study builds upon previous results from Ribeck (2015), where VTFs are automatically extracted from a corpus of 5.2 million words originating from Swedish secondary and upper secondary textbooks. For every word in the VTFs, a parser has added information about part of speech and syntactic function. In the current study these VTFs are analysed quantitatively and qualitatively. Two different analyses are conducted, each relating to one research question. The first step aims at identifying the most common types of VTFs. Here, the VTFs are coded and analysed for their linguistic characteristics. This quantitative analysis will reveal patterns among the VTFs as to what information they convey. In the next step, the common VTFs that have been identified are analysed in relation to the other semiotic resources. The focus is laid on how meaning is construed around Themes and Rhemes and the means used to obtain cohesion between Participants, Processes and Circumstances represented by the different semiotic resources. In the analysis of the thematic progression between Themes and Rhemes (see e.g., Danes, 1974) the role of the VTFs is taken as the starting point for the message that is construed in the text. Thereafter, the roles of all semiotic resources are included in the analysis to describe the information structure throughout the text. The analysis of cohesion between Participants, Processes and Circumstances is bidirectional; first potential cohesive relations to other semiotic resources indicated by the VTFs are analysed, second the content represented by the other semiotic resources are analysed in relation to the VTFs.Expected OutcomesThis study is expected to contribute knowledge about a particular feature that distinguishes the mathematical subject language from other subject languages in natural and social sciences, namely its substantial share of VTFs (cf. Ribeck, 2015). The utilization of two different analyses enables us to elucidate the subject language of mathematics from different point of views. It may be argued that verbal language in multimodal texts only makes sense in their context, and consequently is not meaningful to analyse separately. However, the VTFs are present in the textbooks and the reader needs an understanding of their textual function. Thus, we argue that a deepened understanding of the separate semiotic resources is a necessary first step towards understanding the intricacy in how they together construe subject-specific meaning. The analysis of the role of the VTFs in relation to the other semiotic resources is expected to offer a rich understanding of a crucial characteristic of the subject language in mathematics, namely how the semiotic resources complement each other. The combination of resources may either be necessary for a particular message or redundant to each other, something that will be highlighted by the bidirectional analysis. The results will contribute to characterize the subject language in mathematics, which is necessary to plan and implement teaching that strengthen students’ language competence.ReferencesDanes, F. (1974). Functional Sentence Perspective and the organization of the text. In F. Danes (ed.). Papers on Functional Sentence Perspective, (pp.106-28). The Hague: Mouton. Dyrvold, A. (submitted and preprint). Relations between various semiotic resources in mathematics tasks – a possible source of students’ difficulties. In Dyrvold, A. (2016). Difficult to read or difficult to solve? The role of natural language and other semiotic resources in mathematics tasks. Diss. Umeå universitet: institutionen för matematik och matematisk statistik. Halliday, M.A.K. (1994) An introduction to functional grammar. 2nd ed. London: Edward Arnold. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Lemke, J. L. (1998). Multiplying Meaning: Visual and verbal semiotics in scientific text In J. R. Martin & R. Veel (Eds.), Reading Science (pp. 87-113). London: Routledge Morgan, C. & Tang, S. (2016). To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England, Research in Mathematics Education, 18:2, 142-164, doi: 10.1080/14794802.2016.1174145 O'Halloran, K. (2005). Mathematical Discourse: Language, symbolism and visual images. London: Continuum. Pederson, E., Danziger, E. Wilkins, D., Levinson, S., Kita, S., & Senft, G. (1998). Semantic typology and spatial conceptualization. Language, Vol. 74, No. 3 (Sep., 1998), pp. 557-589 Published by: Linguistic Society of America. Royce, T.D. (2007). Intersemiotic Complementarity: A framework for multimodal discourse analysis. In Royce, T. & W. Bowcher, New Directions in the Analysis of Multimodal Discourse, New York: Routledge, 2007, pp. 63-109 Ribeck, J. (2015). Step by step. A computational analysis of Swedish textbook language. Diss. University of Gothenburg: Department of Swedish. 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 ‐ The International Journal on Mathematics Education, 45 (5), 751‐763.
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