Presentation of NORMA-paper by Martin Carlsen, professor and Svanhild Breive, posdoc, University of Agder.
In this study we problematise the strong associativity of questioning with mathematical inquiry. We argue that in kindergarten we need to adopt a wider analytical focus to capture the complexity of children’s mathematical inquiries, i.e. a multimodal approach to mathematical engagement. We examine how processes of mathematical inquiry unfold amongst collaborating children (and adults) engaged in mathematical activities in kindergarten. The study shows that children’s exploration of mathematical ideas does not necessarily take place through questioning. Rather, the children burst out with imperatives such as “Look!” or “Wow!”, and they initiate mathematical explorations with others through statements about mathematical features they have noticed. Moreover, children’s mathematical inquiry is characterised by its multimodal and argumentative nature, as they use artefacts, gestures, and voice to argue their mathematical insights.
NORMA-presentations by Irene Skoland Andreassen, PhD candidate, Stig Eriksen, Assistant professor, Anders Wiik PhD candidate, Hans Kristian Nilsen, Associate professor and Pauline Vos, professor at University of Agder
Characterizing the relevance of mathematics as perceived by grade 8 students in a workplace related project
Irene Skoland Andreassen, Hans Kristian Nilsen and Pauline Vos, University of Agder
Researchers have found that students ask for the relevance of learning mathematics. Therefore, we carried out a study to characterize the relevance of mathematics as perceived by students after they participated in a workplace related project. In an exploratory case study, 8th grade students collaborated with an enterprise to create a website to inform peers about the enterprise and the mathematics used there. We used Cultural-Historical Activity Theory and a framework conceptualizing relevance as relevance of what, for whom, according to whom, and to what end. We carried out observations and semi-structured group interviews. Many students related the relevance of mathematics to calculations and measurements at the workplace, which we characterized as vicarious (for others) workplace relevance, which was identifiable even if the mathematics was black-boxed. We also found personal curriculum relevance and personal, vague, future related relevance.
13.45 Evaluating example tasks against the new core elements for grade 11 in Norway – what do tasks communicate
Stig Eriksen and Pauline Vos, University of Agder
In August 2020, a new curriculum for primary and secondary education was implemented in Norway. Known as LK20, it aimed at more in-depth learning, inquiry, computing, and relevance. For mathematics, LK20 was defined through six core elements: (1) inquiry–problem solving, (2) modelling–applications, (3) reasoning–argumentation, (4) representation–communication, (5) abstraction–generalization, and (6) knowledge areas, which the students meet through the five first core elements (UDIR, 2020). For each target group, the core element (6) was explicated differently.
Our study focuses on grade 11, which has two mathematics programs: 1P (vocational) and 1T (theoretical). For each of these, UDIR published ten example examination tasks in autumn 2020, so students, their teachers, and other stakeholders could see concretely the goals for the end of the study year. In doing so, assessment can support UDIR’s curriculum reform (Fried & Amit, 2016),
We consider the core elements and the twenty example tasks as resources in a discourse (Morgan & Sfard, 2016), in which UDIR conveys LK20’s intentions to an audience. The two types of resources carry meanings, but they are conceptualized differently. The first is a formal curriculum document with broad aims and few suggestions for classroom practice. The second offers specific student activities, of which teachers and students can envisage what preparations are needed for students to do the tasks. Our study was guided by the research question: to what extent are the twenty example tasks a translation of the core elements of the new LK20 mathematics curriculum for grade 11?
Our methods consisted of an iterative process to control for validity and reliability of our interpretations. For 1T and 1P separately, we translated the six core elements into categories, scored the tasks independently against these, discussed and refined the categories and scores until we agreed. Our results show that the twenty tasks are rich and reflect the core elements in many ways, except for modelling–applications. In the 1T exam, the tasks that explicitly integrate programming contribute considerably to the core elements, yet again except for modelling–applications. The more critical-reflective activities described in the core elements (justifying the choice for using a certain representation, proving, critical evaluation of a model) were not needed to complete any task. At NORMA, we will discuss further results, draw conclusions and offer recommendations.
Trends in everyday mathematics:
The case of newspaper weather forecasts
Anders Wiik, PhD University og Agder
Making sense of weather forecasts in newspapers is a form of everyday mathematics with which many people engage. In this paper, I describe how newspaper weather forecasts have changed between 1945 and 2015, thereby indicating trends in everyday mathematics. Aided by social semiotic theory, a corpus of weather forecasts from two major Norwegian newspapers are analyzed. The findings indicate that newspaper weather forecasts have shifted towards more non-verbal forms of communication (maps, graphs, tables). This shift also changed the readers’ role, from an interpreter of text to an organizer of information. I argue that students need to be better prepared for participating in an increasingly quantified public discourse. I suggest that more interdisciplinary schoolwork between mathematics and other school subjects where students use mathematical literacy skills to explore socially relevant issues is needed.
Grade 8 students creating Sankey diagrams to model, visualize and communicate complex processes
Pauline Vos, University of Agder & Peter Frejd, Linköping University
To increase the relevance of school mathematics, we run a project, in which grade 8 students visit enterprises and do mathematical tasks about these. In the project, we introduce students to a tool to holistically model, visualize and communicate complex, industrial processes: Sankey diagrams. These are flow charts, in which the width of arrows is proportional to the flow quantity. Sankey diagrams are popular in visual media, propelled by the increasing datafication in society. The research question was: to what extent can grade 8 students appropriate Sankey diagrams? We developed a socio-cultural framework based on research on mathematical modelling (Blum, 2015), but with a focus on (1) Sankey diagrams as cultural artefacts developed by people to serve social purposes, and on (2) the social interactions while creating these diagrams. We defined students’ appropriation as ‘taking an artefact for one’s own use’ (Moschkovich, 2004). A researcher can observe appropriation when students spontaneously use the taught artefact in a new situation. At NORMA, we will present results from observations, field notes and students’ written answers. In the lesson the appropriation remained limited. However, some weeks later at an unrelated school event, we witnessed first-hand how the same students used Sankey diagrams to convince the school authorities to improve the waste sorting at their school. We contend that mathematical artefacts that enable student to participate in social decisions increase the relevance of learning mathematics.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In Proceedings 12th Internat. Congress Mathematics Education (pp. 73–96). Springer.
Moschkovich, J. N. (2004). Appropriating mathematical practices: Learning to use functions through interaction with a tutor. Educational Studies in Mathematics, 55, 49–80.
Presentation by Cengiz Alacaci, professor, University of Agder
Title and abstract will come later.
14th of June (Digital at zoom)
Presentation by Markos Dallas, PhD candidate at University of Agder.
In this seminar, Markos will discuss the ICME14 paper and the current progress of his PhD dissertation.
Title and abstract of ICME14 paper:
MATHEMATICS CLASSROOM ARGUMENTATION:
AN INTERACTIONAL PERSPECTIVE
A review of the related literature indicates major notions that could characterize an interactional perspective on argumentation in the mathematics classroom: those of argumentative discourse; behaviour, norm and (mathematical) practice; and participation and participant role. In order to conceptually organize these ideas, a model called the “Mathematics Classroom Interactional Model” (MCIM) is developed which also guides and supports the methodology of my PhD study. In this paper, an attempt is made to operationalize the MCIM model by formulating the research questions of the study and discussing an initial stage of the methods of analysis.