In this talk I will share our work from Brasil, the United States, Guatemala and Nepal and ideas in relation to ethnomathematics, mathematical modeling and how it has become ethnomodeling. The application of ethnomathematics and the tools of mathematical modelling allows us to see a different reality and give us insight into mathematics accomplished in a more holisticm manner. Using this perspective, a pedagogical approach that connects cultural aspects of mathematics with its academic aspects is refered to asethnomodelling. This is a process of translation and elaboration of problems and questions taken from systems that are part of any given cultural group. We would like to broaden the discussion for possibilities for the inclusion of ethnomathematics and mathematical modelling perspectives by using ethnomodelling which, if done correctly, acts against colonialism and respects the social and cultural diversity with guarantees for the development of understanding of our differences through dialogue and respect. Ethnomodelling empowers these members of diverse groups against domination and oppression.

In this talk, an initial analysis of post-teaching conversations about mathematics in a school-based practicum setting is presented. Using data from the practice of mathematics educators, insight is sought on ways for directing reflections to being more mathematics-based. A scheme for planning teaching was introduced to students beforehand to bring into attention different aspects of mathematics teaching. Through the analysis it was possible to detect some features in the conversations that have a potential to develop into reflections about the mathematic. These features make it possible to identify a potentiality zone, in addition to the evaluation-based and subject-based discussions as suggested from earlier research.

The media that adults decide is appropriate for children to engage with has always reflected societal views about appropriate childhoods. However, these views can differ. Although studies have been done on the connection between childhoods and children’s media experiences, in this paper the mathematics in puzzles and handicrafts in a selection of Danish children’s magazines from 1925 to 1930 is analysed. The analysis shows that there were a predominance of measuring and designing activities with children engaging in adult-equivalent tasks, such as building a hen house. These tasks had limited specific instructions, indicating that children needed to persevere in working out the details. On the whole the kind of appropriate childhoods that are presented through these tasks remain consistent across the more than five years of the publications. As well, very few distinctions are made according to gender indicating that the Danish magazine editors in the 1920s did not differentiate their expectations about appropriate childhoods. The puzzles and handicrafts indicate that appropriate childhoods were considered as those which prepared children for adulthood and which valued the importance of doing things.

We describe three PhD proposals that support the project Learning about Teaching Argumentation for Critical Mathematics Education (LATACME). The studies intend to explore how preservice teachers (PTs) include argumentation processes during their teaching practice in grades 1-7 within multilingual classrooms. Argumentation for CME in this case, is understood as a social production with multiple representations, such as oral and written expressions, gestures, and diagrams. In this production, contrasting, evaluating, and confronting the use of mathematical tools to understand social issues are essential for critical argumentation to take place.

For some decades now mathematics has been portrayed as a requirement for citizenship. Using a Foucaultian cultural-historical framework that understands education as processes of governing of subjectivities, the question of which notions of the “mathematical competent citizen” are discursively displayed in curricula and textbooks is addressed. Based on the analysis of Swedish curricula in 1969 and 2011 and corresponding textbooks, we show how these notions have changed. The ethical challenge for mathematics educators concerning the direction of the governing that mathematics education may propose is raised.

Young children’s problem posing and problem solving is rarely the focus on research. In stories told by teachers, in focus group interviews about photos that they took of children engaged in mathematics in their kindergarten, we also found that problem posing and problem solving were rarely discussed explicitly. However, an analysis using Bishop’s universal mathematical activities of Explaining and Playing enabled four different components that the teachers paid attention to, to be identified. These components were to do with the routine or non-routine nature of the problems; known or unknown problem solving strategies; body actions or verbal explanations; playing by exploring different scenarios or following rules. Identifying what teachers noticed about children’s problem posing and problem solving provides insights into their professional knowledge.

In January, a survey was sent to first-year GLU1-7 students asking about their views on the use of modelling, ICT and multilingualism when teaching mathematics in primary school, among other things. We have done quantitative analysis on the data and have found correlations between the topics covered in the survey. In this presentation, we will give an overview of our findings. This process is this is part of the LATACME project.

I will describe the rationale for and research findings from a teacher development project in Johannesburg that worked with professional learning communities among high school mathematics teachers.  The main focus of the project was to support teachers to understand the reasoning behind their learners’ mathematical errors and to develop stronger understandings of learners’ thinking, and to develop their own content and pedagogical content knowledge and their practice. The research analyses looked at teacher conversations in the communities and the teachers’ practices over time. We found that the content of the community conversations was related to the activities, and there were shifts in teachers’ conversations across time and activities. There were shifts in practices for about half of the teachers in the direction of responsiveness towards learners, with nuances among teachers and communities. I will relate the findings to the contextual climate in relation to teacher professionalism and the possibilities for professional learning in communities.

In spite of the widely accepted need for language-responsive subject-matter teaching, few teachers in Europe are prepared for this challenge due to the lack of empirically founded subject-specific professional development (PD) programs for language-responsive classrooms. The design research study presented in this talk pursues the dual aim of (a) promoting teachers’ expertise in language-responsive mathematics teaching using PD courses and (b) investigating teachers’ developing expertise in qualitative case studies. Both aims are pursued based on a conceptual framework for teacher expertise in language-responsive mathematics teaching, starting from typical situational demands that teachers face in language-responsive mathematics teaching and the orientations, categories, and pedagogical tools they need to cope with these situational demands, especially the demand to identify mathematically relevant language demands. For language-responsive teaching, the interplay of categories for mathematical goals and language goals turns out to be of high relevance.

“Culture hides more than it reveals, and strangely enough what it hides, it hides most effectively from its own participants” (Hall, 1959). This quote fits very well with a Persian proverb and well-known aphorism that has been cited in many ethnographic papers: “a fish is the last creature to discover water”. Being immersed in and surrounded by water makes it invisible and almost impossible to notice for the fish. Thus, by incorporating technology (both as a method of data collection and data analysis) this presentation reveals the “visibility” and “familiarity” of everyday classroom interactions from the students’ perspective, which is often invisible and unfamiliar to us as educators. A sample of 120 students in Chile wore a mini-camera that was mounted on their eyeglasses in order to investigate inti students’ gazes, trying to achieve an understanding of the situation by closely attending to and documenting the particulars from the students’ perspective.

In the talk, I will outline the idea and concept of the project «AriAlLe» (Zwischen Arithmetik und Algebra im Lehramtsstudium). In primary-level arithmetic lessons pupils need not only are to acquire pure computational skills, but also understanding of the computational operations and their relationships as well as related (subject-specific) communicative competencies, such as the describing and justifying arithmetic patterns. These abilities are seen as the basis for algebraic thinking. In the project, pre-service teachers work on textbook exercises both individually (paper-pencil test) and collectively (video studies), including the didactic preparation of «their» observations and explorations for lessons. First results from the paper-pencil-test are presented.

We will present preliminary results from a study on Digital Tools in Mathematics Teacher Education. The project is financed by Matric (UiA), where three institutions participate: HVL, UiT and HiØ. In the project, we map students’ attitudes to and experiences with the use of digital tools in mathematics teaching. We have conducted a survey at the three institutions. In this presentation, we have chosen to focus on GLU 5-10 students’ attitudes and experiences with programming. This is a current topic in connection with the subject renewal. We have examined the students’ perceptions of the utility’s usefulness in specific mathematical topics, and in the work with the multicultural classroom, adapted training and problem solving. We have also investigated whether gender is a factor. The students may think that programming can solve many of the school’s challenges, but if we look more closely at those who have experience with programming, the answers are more nuanced. There are also results that indicate that students need training and experience in programming, both programming skills and reflections on the use of programming in mathematics teaching.

The members of the group [Medlemmene i gruppa]: Tamsin Meaney (HVL), Bodil S Kristensen (HVL), Odd Tore Kaufmann (HiØ)), Marianne Maugesten (HiØ), Hilja Huru (UiT), Mona Kvivesen (UiT)

My presentation will start with some thoughts on visual and symbolic mathematics and its similarity with oral and written language. I will also give my proposition to why so many of our students are illiterate when it comes to algebra. Then visualizing multiplication in the number systems N and Z and showing that minus times minus is a positive number by extending the pattern. If time permits visualizing Q and R and showing how to construct/find rational approximations to irrational numbers.

In this seminar, Naomi will explore her research into individuals’ relationships with mathematics and how these relationships impact mathematical and pedagogical practices. These understandings have led to how Naomi works with preservice and inservice teachers, where she supports them to explore and grow their own relationships with mathematics within the context of doing mathematics. They are encouraged to establish an ethic of care within their own classrooms, where students can be supported to engage in dialogue and work cooperatively to discuss completed or partially completed mathematics explorations with the rest of the class, to argue and disagree, and to embrace confusion – and thus engage in the social, messy and rewarding practices of doing mathematics.

Science, Technology, Engineering, and Mathematics (STEM) is the leading education reform worldwide, yet, many teachers’ lack the knowledge and confidence to teach integrated STEM. This study examines an initiative of teaching STEM integrated approach through the collaboration of mathematics and science university lecturers and pre-service teachers in a Teaching and Learning subject-specific course. The study presents the pre-service teachers’ knowledge development of integrating STEM and their views and attitudes towards STEM. Data were collected through pre-surveys, post-surveys, lesson plans, and presentations from 51 pre-service mathematics and science teachers. Results show that experiences of pre-service teachers with STEM learning and teaching had a positive impact on their understanding and importance of STEM, as well as their motivation and enthusiasm to design and present STEM lesson plans in group settings while integrating mathematics and science.

In our talk,  we will discuss the ideas of Lord (1994) about critical colleagueship to understand how (mathematics) teacher educators can work together to become more critical in their teaching practices. Lord (1994) emphasised professional development of teachers and discussed critical colleagueship, which supports a critical stance toward teaching, as one kind of colleagueship to support teachers’ reflections. In this presentation we use the framework to discuss teacher educators’ collaboration and reflections. Our study examines a group of teacher educators working together to develop novel teaching and do research about initiating critical discussions. During two meetings, they discussed their different perspectives after using indices such as the Body Mass Index (BMI) in teaching. Even though the examples are mostly from the mathematics education, the critical colleagueship ideas can be used in similar ways to collaboration between teacher educators in general. The talk can therefore be of interest for all teacher educators.