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.