This paper problematizes what can happen when different practices meet in the mathematics classroom. In an educational design research project, researchers and teachers together promote students’ participation in mathematical dialogue through the use of digital tools. Tensions on what is put in the foreground – the mathematical dialogue or the digital tool - as well as tensions of how students can be included or excluded in the dialogue, are analysed using the Learning Design Sequence model. Through the analysis of tensions, further areas for improvement can be identified.

How can teachers refne their strategies for purposefully engaging students in mathematicaldiscussions when students are working in groups and the teacher enters an ongoing groupconversation? In three educational design research cycles, four teachers collaborated witha researcher for one year to analyse, design and evaluate strategies for engaging students insmall-group mathematical discussions. The idea of noticing (Mason in Researching yourown practice: the discipline of noticing, RoutledgeFalmer, London, 2002; Sherin et al. inMathematics teacher noticing: seeing through teachers’ eyes, Taylor & Francis, New York,2011) was used to organize the fndings—by paying attention to aspects in the mathematical discussions and interpreting the interactions, teachers could together refne their ownactions/responses to better support students’ work. The Inquiry Co-operation Model ofAlrø and Skovsmose (Dialogue and learning in mathematics education: intention, refection, critique, Kluwer Academic Publishers, Dordrecht, 2004) was used as a theoreticalbase for understanding qualities in mathematical discussions. Ehrenfeld and Horn’s (EducStud Math 103(7):251–272, 2020) model of initiation-entry-focus-exit and participationwas for interpreting and organizing the fndings on teachers’ actions. The results show thatteachers became more aware of the importance of explicit instructions and their own role asfacilitators of mathematical questions to students, by directing specifc mathematical questions to all students within the groups. In this article, by going back and forth between whathappened in the teachers’ professional development group and in the classrooms, it waspossible to simultaneously follow the teachers’ development processes and what changedin students’ mathematical discussions.

In Swedish mathematics classrooms, students have different opportunities to participate in mathematical dialogue, and therefore also different opportunities to learn. This is a problem not only for students, but also for teachers, school developers, and researchers. By moving back and forth between two settings – the upper secondary mathematics classroom and the professional development group – this thesis aims to explore how questioning and listening can promote participation in mathematical dialogue. The following three research questions are in focus: What aspects of students’ questioning and listening do teachers need to pay attention to when promoting students’ participation in mathematical dialogue? What aspects of teachers’ questioning and listening are important when teachers promote students’ participation in mathematical dialogue? How can teachers, in cooperation with researchers, develop an awareness and refine their teaching in relation to students’ listening, questioning, and participation in mathematical dialogue?

By using educational design research, two sub-studies were conducted – one with a focus on students and one with a focus on teachers – and the results were described in four articles. Theories on three different levels were used and coordinated to understand mathematical dialogue: sociocultural theory to situate the research study on an overall level where interaction and communication are essential; the concept of mathematical dialogue by Alro and Skovsmose (2004), including their Inquiry Co-operation model to understand quality in mathematical dialogue; and local theories to study facets of mathematical dialogue concerning questioning, listening, and participation.

The results point to how important both students’ and teachers’ questions are for creating equitable participation opportunities, and how teachers can promote mathematical dialogue by using pre-thought specific mathematical why-questions that invite all students to participate in small groupproblem-solving work. The results also point to the importance of working with productive listening, a process that requires both requests for listening and willingness to listen to others. For teachers to develop an awareness and to refine their teaching in relation to mathematical dialogue, the cyclic structure of EDR, working with teacher noticing and moving back and forth between the two settings, help visualize their development processes.

The main contributions of the thesis are (1) the framework for productive listening, (2) the empirical results concerning how mathematical questioning is used to promote students’ participation in mathematical dialogue, and (3) the learnings of how mathematics education theories can be used and coordinated to increace understandings on mathematical dialogue. At the end of the thesis, a meta-reflection is made on how collaboration between different actors – students, teachers, school developers and researchers – can build bridges and deepen the understandings of the complexity of mathematical dialogue.

Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students' listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, "productive listening," is described which focuses on observable features connected to students' ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker's contribution as being valuable and feeling that one's own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others' mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

Digitalisering och kollegialt lärande utgör två centrala, men ofta separata, delar av skolors utvecklingsarbete. Den här boken utforskar mervärdet som uppstår när dessa två delar integreras i en gemensam skolutvecklings- och lärandeprocess. Boken erbjuder en gedigen genomgång av områdena digitalisering och kollegialt lärande var för sig, samt ett integrerande perspektiv. Del ett introducerar tre skolutvecklingsprojekt som sedan följer med genom bokens alla delar. Del två, om digitalisering, tar sin utgångspunkt i skolans styrdokument och identifierar fem nyckelprocesser som samverkar i digitaliseringen av skolan. Därtill diskuteras teknikinvesteringar utifrån frågor som rör ekonomi, ägandenytta och vanliga misstag. Del tre, om professionsutveckling, djupdyker i begreppet kollegialt lärande utifrån aktuell forskning. Särskild fokus läggs på struktur och organisering av den kollegiala processen och vikten av samarbete mellan professionsgrupper. Slutligen knyter del fyra samman områdena digitalisering och kollegialt lärande och analyserar hur möjligheter för integreringsvinster kan skapas. Boken vänder sig alla som arbetar med skolans utvecklingsprocesser: skolchefer, skolledare, lärare, IT-pedagoger och bibliotekarier. Dessutom vänder den sig till lärarutbildare, rektorsutbildare, politiker och beslutsfattare inom utbildningssektorn.

In this paper, students’ questions while working in small groups on mathematical problem-solving tasks are investigated. In order to improve students’ reasoning and communication abilities in mathematics, an intervention study was designed in a multilingual upper secondary mathematics classroom in Sweden. In their discussions students used Swedish, which was their second language and also the language of instruction. The changes in students’ ways of using questions across the three cycles of the intervention were analysed. The results showed how students over the cycles changed their ways of framing questions from looking for the correct answer towards clarifying other students’ meaning in order to understand each other’s reasoning. The implication from the study is that it is important to promote interactions between students rather than focusing on students’ need to develop their second language competencies.

When students actively listen and interact with each other, their opportunities for developing reasoning and communication abilities in mathematics increase (Sjöblom, 2015). However, they are not always given opportunities to work dialogically during mathematics lessons, and there is little research in upper secondary classrooms about how teachers can promote student-to-student interaction. This poster presents an educational design research project (McKenney & Reeves, 2012), in which the intervention focuses on teachers’ work to make multilingual students interact while working with mathematical problem solving. The design and analysis build on the inquiry co-operation (IC) model (Alrø & Skovsmose, 2004) and Fuentes’ (2009) framework on student communication. The aim of the intervention is to find ways for teachers to promote and support student interaction, so that students engage in all dialogic acts in the IC-model, and hence listen actively to each other and ask/answer questions. It is expected that the design will need to take into consideration how students perceive group work, how they understand the purpose of questioning and listening, what role language and/or multilingualism plays in interaction, and how teachers can cooperate with other teachers to develop their teaching. Sjöblom (2015) provided results on these issues concerning the students; so now teachers are in focus. The poster presentation has the aim of discussing insights on: 1) What kind of language do students need in order to participate in fruitful student-to-student interaction, and what do teachers need to promote this? 2) How to design tasks and support means for students, such as problem-solving strategies or communicative roles, in order to make students listen and ask mathematical questions? 3) What can other possible frameworks offer to continue the investigation?

Th is educational design research study contribute s to understanding s about the impact the complex ity in multilingual upper s e condary mathematics classroom s has on attempts to improv e student - to - student interaction s . The research study was carried out in a cyclic process in three cycles as an intervention to give all students the opportunit y to develop their reasoning and communication abilities in mathematics. In the intervention, students in a first year class of the social scien ce program in a n upper secondary school were followed during one semester while they worked in small groups with various problem - solving tasks in mathematics . The intervention included three sets of open problem - solving tasks and three support means in the form of question lists, problem - solving support lists , and various communicative roles. The student s’ interactions were recorded , and interviews were conducted in each cycle . Both the students’ interactions and perceptions about working with mathematics w ere then analy s ed . The research questions were: 1. How did the students’ interactions and perceptions change over time as a result of an intervention to improv e student - to - student interactions? 2. What contribute d to the changes in the students’ interactions an d perceptions when an intervention was provided to improv e student - to - student interactions? 3. What did working with an intervention on improving student - to - student interactions indicate about the complexity in the multilingual upper secondary mathematics classroom? The results showed possibilities for chang ing student - to - student interactions through improving how students listened to each other, built onto each other’s interactions, worked with mathematical questions , and determined what they focused on in gr oupwork. The intervention was developed over the cycles by adapting the tasks and support means according to the results from the previous cycles. Tasks were formulated more openly, groups were arranged so that everyone had the opportunity to speak, and ma thematical questions became an important part of student - to - student interaction s . In the study , two theoretical frameworks were used — Alrø and Skovsmose’s (2004) IC - model and Fuentes’ (2009) framework for analysing student communication. The frameworks we re coordinated and then used to justify choices in the intervention and to analy s e interaction s . Interviews were used to learn mo re about students’ perceptions. Complexity in multilingual upper secondary mathematics classrooms was connected to three perspe ctives : teaching and learning, research , and school development. In the study, complexity from the teaching and learning perspective was discussed concerning how students were given equitable learning opportunities, how language affected attempts to improv e the student - to - student interaction s , and how the students’ interactions and perceptions affected groupwork in mathematics . It proved to be important not to see multilingual students as a homogenous group with special needs simply because they are multili ngual, but rather , to be flexibl e in meet ing the needs of the students. From a r esearch perspective, complexity was discussed in relation to how educational design research and the two theoretical frameworks were used to promote improved student - to - student interaction s in mathematics . Finally, from a school development perspective, complexity concerning generalizations was discussed. This study point ed out the difficulty of making generalizations about promoting improved interaction s. Since many factors aff ected interaction s between students , instead it was considered important to be flexible and study the interaction s and students’ perceptions side - by - side to make changes.

The aim of this paper is to investigate possibilities for coordinating two theories in order to analyse interactions in a group of four students completing a mathematics task in upper secondary school. The investigation suggests that the theories can be coordinated, but their interpretations of the interactions provide information on different levels. Alrø and Skovsmose’s IC-model gives a more general picture of what is happening in the interaction between students, whereas Fuentes’s framework gives details to what is happening in the different dialogic acts in the IC-model.

To reach the goals of communication and reasoning in mathematics in upper secondary school, students need to talk about mathematics but sometimes this is not as easy to achieve as it first seems. In this paper, an initial analysis is provided of tasks and strategies from an educational design research project promoting student-to-student interaction. The data include students’ interactions and perceptions on working with mathematics in groups from the first of three cycles. They are analysed and discussed in relationship to the choice of analytical tools, means of support and tasks for the remaining cycles