10:30

Coffee/tea and registration

11:00-11:45

Opening (Room M208, Chair Tamsin Meaney)

• Opening by Pro-Dean for research Vegard Fusche Moe
• Introduction to the project by Professor Tamsin Meaney
• Overview of the day

11:45-12:30

Lunch

12:30-14:00

Overview presentations (M208, Chair Toril E Rangnes)

1. Tamsin Meaney & Troels Lange: Discussing mathematics teacher education for language diversity
   Abstract
   As part of a large research project about supporting preservice teachers to learn about teaching argumentation for critical mathematics education in multilingual classrooms, we outline a framework for considering the knowledge, skills and practices that we, as teacher educators, consider mathematics teachers need. Our objective for describing such a framework is to provide a discussion document for teacher educators, primarily at our institution, but also for others who aim to improve their mathematics teacher education practices and want to determine theoretically how to navigate the complexity of changing our practices.
2. Nils Henry W Rasmussen: Surveying preservice teachers’ understanding of aspects of mathematics teaching – a cluster analysis approach
   Abstract
    Preservice teachers begin their teacher education with experiences that affect their possibilities for accessing and integrating new learning into their teaching practices. Yet often mathematics teacher education courses treat preservice teachers as a homogenous group. Responses to an electronic survey from the beginning of two compulsory mathematics education courses showed that preservice teachers could be divided into two clusters. The preservice teachers in each cluster give similar responses to different aspects of mathematics teaching, suggesting their share similar sets of views. These differences should be recognised in their future mathematics teacher education courses. 
3. Lisa Steffensen & Georgia Kasari: “Forced to flee” – mathematical modelling in primary school
   Abstract
   In this paper, we investigate the characteristics of pre-service teachers’ problem-posing activities on a modelling problem related to refugee crises. We use socio-critical perspectives of modelling and problem-posing. We draw on data from one group of pre-service teachers’ assignment and follow-up interviews, where they reported on their experiences of planning and implementing the modelling activity with 7th-grade students. After thematic coding, we found multiple characteristics in pre-service teachers’ reflections. We focus on those regarding posing questions with the students linked to the refugee crisis, feeling the numbers, taking action as part of the classrooms’ modelling activity, and modelling for lived democracy. We consider these characteristics relevant for teacher educators to support problem-posing in modelling activities related to socio-critical issues.

14:00-14:15

Coffee/tea

14:15-15:45

Modelling presentations (M208, Chair Rune Herheim)

4. Suela Kacerja & Inger Elin Lilland: “A bit uncomfortable”- Preservice primary teachers’ focus when planning mathematical modelling activities.
   Abstract
   The purpose of this study is to get insight into the aspects of mathematical modelling (MM) that 16 primary preservice teachers (PTs) focus on when planning teaching for school practicum. The analyzed planning session was part of the PTs mathematics education course in their second year. All the PTs have the concern to choose a topic that interests the students for the modelling activity, and to let students make choices by themselves during modelling. The unpredictability of the MM is experienced as uncomfortable. Three categories are identified in the data: student perspective, teacher perspective and activity perspective. The results are relevant in exploring the gap between the potential that MM holds for the students’ learning and the teachers’ reluctance to implement it.
5. Shengtian Zhou & Ragnhild Hansen: When mathematics in three acts meets mathematical modelling.
   Abstract
   We investigate how the introduction of the pedagogical method, “mathematics in three acts” to preservice teachers influenced their mathematical modelling, while on practicum. We analyzed documentation, of groups of preservice teachers, on their experience of teaching modelling lessons. One finding was that the groups were able to use “mathematics in three acts” to produce modelling problems that fulfilled certain criteria in our selected framework, but they had difficulty finding modelling problems for the lower grades (grades 1-3). We also found that the preservice teachers appeared to emphasize the subprocess of working mathematically and devalue the subprocesses simplifying/structuring, mathematising, and validating, when guiding the pupils through a modelling process in a “mathematics in three acts” lesson.
6. Beate Lode: ‘Should the turn be counted, or not …?’ Analysing learning loop contexts of preservice teachers professionalising in the teaching of mathematical modelling.
   Abstract
   This study presents an analysis of preservice teachers (PTs) teaching mathematical modelling to seventh-grade pupils (Ps) in a school-based practice setting. Using data from the practice of mathematics educators, I examine preservice teacher development in the teaching and learning of mathematical modelling. An analysis of shared contexts in the Learning Loop of PTs and Ps shows that PTs and Ps can situate each other’s learning. The contexts can strengthen PT learning and professional development at a later stage. One shared context episode provides valuable PT insight into risk-taking reflection. Risk-taking can stimulate Ps to think critically about mathematics and demonstrate autonomous teaching. An important result of this study should be to inspire PTs to take risks in teaching mathematical modelling.

15:45-16:00

Coffee/tea

16:00-17:00

Discussions about the presentationsn in 3 groups

1. Implications for school mathematics education (M208, Chair Rune Herheim)
2. Implications for mathematics teacher education (M209, Chair Toril E Rangnes)
3. Implications for mathematics education research (M308, Chair Ragnhild Hansen)

17:00-17:30

Plenary about group discussions (M208, Chair Tamsin Meaney)

18.00

Dinner at Kronstad

9:00-10:30

Modelling presentations (M208, Chair Troels Lange)

7. Ragnhild Hansen: Supporting structural development in modelling at first grade
   Abstract
   This paper reports on a case study following four preservice teachers (PTs) who implemented modelling in their practice teaching at first grade. During the modelling activity the students made, and responded to, different forms of mathematical representations. We have applied a categorical framework to classify the responses into four broad stages of structural development. The aim was to investigate how the PTs supported the students at various stages. One finding was that the PTs had tendency to overlook responses that could be classified into the pre-structural stage. When the PTs themselves offered representations, these were aiming towards a more sophisticated level.
8. Toril E Rangnes & Tamsin Meaney: Preservice teachers learning from teaching mathematics in multilingual classrooms
   Abstract
   In this presentation, we investigate one group of preservice teachers’ descriptions of their practicum experience at the beginning of their second year of their teacher education. The four preservice teachers were placed in a class where 19 of the 24 students did not have Norwegian as their first language. The preservice teachers discussed their experiences both in writing and in an oral presentation, particularly in relationship to the teaching of a unit of work on mathematical modelling. From examining what the teachers seemed to notice and what they explicitly highlighted about how the context affected their considerations about their teaching and the children’s learning, we describe the role that multimodality had in supporting multilingual students’ mathematical meaning making. This provides us, as teacher educators, with an understanding of how practicum teaching involving an innovative project can support preservice teachers to improve their understandings about teaching in multilingual mathematics classrooms as well as what may still be needed to increase their professional competence.
9. Lisa Steffensen, Kjellrun R Hauge & Rune Herheim: Ethical thinking and programming.
   Abstract
   There is an increasing prevalence of programming in mathematics education. In this paper, we focus on ethical aspects of programming by first presenting a literature review. Three interrelated topics are identified in the review: reasons to include ethics in programming, code literacy, and facilitating ethical thinking. These three topics are then used to reflect on ethical thinking and programming in three tasks developed by a lower secondary school teacher. We argue that the context of programming tasks such as climate change, sustainability, and decision-making of self-driving cars, can facilitate students’ ethical thinking alongside their learning of how to program.

10:30-11:00

Coffee/tea

11:00-12:00

ICT/programming presentations (M208, Chair Ragnhild Hansen)

10. Inge O Hauge & Johan Lie: Critical democratic competence, empowerment and block and text-based programming in mathematics education
    Abstract
    We will look into some critical aspects of students’ collaboration, while programming, in order to development of critical democratic competence in mathematics education. We take a closer look at what programming in Scratch and Python programming tool can contribute to critical democratic competence though Tissenbaum, Sheldon and Abelson´s term digital empowermet, and Ernest´s term empowerment. We study democratic challenges in the learning of mathematics through analysis of pairs of students’ dialogue and argumentation as they collaborate on programming in the mathematics classroom.
11. Rune Herheim & Marit Johnsen-Høines: A culture perspective on students’ programming in mathematics
    Abstract
    Digital technology has become a key part of the development of society and influences people’s ways of being, thinking, and communicating. Young people’s digital cultures are continuously developing, and this article investigates how two students’ productive struggle when programming in mathematics can be analyzed and understood from a cultural perspective. The data consists of two seventh-grade students who share a computer and program a pentagon. The task proves to be challenging and the students face several kinds of struggles. However, the students are persistent, apply communication qualities, and make continuous refinements in ways that create an interesting interweaving of mathematics and programming. The students’ communication qualities are used to describe characteristics of a productive struggle in the mathematics classroom and how such a culture can be supported. 

12:00-13:00

Lunch

13:00-14:30

ICT/programming presentations (M208, Chair Rune Herheim)

12. Elena Severina: Scratch programming and student’s explanations
    Abstract
    Herheim and Severina (2020) found that ScratchJr has some potential to foster mathematical argumentation, although “it requires appropriate mathematical tasks and teacher awareness about how to support the students’ work.” This result does not apply to the ScratchJr alone as teaching mathematical argumentation in ICT rich environment requires certain TPCK-skills. Severina (2022, in progress) discusses opportunities for expansive learning when mentoring pre-service teachers in task design, which brings some light on what teacher educator needs to be aware about. Both studies are concerning the same mandatory assignment on Mathematics 1 course, although its different steps during different years.  So, what do scratch programming and student’s explanations have in common with mentoring pre-service students in task design for ICT rich environment? What teaching of mathematical argumentation in ICT rich environment requires from teacher educator is what I would like to reflect on.
13. Diana Paola P Moreno: Motivational and fun! Pre-service teachers’ recontextualizing discourses on ICT integration in mathematics
    Abstract
    Even though educational policies and research worldwide have advocated for the transformative integration of digital tools into mathematics teaching, this has not occurred, even with young teachers who have likely grown up surrounded by digital technologies. However, rather than considering pre-service teachers’ lack of knowledge and competencies, this paper focuses on pre-service teachers’ sense-making around ICT integration during their initial experiences in teacher education. Bernstein’s concept of recontextualization is used to identify the discourses used and adapted by the pre-service teachers in their sense-making. The discourses show, for example, how the pre-service teachers recontextualize curricula references to playing games with digital tools into discussions about fun and motivation.
14. Tamsin Meaney & Toril E. Rangnes: Evaluating Minecraft as a mathematical language resource
    Abstract
    Adapting mathematics classroom practices to support students with language diverse backgrounds has been raised as part of recent discussions about social justice. In these discussions, the importance of resources as contributors to students’ learning opportunities has been highlighted. However, as yet, very little attention has focused on digital resources, even though these are often touted as valuable for all mathematics learners. By analysing interactions between students in grade 7 about multiplicative problems, it is possible to identify the kinds of support that Minecraft made available for students’ mathematical argumentation. The results show that experiences of using digital games at home and learning mathematics at school affected the possibilities that Minecraft made available, including what languages were supported.

14:30-15:00

Coffee/tea

15:00-16:15

Discussions about the presentations  in 3 groups

1. Implications for school mathematics education (M208, Chair Rune Herheim)
2. Implications for mathematics teacher education (M209, Chair Toril E Rangnes)
3. Implications for mathematics education research (M308, Chair Ragnhild Hansen)

16:15-17:00

Plenary about group discussions (M208, Chair Tamsin Meaney)

17:30

Dinner at Kronstad

9:00-10:00

Argumentation presentations (M208, Chair Toril E Rangnes)

15. Silke Lekaus & Magni E Hope Lossius: Exploratory talk about fractions
    Abstract
    We report about data that was collected during an introductory session for PTs about exploratory talk. We look at the data material from two perspectives to identify aspects that supported and hindered exploratory talk: our analysis of transcripts of group discussions about a fraction problem and the PTs’ own reflections.
16. Trude Fosse & Tamsin Meaney: Year 2 children posing and solving their own written problems
    Abstract
    Pupils’ writing in mathematics is highlighted as a way to improve their mathematical thinking. However, it is not known what kind of support students need to improve mathematical writing and thinking. By examining 170 arithmetic narratives from children in the 2nd grade, it is possible to identify differences in their written problems and how they incorporate connections, images and symbols in their problems. Many students show competence in one or more areas, but no child uses all the different modes to the highest level. In particular we focus on the use of pictures as an intermediary between the mathematical thinking and the symbolizing of a problem. These results suggest how teachers could support students is to improve their mathematical writing, which is likely to help improve their mathematical thinking.

10:00-10:30

Coffee/tea

10:30-12:00

Multilingual classrooms presentations (M208, Chair Ragnhild Hansen)

17. Georgia Kasari: “I don’t think it would be enough, but I can give it a try”: The tensions and complexities of mathematics teacher education for language diversity
    Abstract
    The work of mathematics teacher educators in integrating social justice issues, such as language diversity, into their practice is complex. Teacher educators navigate a number of tensions when planning mathematics teacher education with such a focus. As part of an action research project, I analyse my reflections on planning my own mathematics teacher education practice for raising issues of language diversity with pre-service teachers. Three main tensions were identified with respect to: my relationship with the pre-service teachers; the changing and non-changing of my practice; and the possibilities and uncertainties for my practice. Understanding how these tensions affected my planning in different moments of the action research contributes to what has previously been documented about the complexities of integrating issues of language diversity into mathematics teacher education.
18. Toril Rangnes & Tamsin Meaney: Possibilities for learning about mathematical argumentations using the language resources of multilingual preservice teachers
    Abstract
    Although preservice teachers’ and teacher educators’ views on multilingual school students’ mathematical learning possibilities have been researched in the last decade, there are limited studies on how utilising language differences in mathematical argumentation can offer opportunities for developing mathematical concepts. Using multilingual preservice teachers’ discussion of examples of Grade 4 students’ multimodal mathematical argumentation, the influence of different cultures and languages on those evaluations is explored. Although differences in evaluation criteria were evident in the workshop, the teacher educator was only able to make use of some of them to broaden understandings about mathematical argumentation. This raises some implications for multilingual mathematics teacher education courses.

12:00-13:00

Lunch

13:00-14:00

Critical mathematics education and learning presentations (M208, Rune Herheim)

19. Trude Fosse, Troels Lange & Tamsin Meaney: Issues with using Activity Theory to understand how Master students view their research skills as contributing to their future teaching
    Abstract
    Although preservice teachers’ and teacher educators’ views on multilingual school students’ mathematical learning possibilities have been researched in the last decade, there are limited studies on how utilising language differences in mathematical argumentation can offer opportunities for developing mathematical concepts. Using multilingual preservice teachers’ discussion of examples of Grade 4 students’ multimodal mathematical argumentation, the influence of different cultures and languages on those evaluations is explored. Although differences in evaluation criteria were evident in the workshop, the teacher educator was only able to make use of some of them to broaden understandings about mathematical argumentation. This raises some implications for multilingual mathematics teacher education courses.
20. Eva Elise Tvedt, Tamsin Meaney, Toril E Rangnes, Troels Lange: Truth, lies and bullshit in critical mathematics education
    Abstract
    Having learners engage in critical mathematics education projects is supposed to lead to learners gaining insights into how mathematics can contribute to understandings about the role of mathematics in society. However little research has been done on how learners make sense of using mathematics to change and improve societal issues. An analysis of preservice teachers discussing how to persuade an audience to  change their behaviour in regard to cigarette butt pollution showed that sometimes the preservice teachers considered that strengthening the case for change by adjusting the presentation of data overrode concerns about truth. The philosopher, Frankfurt’s (2005) description of the difference between truth, lies and bullshit are used to discuss the preservice teachers’ actions and reasoning.

14:00-15:45

Discussions about the presentations in 3 groups – including coffee/tea

1. Implications for school mathematics education (M208, Chair Rune Herheim)
2. Implications for mathematics teacher education (M125, Chair Toril E Rangnes)
3. Implications for mathematics education research (M309, Chair Ragnhild Hansen)

15:45-16:30

Plenary about group discussions (M208, Chair Tamsin Meaney)

16:30-17:00

Conclusion to the conference (M208, Chair Tamsin Meaney)

18:00

Dinner for invitees and presenters