“Geometri er kunsten av å resonnere godt på dårlig utført tegninger.” – Niels Henrik Abel. 

Drawing is the basis for solving geometric problems. How do modern students draw geometric drawings? What is preferable for a modern school: pencil and paper or using a ruler and compass or using computer programs. At the seminar of 4th of March, we will look at a methodics of several geometry problems. For example, comparing solutions on paper and using various programs: desmos, GeoGebra, Euclidea, Mathigon. Besides, we will look on beauties in MathEtudes and try to do something useful for teachers on cloud-based digital learning environment Stepic (made for instructors by instructors). In process of our common work, we will discuss differences between Norwegian and Russian teaching of math. 

The aim of the study is to describe the semiotic resources that children used in mathematical explanations of hypothetical situations. The empirical material consists of a short video from a Norwegian kindergarten, where four five-year-old children and a kindergarten student teacher discuss real and imaginary page layouts of a photo book. When explaining their reasoning about the amount of photographs in the layouts, the children used oral language, gestures and physical objects like number charts. The use of these resources in different kinds of explanations is discussed. Our results suggest that by using a range of semiotic resources children are able to provide explanations of hypothetical situations using mathematical ideas at a younger age than previously suggested. 

Keywords: semiotic resources, explanations, hypothetical situations, imaginary objects, gestures 

Criticising alphabets, for the bad words that they might produce, seems like a meaningless activity. Yet, praising alphabets for the prospect of producing useful words seems as futile. I argue alike for mathematics. Criticising mathematics as a set of universal and abstracted algorithms and rules does not take one very far, but giving mathematics power and value for the anticipation of being useful to people, to children and to communities is equally futile, to say the least, and dangerous to say the most. In what other ways can one hope for a more just mathematics teaching and learning ? Rorty (1999) says, no one can reasonably hope for a utopian society. Rather, all we can do is supplement our pre-existing societies, not by increasing our philosophical sophistication but instead “by having our attention called to the harm we have been doing without noticing that we are doing it” (p. 237). For Rorty, hope is more than a state of mind and a goal in action. Rather, hope is understood as a narrative – as “a story that serves as a promise or reason for expecting a better future” (p. 97).  

In this talk, I like to tell a story of my personal ethical dilemma, highlighting the possible harm that mathematics education could cause to different none western communities, while we draw on cultural, historical, linguistic and social resource these communities to teach dominant mathematics. I call our attention to this possible harm, in a hope for a more just future for mathematics teaching and learning.  In being systematics about being aware of, noticing and critiquing this possible harm, I draw on two opposing view: the wholeness view of wisdom and compartmental comprehension of cleverness. 

Programming is being included in many educational policies, also in Norway. A study involving first-year pre-service teachers and year four students is undertaken to address the increased emphasis on programming. The focus is on links between ScratchJr functions and students’ mathematical explanations and justifications. The results indicate that some functions in ScratchJr have the potential to foster such mathematical argumentation, but it requires appropriate mathematical tasks and teacher awareness about how to support the students’ work. 

Keywords: programming, mathematical explanations and justifications, task design 

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.  

Keywords: mathematical modelling, preservice teachers, primary school.  

In this talk will discuss the potential and use of so-called Fermi problems to introduce mathematical modelling to students at all levels and primary preservice teachers. The talk includes a general overview of the use of Fermi problems in education, and a discussion of two frameworks that are being used to investigate various aspects of solving and using Fermi problems in mathematics education (the MAD framework (Modeling Activity Diagrams) and FpATs (Fermi problem Activity Templates)). In particular, I will provide examples from a research project using FpATs a didactical tool with preservice primary teachers aiming at facilitating their future use of Fermi problems as teachers to connect and structure their mathematics teaching to real-life contexts and mathematical modeling.