The aim of this study is to compare two Swedish and two Maltese textbook series in mathematics in the Swedish grade 4 from a mathematical didactic perspective, focusing on how fractions is presented, such as for instance as a number, part of a whole, part of a number, division as a metaphor or a scale, and visualized. The study is based on a comparative approach in which the teaching materials analysed represents their respective countries and schools. Four questions are addressed in this study. These are: 1. What share of the problems in the analysed books covers fractions? 2. How is the subject of fractions presented in the analysed books from Sweden and Malta respectively, for instance as a number, part of a whole, part of a number, with division as metaphor or as a scale? And which is the most common? 3. How is the subject of fractions visualized and how many times does this occur in the analysed pages? 4. What similarities and differences is there regarding the presentation and visualization of the field of fractions between the textbooks analysed from Sweden and Malta? The chosen textbooks from Sweden are Koll på matematik 4A and B and Matte Eldorado 4A and B. The ones from Malta are the textbook serie Abacus for Malta Number 6, Textbook 1 and 2 and the textbook series Busy Ant Maths 6A, B and C. The theoretical framework consists of Karlsson and Kilborn`s definition of the theory ‘konkretisering’, visualizing, and the different way fractions can be presented in. The results show that the analyzed books from Sweden mainly present fractions with division as a metaphor and the visualizing was mainly through everyday connection and through both the inductive and deductive method. The textbook from Malta mainly presents fractions as a number and the visualizing was in wording through the deductive method.

This paper is about problem solving. One common result of previous research is that pupils’ learning is greater in classrooms where they are engaged in problem solving tasks that are cognitively demanding. Therefore the purpose of this study is to analyse the didactic choices two teachers make when they are using mathematical problem solving in their classrooms. One teacher in Sweden who teaches pupils’ mathematics in grade 4 and one teacher in Malta that teaches mathematics in Year 6 takes part in the study. The pupils in both Sweden and in Malta are 10 years of age. Three questions directed this study: How cognitively challenging are problem solving tasks in the Swedish and Maltese mathematics classroom? How does a teacher in Sweden and a teacher in Malta define and exemplify the concept of problem solving? What similarities and differences are there between the Swedish and Maltese mathematical classrooms regarding two teachers’ didactic choice of mathematical problem solving, and the teachers working methods around these tasks? The study was based on observations and interviews. The purpose of the interviews was to get answers to how the teachers interpret the concept of problem solving and how they relate to it. The aim of the observations was to see how the teachers involved incorporate problem solving during the maths lessons and how the tasks carried out are cognitive. The results show that in the Swedish and the Maltese mathematical classroom, the teachers give reference to and work with cognitive demanding tasks that require a connection to conceptual and procedural knowledge. The differences between the two observed classrooms are significant. The teacher in Sweden provides space for discussion and creative reasoning and pupils often solve mathematical problems individually. The teacher in Malta provides students with mathematical skills of how pupils can solve mathematical problems using different models. The pupils in Malta are often working on problems together, with the teacher in a dialog.