This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the El´konin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic thinking. Further analysis showed that these arguments were characterised by interplay between fractional and algebraic thinking except in the conclusion stage. In the conclusion and the evaluative arguments, these two types of thinking appeared to be intertwined. Another result is the discovery of a new type of argument, identifying arguments, which deals with the first step in task solving. Here, the different types of arguments, including the identifying arguments, were not initiated only by the teachers but also by the students. This in a multilingual classroom with a large proportion of students newly arrived. Compared to earlier research, this study offers a more detailed analysis of algebraic and fractional thinking including possible patterns within the collective mathematical reasoning. An implication of this is that algebraic and fractional thinking appear to be more intertwined than previous suggested.

Contemporary society is characterized by rapid changes in the labor market, increased flow of information, and more opportunities to make choices in relation to education and career. Previous research has demonstrated how many young people in school don't think they get the support they need to make such choices. The overall aim of this article is to contribute to more in-depth knowledge of what kind of support and knowledge young adults describe as important in order to be able to make informed choices. This knowledge might help school to better support young people in acquiring the knowledge, skills, and attitudes in relation to their education and career choices. The article is based on interviews with 25-year-old men and women. 23 interviews were conducted. In sum, the analysis indicates that guidance activities that aims to contribute to knowledge about the labor market, programs and courses and requirements for different education programs would probably be perceived as more fruitful by the young adults if they are organized in a combination of different levels, i.e. both as group activities (exhibitions, general information/discussion) and individual activities (personal information/discussion). Further, the authors demonstrate that roles and expectations between pupils, teachers and guidance counselors should be discussed and clarified.

This article discusses algebraic thinking regarding positive integers and rational numbers when students, 6 to 9 years old in multilingual classrooms, are engaged in an algebraic learning activity proposed by the El’konin and Davydov curriculum. The main results of this study indicate that young, newly arrived students, through tool-mediated joint reflective actions as suggested in the ED curriculum, succeeded in analysing arithmetical structures of positive integers and rational numbers. When the students participated in this type of learning activity, they were able to reflect on the general structures of numbers established as additive relationships (addition and subtraction) as well as multiplicative relationships (multiplication and division) and mixtures thereof, thus a core foundation of algebraic thinking. The students then used algebraic symbols, line segments, verbal, written, and gesture language to elaborate and construct models related to these relationships. This is in spite of the fact that most of the students were second language learners. Elaborated in common experiences staged in the lessons, the learning models appeared to bridge the lack of common verbal language as the models visualized aspects of the relationships among numbers in a public manner on the whiteboard. These learning actions created rich opportunities for bridging tensions in relation to language demands in the multilingual classroom.