Previous research has shown the importance of affect when seeking knowledge about students’ achievements. However, there are surprisingly few studies looking at students’ expressed effort on a longer time scale. Using data spanning over almost three decades, in this paper, we analyze Swedish lower secondary school students’ responses to items in relation to large-scale assessments in 1992, 2003, and 2019. The two general results were that students express a lower level of goal-directed motivation, whereas the responses regarding students’ motivation as an evaluation of effort, most students state that they do not give up when facing a difficult task, that they would learn more and do better if they put more effort into their studies, and that they are happy with their achievement. Looking at changes between the different years, several items show a significant difference in the Swedish students’ answers between 1992 and 2003 and no difference by 2019. The results might explain the changes in achievement that took place between 1992 and 2003.

Previous research has stressed the importance of a good understanding of mathematical equivalence. However, despite decades of research, we still do not know to what degree the theory of operational understanding can explain errors. In this paper, children’s understanding of mathematical equivalence is studied using answers (n = 1608) and written solutions (n = 340) to a large-scale test. We identified tasks within the test designed to assess mathematical equivalence and first studied the consistency. Then, we did a qualitative analysis focused on error characteristics in the students’ answers. The results show that a large portion of the errors can be explained by an operational understanding, interpreted as grave errors. One conclusion is that most errors can be explained by the theoretical concept “operational view”. However, further quantitative analysis shows a considerable variation in the response rate, indicating students have both an operational and a relational understanding.

Algebra is a core aspect of mathematics, often functioning as a gatekeeper to further studies in mathematics. Although a well-researched area, we still do not know how students’ algebraic reasoning can vary, including the understanding of the roles of various mathematical arguments. In an explorative study, using semi-structured, non-participant observations and Interpersonal Process Recall interviews, we analyse eight upper secondary students’ collective mathematical reasoning when solving algebraic tasks about arithmetic sequences. The results show that the majority of expressed arguments were anchored in relevant mathematical properties covering a wide spectrum of algebraic reasoning. The results indicate that it is in the first instance of the reasoning, the task situation, where the students interpreted the pattern differently, where the biggest variation of different aspects of algebraic reasoning was displayed. In addition, the identifying arguments constituted the main part of all expressed arguments, indicating that the core part of the reasoning was in the interpretation of the task. There were few arguments about the choice of strategy and its implementation, signalling that once an interpretation was made and agreed upon, the strategy choice did not have as dominant role as previous research has suggested. In most cases, the arguments provided for the conclusion, evaluative arguments, were implicit and connected with previously expressed identifying arguments. The results also show that identifying arguments was connected to the mathematical content of the task, whereas the difference in algebraic reasoning appears depends on students' solution constructions and their degree of conventional syntax.

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different aspects of the concept are used as a theoretical base. In this paper, we analyse different definitions used in empirical studies. First, we did a systematic research review resulting in 19 empirical studies focusing on functional thinking with an appropriate theoretical underpinning. The definitions were analysed using an AI tool. After that, we analysed the results using intrinsic mathematical properties of how functions can be defined in mathematics to identify core aspects of the definitions. According to the analysis, two definitions capture most of the key aspects of functional thinking, and most empirical studies use these key concepts. These two definitions treat functional thinking as products or products and processes. One definition used in one empirical study stands out by theoretically operationalizing functional thinking as a process. As such, different ontological assumptions are made in the studies; however, in some cases, having the same epistemological outcome. From a methodological point of view, the cosine similarity matrix was a useful tool for an ontological analysis, but a qualitative analysis is still needed to make meaning of it.

Recently, the importance of statistical literacy has been stressed, and three central concepts in statistical literacy are the measures of central tendency: mean, median, and mode. This study explores aspects of statistical literacy expressed by 12–13-year-old students, focusing on mean, median, and mode. Their responses were analysed using a framework of statistical literacy that includes knowledge and dispositional elements. The results showed that students’ descriptions of the measures were mainly based on mathematical and vocabulary knowledge. When discussing what measure was easiest or hardest to explain, a variety of conceptions were expressed. Some explanations about the usefulness of the measures were related to context knowledge. Here, the median was an exception as students gave neither examples of contexts nor found the median useful outside the classroom.

We live in an increasingly worrying future, where researchers are looking at how we can create education for a sustainable world. In this study we investigate what such education could look like, especially for young students, reinforcing hope and an ability to act and come up with ideas of sustainable solutions with no obvious 'good' solution. The analytical tool suggested in this paper addresses the challenge of promoting and illuminating ethical reasoning in early childhood education for sustainability and mathematics. The teaching of ethics should use children's experiences as a starting point rather than theories of ethics. Using the topics of sharing as an example, and the results from a series of empirical studies, we illustrate how ethical arguments can function as backing for mathematical reasoning, and how mathematical arguments can play a similar role in ethical reasoning. We argue that the tool could assist in teaching where mathematics and education for sustainable development merge through ethical reasoning but also as an analytical tool for research.

This study investigates how collaborative, collective mathematical reasoning emerges when students jointly solve problems regarding fair sharing. Three 6-year-old children worked collaboratively in a group with a problem related to fair sharing, and their teacher was present. The data, captured in video recordings, was analysed using two frameworks: collective mathematical reasoning, and the theory of joint problem space. The results show that different things, such as physical artefacts aimed at sharing resources, challenges related to the task, and the students’ conceptions of mathematics, affect the students’ possibilities to engage in collaborative collective mathematical reasoning.