The Role of Different Arguments: Upper Secondary School Students’ Collective Mathematical Reasoning in Algebra

Abstract 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.