The work done when solving linear equations: altering experiences due to change of numbers

Paper in proceeding, 2024

This paper investigates how one student solves linear equations with a focus on how different numbers (e.g., natural numbers, numbers with decimals, and negatives) in the equations influence reasoning. The choice of coefficients in equations is not usually the focus in research nor in teaching.
However, as students are used to taking numbers into consideration, the influence of coefficients on equation solving is an important topic to address. In a previous study, a model for how students experience equations was suggested. Here, the model is used to analyse one interview with a student
in upper-secondary school, solving several similar equations but with numbers from varying number domains. The results show the decisive role that numbers play in how this student perceives the equations. Using a wide range of numbers also helped to challenge the student to explore the properties of the equations’ structure. Possible applications in the classroom are discussed.