Exploring the Primary School Teachers' Reasoning and Individuals with Limited Education When Solving False Proportionality Problems

In this study employing a qualitative approach, we explore and compare the mathematical reasoning of active primary school teachers and individuals with limited education when tackling problems involving false proportionality and lack of authenticity. The research is justified by the importance of understanding how these issues are addressed in various educational groups and how teaching strategies in this area can be enhanced. An individual questionnaire containing five problems was administered to five participants in each group. The results indicate that teachers tend to more frequently succumb to the illusion of linearity, incorrectly applying linear relationships to non-proportional problems compared to individuals with lower educational attainment. This suggests a greater influence of algorithmic approaches and clauses of the didactic contract on their mathematical reasoning. This tendency could be attributed to a greater exposure to algorithmic approaches during the formative stages, as well as certain clauses in the experimental contract. Conversely, individuals with limited education approached problems with greater flexibility, linking their responses to everyday experiences. The study concludes that it is imperative to implement educational strategies aimed at overcoming limitations such as the illusion of linearity and fostering meaningful problem-solving skills from the early stages. It is recommended to developteacher training programs that promote a more contextualized and flexible approach to mathematics teaching, as well as the include contextualized and meaningful problems in the school curriculum.