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

Abstract

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.