Levels of proportional reasoning and microworlds. A study on unitary tele-secondary education - Lugo Lugo, Carlos Alberto (2024)
[Objective] Proportional reasoning is a type of complex thinking that involves recognizing comparisons such as the covariation between magnitudes and multiple comparisons. The aim of this study was to analyze proportional reasoning of students from unitary tele-secondary education using the levels proposed by Karplus (1983) through a microworld like GeoGebra. In the microworld, students can explore and construct meanings about mathematical objects. [Methodology] Four activities were designed in GeoGebra, which were administered to 18 students from a unitary tele-secondary school, an educational modality in Mexico. [Results] It was found that participants are at initial levels that correspond to additive, qualitative, or erroneous structures to justify their procedures. The more complex levels of proportional reasoning, related to the use of ratios and constants of proportionality, were achieved when students interacted with each other and with the microworld. The reasoning levels are not mutually exclusive, as students can reason differently depending on the situation and the software's capabilities. [Conclusions] The use of microworlds in exploring proportional reasoning enables actions that cannot be carried out with pencil and paper, providing opportunities to interact with moving constructions. Additionally, it fosters interactions that reinforce or build collective knowledge.