Scientists from Geneva University (Unige) in collaboration with Paris University Cy Cergy (CYU) and the University of Burgundy (UB) conducted an analysis of the drawings created by children and adults in solving simple mathematical problems. The study revealed that the most effective strategies for problem-solving are linked to specific types of graphic representations, irrespective of the participants’ age. This discovery has the potential to revolutionize the way mathematics is taught.
Mathematics education often involves solving practical tasks that relate to everyday scenarios, such as determining the correct amount of flour for a recipe or calculating change after a purchase. Participants in the study were tasked with solving simple problems using the fewest computational steps while explaining their strategy through a drawing or diagram.
The tasks encompassed both cardinal properties, focusing on the number of elements, and serial properties, which involved the elements’ positions in an ordered list. The researchers aimed to investigate whether the types of graphic representations could forecast the selection of problem-solving strategies.
Analyzed data from the 52 adults and 59 children showed that participants’ choice of strategies was primarily influenced by their understanding of the task, rather than the specific mathematical information provided. The researchers observed that drawings featuring ordinal representations were more frequently associated with one-step problem-solving, even when the task itself was cardinal in nature.
From an educational standpoint, this suggests that certain characteristics in students’ drawings may indicate whether their approach to the problem is the most efficient for minimal calculations. Therefore, analyzing students’ drawings in mathematics could assist teachers in aligning tasks with optimal graphic ideas, consequently aiding students in grasping the most effective problem-solving strategies.