Resumen de Early stages of proportional reasoning: A cross-sectional study with 5- to 9-year-olds

Elien Vanluydt, Tine Degrande, Lieven Verschaffel, Wim Van Dooren

• The present study cross-sectionally investigated proportional reasoning abilities in 5- to 9-year-old children (n = 185) before they received instruction in proportional reasoning. This study addressed two important aspects of the development of proportional reasoning that remain unclear in the current literature: (1) the age range in which it develops and (2) the influence of the nature of the quantities (discrete or continuous) on children’s performance. Three proportional reasoning tasks (i.e., one with two discrete quantities, one with a discrete and a continuous quantity, and one with two continuous quantities) were used. A two-step cluster analysis was conducted on the groups of children based on qualitative differences in understanding. Six different early stages of proportional reasoning were revealed, showing differences in understanding depending on the nature of the quantities involved and which quantity was unknown. The development of proportional reasoning starts at a very early age but it is not yet fully mastered at the age of 9.