Rational number

Educational psychology

Mathematics education

Engineering

Discrete mathematics

Logical reasoning

Secondary education

Systems engineering

Archaeology

Pedagogy

Fraction (chemistry)

Physics

Organic chemistry

Psychology

Task (project management)

Mathematics

Astronomy

Geography

Decimal

Natural number

Natural (archaeology)

Primary (astronomy)

Proportional reasoning

Combinatorics

Chemistry

Arithmetic

European Journal of Psychology of Education

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called natural number bias). Focusing on rational number comparison tasks, recent research has shown that other incorrect strategies such as gap thinking or reverse bias can also explain these difficulties. The present study aims to investigate students' different ways of thinking when working on fraction and decimal comparison tasks. The participants were 1,262 primary and secondary school students. A TwoStep Cluster Analysis revealed six different student profiles according to their way of thinking. Results showed that while students' reasoning based on the properties of natural numbers decreased along primary and secondary school, almost disappearing at the end of secondary school, students' reasoning based on gap thinking increased along these grades. This result seems to indicate that when students overcome their reliance on natural numbers, they enter a stage of qualitatively different errors before finally reaching the stage of correct understanding.

Various ways to determine rational number size: an exploration across primary and secondary education