Early Developmental Trajectories Toward Concepts of Rational Numbers

ABSTRACT

Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of the size of rational numbers across a 1-year period. On three occasions, students answered a test about the size of decimals and fractions. Latent transition analysis allowed profiling five different rational number size concepts and mapping students' developmental trajectories during the early learning of this topic. Development from natural number-based reasoning to mathematically correct understanding was almost nonexistent during this time period. Instead, students appear to move through intermediary concepts. Locating these temporary and mediating number concepts supports the idea of a slow and gradually developing conceptual change in rational numbers.

Acknowledgments

The present study was funded by grant 274163 awarded to the last author by the Academy of Finland.

Notes

* NNB is used to refer to the theoretical idea of natural number bias, whereas NnB refers to the specific latent class found in our analysis.