Educational Alternatives, Volume 15, 2017

Abstract: Traditionally, students' mathematics skills are measured by standard tasks, which can be solved with algorithms intensively studied in class. The problem is that many of the children are able to memorize these algorithms and to solve the tasks, but they are unable to understand the deep causality behind these algorithms and to generalize from learning. We created a test to study the deep mental representations of the studied mathematical material for children from 4th grade. We tried to estimate the depth of their internal mental representation using an indirect measure, namely the extent to which they use deep relational structures for unusual tasks. Data for the reliability and validity of the test are presented. Comparative data are presented for different regions of the country; as well for children, which follow different educational systems. A validation of the test was presented through parallel data for the mathematical achievements of children, as well as their overall success in school.