Early generalizations as a source of mathematical misconceptions: examples of zero and fractions - Vučić, Miloš; Lužanin, Zorana (Norma, 2026)
The subject of this paper is early generalizations as a possible source of mathematical misconceptions in early mathematics education, with particular emphasis on the concepts of zero and fractions. The aim of the paper is to show how intuitive rules, formed on the basis of a limited number of examples and experiences with natural numbers, may become problematic when uncritically transferred to new numerical contexts. By applying a theoretical-analytical approach and reviewing relevant literature, the paper analyzes the relationship between procedural and conceptual knowledge, as well as typical forms of students’ reasoning. The results of the analysis indicate that locally valid rules may develop into stable misconceptions if the conditions of their application are not specified. It is particularly emphasized that understanding zero and fractions requires a reexamination of early intuitive rules, as well as the use of counterexamples, different representations, and the critical use of digital tools in developing conceptual understanding.
Keywords: early generalizations; mathematical misconceptions; zero; fractions; conceptual understanding; methodology of mathematics teaching