The Future of Education

The latest reform in primary mathematics education in Bulgaria, implemented in 2017, initiated significant changes in curricula and led to the approval of seven new textbook sets for the primary stage. This publication is dedicated to a thorough theoretical and practical analysis of the methodology for studying the division of multi-digit numbers by a single-digit number in the fourth grade. This topic is of critical importance for the formation of mathematical literacy and logical thinking in primary school students.

The paper identifies and argues eight key methodological cases, arranged in a strict logical sequence according to their cognitive complexity. This system begins with oral division of numbers with positional units and progresses through algorithms without regrouping, cases with one or more regroupings in adjacent and non-adjacent rows, to the specific difficulties of having a zero in the quotient and situations where the first digit of the dividend is smaller than the divisor.

A central part of the study is the comparative analysis of the current textbook sets from the publishers "Arhimed", "Riva", "Prosveta Plus", "Bulvest 2000", "Anubis", "Prosveta", and "Bit i Tehnika". It tracks how each of the authorial teams implements the proposed sequence and identifies where methodological differences or unjustified jumps in difficulty occur. The results of the analysis show varying degrees of compliance with the logical gradation of the material, which directly affects the quality of mastering written algorithms. The publication offers valuable guidelines for primary teachers and methodologists, emphasizing the need for a systematized approach to teaching arithmetic operations in the fourth grade.

Keywords: primary mathematics education, division of natural numbers by a single-digit number