Pedagogical Technology for Mastering the Division of Natural Numbers by a Two-digit Number

Vladimira Angelova

University of Plovdiv “Paisii Hilendarski”

https://doi.org/10.53656/ped2025-7.02

Abstract. The educational reforms implemented in Bulgarian education over the past few years have affected mathematics education in the early stages of schooling. The changes that have taken place are clearly distinguishable in the curricula for mandatory education. The current mathematics curriculum for the fourth grade in secondary school defines seven global topics, within which the planned educational content is structured.. This study focuses on developing an innovative methodology for teaching the arithmetic operation of dividing natural numbers by a two-digit number – one of the most complex topics in mathematics education. The aim of this publication is to present the developed and experimentally tested original technological approach for teaching the algorithms for performing the division of a natural number by a two-digit number within a specific methodological system. The components of the developed instructional approach include digital educational resources in the form of video films. During the 2023/2024 academic year, an experimental study was conducted with 192 fourth-grade students, divided into two groups – an experimental group and a control group, each consisting of 96 students. The author’s instructional technology was integrated into the teaching of the experimental group. The main criterion for measuring its effectiveness was the degree to which students acquired competencies in dividing a natural number by a two-digit number, assessed based on ten indicators. A quantitative and qualitative analysis of the results from the experimental study is presented. The obtained results conclusively prove the effectiveness of the developed pedagogical technology for mastering the division of a natural number by a two-digit number. After integrating this technology into the learning process, students acquire competencies in using the algorithms for performing this operation in various contexts, including: finding a number using the concept of “… times smaller”; comparing the values of numerical expressions; determining the value of a composite numerical expression; finding an unknown number in an equation—unknown factor, unknown divisor; modelling a word problem with numerical expressions; solving a geometric problem.

Keywords: primary school; math education; division of natural numbers by a two-digit number; digital resources

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