The Future of Education

One of the expected outcomes set out in the mathematics curricula for second, third, and fourth grades (general education) in the Republic of Bulgaria is the acquisition of skills for finding unknown addends and unknown multipliers (second grade), unknown subtrahend and unknown divisor (3rd grade), and unknown subtrahend and unknown divisor (4th grade).

This publication focuses on the acquisition of skills by 8-10-year-old students for finding unknown components in equations. Its aim is to present the author's model for teaching primary school pupils (aged 8-10) to effectively master the activity of finding unknown components in equations. To test the effectiveness of the model, a long-term pedagogical experimental study was conducted in the period 2022–2025, covering three consecutive school years. It involved 250 students, 125 of which in a controlled group and 125 students in an experimental group tracked from second to fourth grade, which allowed for an analysis of the sustainability and accumulation of results over time.

The analysis of the results obtained from this study shows that the implementation of the author's model in mathematics education of the experimental group from 2nd to 4th grade supports a more conscious and in-depth mastery of competencies for finding unknown components in equations.

The application of systematic training in finding unknown components also helps students aged 8–10 to apply these competencies more easily and effectively when solving problems for composing equations with unknown numbers in mathematical texts and when solving word problems.

Key words: primary school, mathematics, unknown component