Methodology for the Learning of an Unknown Addend in the New Bulgarian Mathematics for the Second Grade

Abstract

In the last few years, educational reform has taken place in Bulgaria. It also affects the training in mathematics in the elementary classes. A new Law on Pre-school and School Education36 was adopted in 2015, which initiated the reform. Subsequently, the curricula for individual subjects for all grades and educational degrees were established and officially approved by order of the Minister of Education and Science. From the 2017/2018 school year a new curriculum in Mathematics for the second grade37 is in force. One of the elements of the curriculum in this program is the study of the rules for finding unknown addend and finding an unknown multiplier. At the initial stage of primary education study six subjects for finding unknown components are learned: addend and multiplier in the second grade, minuend and divisible in third grade and subtrahend and divider in the fourth grade. With some conditionality, it can be assumed that these elements of the curriculum are preparing for the study of equations in the algebra course in the following grades. In the Bulgarian pedagogical practice, tasks for an unknown component have never been taught in algebraic ways, on an algebraic basis. In the initial grades these tasks and the related rules are always clarified on an arithmetical basis – based on the dependencies that exist between the components and the results in the pairs arithmetic operations: addition and subtraction, on the one hand, and multiplication and division, on the other. Knowledge of the relationship between pairs of arithmetic actions Bulgarian pupils receive yet in the first grade. Then they assimilate the ability to do a check on the action of subtraction using the action addition. Later, in the second grade, as soon as the two new arithmetic actions were taken – multiplication and division, the students assimilated the ability to test the division by multiplication. Moreover, the action division itself in the Bulgarian school is introduced as the opposite of the action multiplication. On the basis of the new curriculum in Bulgaria, a total of nine mathematics training sets were created, approved by the Ministry of Education and Science, as well as by the teachers and distributed in the school network. As far as they are based on a unified curriculum, it cannot be said they are alternative textbooks. These textbooks are variants. In their development, the authors’ teams have applied a variety of methodological approaches to elucidate the new learning content in the lessons of new knowledge. The purpose of the study in this publication is a comparative analysis of the methodological methods of introducing an unknown addend into the nine new mathematics textbooks for the second grade in the lessons of new knowledge. For theory and practice, there is an interest in the advantages and disadvantages of applied approaches in developing and clarifying this component of the curriculum.