Starting with 2018/2019 school year in Bulgaria, the math education in the third grade is implemented through new training kits. They were developed on the basis of the new third-grade mathematics curriculum, approved by Order No. РД 09-1093 / 25.01.2017 of the Minister of Education and Science, Annex No. 8, supplemented by Order No. РД 09-2555 / 15.06.2018 of the Minister of Education and Science. Training kits are approved by the Ministry of Education and Science and are 7 in total. Geometric learning content in new math textbooks is the second most important element after arithmetic content. It is combined with the arithmetic learning content, and by this the foundation of the successful study of geometry in the next school grades is laid. The new geometry knowledge that is included in the third grade curriculum is the following: straight line, curve, beam, angle, right angle, obtuse angle, acute angle, right triangle, acute triangle, obtuse triangle; naming geometric figures with Latin alphabet letters [11]78. It is important in a modern mathematics textbook to have a rich and varied geometric content. It is important that the new types of geometry tasks are introduced with rich visualization using a specific-inductive approach. The relative number of tasks of a given type is an important prerequisite for the successful formation and improvement of skills for solving geometric problems in pupils at the age of 9-10. This article will present a comparative analysis of the geometric content in the seven approved Bulgarian third-grade mathematics textbooks, which are used in the mass practice of this school year. For the purpose of the study, a classification of all types of tasks and exercises with geometric content has been developed. Then the tasks in the seven textbooks are systematized by the so chosen classification. The data are statistically processed taking into account the relative share of tasks of each type within a textbook, as well as a comparison between the relative shares of the geometric tasks in the different textbooks. The established differences in the number and relative share of different types of geometric tasks make it possible for the analyzed textbooks to be ranked. Such a study has not been published so far. It has a relation to the assessment of the quality of the textbooks offered. The conclusions formulated in this article can help primary teachers in their choice of textbooks to teach to their third grade students.

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.

The emphasis of the educational reform currently underway in Bulgaria is on the formation of key competencies of the pupils. Mathematical competence is one of them. The mastering of basic mathematical knowledge in primary grades remains a priority. At the same time, specific mathematics curricula are explicitly laid out such as solving practical tasks, forming teamwork skills, search of information from different sources by the students themselves, project work, etc. In my research work over the past few years, I have tried experimentally with my own ideas for project work with primary school pupils. In this publication, I will present my concept of work on the project “Sofia – Capital of Bulgaria” for students of the fourth grade. It will integrate mathematical knowledge and skills with knowledge of Man and Society and a number of components of civic education. Mathematical knowledge and skills will include: adding and subtracting numbers over 1000 without passing, finding an unknown subtrahend, solving numerical expressions with parenthesis and without parenthesis, units of measure (meters, grams, kilometer, centimeter). From the knowledge and skills of Man and Society (Man and Society curriculum for the fourth grade at https://mon.bg/bg/2190), the topic: “Sofia – Contemporary Capital” is taken and the related competencies (tell about the location of the capital of Bulgaria with the help of a map; recognize on image the famous cultural monuments and natural assets of the Bulgarian capital; connect important sights of the capital with the historical ages to which they belong; understand the importance of the capital as a modern administrative centre of the country). Working on this project, pupils in the fourth grade will also acquire the following competencies: digital competence (using information in electronic form to produce short presentations on geographic, historical, cultural themes; using electronic presentations as a source of information about events and individuals); learning skills (working with maps and reference books – guides, children's encyclopaedias, extracting information about the past and the present from illustrative material, searching for information on a particular problem from written documents in the textbook); social and civic competencies (solving of problematic situations requiring hearing, exposing the personal point of view and maintaining one's own opinion; collecting curious facts about popular personalities or events from Bulgarian history; making albums with personal photos from visiting cultural, historical and natural sites; drawing up tables for the holidays of different communities – religious and ethnic; creating projects on a studied historical or geographic theme; visiting the municipality, the mayoralty, the National Assembly etc.; cultural competence and skills to express through creativity (making of albums with drawings from exhibits of visited museums, observation of natural and historical sites, elaboration of group presentations for selected natural sites). One of the distinctive aspects of the project activity with primary school pupils is the integrative nature of the project activities. The project “Sofia – Capital of Bulgaria” presented in this article is suitable for the first school term of the fourth grade. This is a medium term project that lasts for a month or two. It finishes with an open lesson in mathematics (one or two study hours), during which pupils resolve mathematical and application-practical tasks and present the results of their preliminary project work (preliminary project activities). Tasks in the project are three types: individual, group and class. Each pupil receives from all three categories of tasks. The task of the teacher is the preparation and distribution of the individual, group and class-related tasks, the determination of the deadlines for the implementation of the commitments undertaken by the pupils, as well as the ongoing control over the tasks.

Since 2015, educational reform has been implemented in Bulgaria. It was initiated with the entry into force of the new Preschool and School Education Act36. On the basis of this law, new curricula were adopted in all subjects, including elementary classes in mathematics. Mathematics kits for elementary classes, along with textbooks, study notebooks, a teacher’s book already include electronic readable textbooks and e-textbooks. “Electronic Readable Textbook” is an electronic product whose content is exactly the same as the content of the approved textbook created as a print edition37. The e-textbook is an electronic product that contains additional electronic resources to the individual development of lesson topics, such as tasks, exercises, tests and more. This educational content enables modern students, aged 7-10, to work with electronic resources independently or under the guidance of a teacher, to reflect and consolidate mathematical knowledge and skills, to develop their digital skills, to increase their interest in mathematics. Modern academic preparation for elementary teachers should also include such theoretical and practical knowledge, skills and competences for working with electronic textbooks and with the electronic resources in them. The purpose of my research is to make an analysis of the content included in the electronic textbook for mathematics for the first grade of the Anubis publishing brand of the publishing house KLETT – Bulgaria.38 On the basis of this analysis, methodological guidelines will be developed for working with the different types of electronic resources, which will become part of the academic preparation of the pedagogical students in the university discipline “Didactics of mathematics in elementary classes”. A survey of 166 pedagogical students in bachelor’s and master’s degree on their opinion on e-textbooks conducted this year has yielded interesting and revealing results that confirm the need for updating their academic training in the field of e-textbooks. The majority of respondents believe that primary teachers should use e-books in their work – 83%. When asked which subject is most appropriate to use e-textbooks, mathematics ranks immediately after the natural and social sciences, with 58.4% of the respondents citing it as the most appropriate subject for applying e-textbooks. At the same time, one third of respondents (33.1%) said they did not feel prepared to work with e-books. Of all those surveyed, 81.4% believe that it is necessary to include preparation for work with e-textbooks in university courses in private didactics. This gave me reason to head to the topic of this article and to make a content analysis of an electronic first grade mathematics textbook by classifying the types of additional electronic resources in it.

One of the important components of mathematical competence is the ability to solve practical tasks. According to G. Hristova “... with the teaching of mathematics in elementary classes, the skills to learn, to handle information, to communicate, to work independently and to work in a team are formed in the students” [4]. K. Alexieva stresses in her publication that “key competences are interdependent and represent a set of knowledge, skills and relationships necessary for the individual's personal development throughout life, for building an active civic position and participation in social life as well as for the suitability for his/her realization on the labour market. Through learning in each of the subjects, key competence learning skills are acquired, which includes understanding the personal needs in the learning process and discovering the opportunities and abilities to overcome learning difficulties, both individually and in groups; critical thinking, problem solving and decision making, initiative, creativity, responsibility, teamwork, and other key competences specified in the curriculum [1]. The ability to solve practical tasks develops to a greater extent in group, teamwork on projects. Project work is one of the active learning methods. It is not widely accepted in modern mathematical education in Bulgaria. The reasons for this are many. One of them is the lack of methodological literature on the subject for elementary teachers. Many specialists organize project work with their students, including mathematics, but their experience remains unpopular. Project work is difficult to organize, involves serious planning, and often involves spending money to buy the necessary materials. To successfully integrate into project activities, it is necessary for the young students to have a certain degree of autonomy, organizational skills, communicative skills, teamwork skills, skills for individual search of information, presentation skills, and so on. Teachers with creative abilities and innovative ideas develop, organize, and work on projects in primary school but this is a matter of their goodwill and professional skills. Mathematics teaching specialists in primary schools are in debt to primary school teachers in terms of published methodological work and project activities, including mathematics. Teachers' books for mathematics curricula for primary classes should include developments of at least one class project. This is done in the Bulgarian mathematics training kits of Anubis Publishing House, where I am the author [2] [3]. In this article I will present a description of the project – Thematic Classroom “The Room of Mysteries” for the third grade. It would be good the lesson to be held at the end of the school year. It solves tasks from all of the learning content studied in mathematics in the third grade. The idea of the project is based on the so-called “Escape Room” – a place where participants have to solve a series of puzzles to leave the room. Students of the class will not be locked in their classroom, of course. They will find a locked suitcase in their room that they want to unlock to see what's in it. For better motivation students will be given the role of police inspectors, who will be divided into 6 teams to solve a series of challenges – tasks. The lesson is held in the presence of parents and relatives of the students. A team of “veteran investigators” is formed from the parents, who also have to solve puzzles. Solving each task will lead to the opening of a new puzzle, and so pupils and parents will have to deal with a series of challenges that will lead to the discovery of 7 keys, identical at first glance, only one of which unlocks the briefcase. The prize, hidden away from the students, may be their annual third-grade certificates, may be holiday books for the end of the year as well as small gifts. Materials required for the project are purchased in advance with funds collected from students' parents.