The article considers the prerequisites for the inclusion of problems with elements of probability theory in mathematics education in grades 1-4. This type of task is generally not present in the compulsory curriculum in mathematics in primary school, but they could be used in classes for compulsory, extended, and additional training, thus creating conditions for implementing developmental learning. Some theoretical statements about the theory of probabilities are systematized, related to the tasks included in the constructed and approbated methodological system of work. Some of its characteristics are presented. This article offers some of the tasks for grades 1-4. A longitudinal empirical study was conducted with students of the 1-4th grade in the period 2015 to 2020. The results of the outgoing diagnostics in 4th grade are processed by mathematical and statistical methods and are presented graphically. They show that fourth-graders successfully solve problems with elements of probability theory, and a primary school teacher could use them in the systematic work in mathematics at the initial stage of the basic educational degree. Solving non-standard mathematical problems is an element of probability theory that helps arouse interest, motivate students, and place them in an active cognitive position by solving problem situations in the pedagogical interaction in mathematics in primary school.
The choice of strategies and their correct combination over the course of training of the students to solve tasks from the area of combinatorics for composing combinatorial compounds from permutation type is one of the important factors for performance of efficient education in mathematics during the classes for extended and additional training in the Primary school. Object of the study is the influence of the applied strategies on the process of acquiring of knowledge, development of skills and competencies in the students for solving tasks from the area of combinatorics in the education in mathematics during the classes for optional education in Grades 1. -4. The research work was performed in qualitative and quantitative aspects. The following methods were applied: experiment, observation, test, analysis of the content, mathematical-statistical method for data processing. As a result of the study it was found out that due to the applied methodology system of work where different strategies were combined, the competences and competencies for solving tasks from the area of combinatorics were developed in the students from Grades 1.-4.
INTRODUCTION: The question of intellect and its development is an important topic for contemporary pedagogy science. The approach to education from this point of view gives a better idea regarding its social-cultural and psycho-pedagogy dimensions.AIM: The research study systematized and presented theoretical concepts as well as certain practical aspects based on the specifics of developing education through the process of solving mathematical tasks.METHODS: To achieve the aim the following methods were used: analysis of the content; pedagogical observation; pedagogical experiment; method for determining the standard for success and level of correlation. FINDINGS AND RESULTS: The results received from the theoretical and the experimental work demonstrated that a divergence occurs through the process of solving mathematical tasks both as a conceptual foundation for the development of skills and a pre-requisite for assuring the so called “I-inclusion” of the student.CONCLUSIОNS: The result of the research in the theoretical, methodological and practical aspects are focused on integration with the intellectual development of children and school students.
Development of knowledge, skills and competences for the mathematical quantity of “length” and its measurement units represent important part of the overall education in mathematics for students from Grades 1. – 4. This research work systematizes some theoretical concepts related to the competences. Based on the analysis of the relevant legislation in force in the Republic of Bulgaria researchers presented the relations between the specific mathematical competences and terminology from the competency Cluster “Measurement”. The research work is aimed at the development of such a methodology system of work which gives priority to practical productive activities thus facilitating development in primary school students of a higher level of knowledge, skills and competences related to the mathematical quantity of “length” and its measurement units. The new system of work was applied during the compulsory classes in mathematics in Grades 1. – 4. The research work presents some of the developed and applied options of practical activity. The researchers studied the objectiveness, the validity and the reliability of the set of tools and means used for doing diagnostics as well as the difficulty and the dividing (separating) strength of the mathematical tasks included in it. The results from the experimental work were statistically processed.
The development of knowledge, skills and competences related to values and their measuring units represents an important part of the overall education in mathematics for primary school students in Grades 1-4. The research studies different theoretical concepts related to the competences and the approaches in the primary school education. Based on the analysis of the respective legislation the researcher presents interconnections between the specific mathematical competences and the term “mass” from the competency cluster “Measurement”. The newly developed methodology system of work for learning the term “Mass” is applied during both the mandatory and the additional mathematics classes in Grades 1-4. Different approaches for education are simultaneously applied but priority is given to the system-acting approach with the idea to achieve unification between the act of teaching and the control of the cognitive and practical productive activities of the students. As a result of applying the newly developed methodology system of work the students actively participate in the pedagogy interrelations and co-operation with the rest of the students, they have the opportunity to express their own intellectual and emotional potential. When the students make mistakes, during the practical individual, team and group activities they get the opportunity to correct these mistakes and to develop their own logical thinking.
Communicational transversal competency represents an important part of the mathematical knowledge, skills and competencies in the process of students’ development in Grade 1-4. The creation and formation of communicational transversal competency helps to put students into an active cognitive position in the course of pedagogical interactions in mathematics classes. Further, creation of communicational transversal competencies develops not only students’ analytic – synthetic activity during the process of solving different types of mathematical tasks but also their creative thinking. This longitudinal research presents some theoretical concepts related to the transversal communicational competency and to its development during the educational process in mathematics in Grade 1-4. During this empirical study a completely new methodology system of work was developed with the purpose to facilitate development of mathematical knowledge, skills and competencies including the communicational transversal competency. The new system was tested and applied during the compulsory, additional and extended classes in mathematics in Grade 1-4 and consequently was improved after the performance of entry and intermediate diagnostic. Also, this article presents some of the mathematical tasks included in the tests. The researcher studied the objectiveness, the validity and the reliability of the diagnostic tools developed for the purpose as well as the tasks included in the tests in respect of their difficulty and separating force. The presented results of the experimental work were processed using mathematics-statistics methods.
Introduction: Creative work with text tasks helps to improve the educational process in mathematics for Grades 1-4, to create opportunities for developing education, to provoke the cognitive activity of the students and to develop their thinking. Object: The object of this research work is to study certain tendencies for creative work with text tasks and to develop their respective methodology options for work in the education of mathematics for Grades 1-4. This research work presents some theoretical concepts related to: text tasks; the stages for their solving, some of the tendencies for creative work with them; and the problem-productive strategy for education in mathematics in the primary school. Methods: The experimental work includes qualitative and quantitative research of the problems specified in the above paragraph. The following methods were applied: didactical experiment, observation, test, content analysis, mathematicalstatistical method for data processing. Results: As a result of the experimental work it was found out that the percentage of the students from Grade 4 who failed to solve the text tasks with direct and indirect use of relations decreased from 31.2 % to 8.5 %. The percentage of the students who failed to describe situations from their surrounding environment using a mathematical model decreased from 45.3 % to 10.1 %. The percentage of the students who correctly composed text tasks increased from 29.5% to 71.6%. The difference in the results was proven to be statistically significant. Conclusion: The applied methodology system of work with text tasks helped to develop knowledge, skills and competencies from a competency cluster "Numbers" and "Modelling", and to develop creative thinking in the students from Grades 1-4.
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