Research purposes: Based on theoretical and practical research related to issues of language, mathematical language, thinking, the relationship between language and thinking, mathematical language and mathematical thinking, we propose some measures for developing mathematical language to contribute to improving the quality of teaching for pre-university students in the Central Highlands.
MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY KIEU MANH HUNG CONTRIBUTING TO THE DEVELOPMENT OF THE MATHEMATICAL LANGUAGE FOR PRE-UNIVERSITY STUDENTS IN THE CENTRAL HIGHLANDS Major: Reasoning and methodology of teaching mathematics Code: 9140111 SUMMARY OF DOCTORAL THESIS IN SCIENCE EDUCATION NGHE AN - 2020 The thesis was completed at Vinh University Supervisors: Dr Nguyen Van Thuan Assoc Prof Dr Nguyen Thanh Hung Reviewer 1: Assoc Prof Dr Vu Duong Thuy Reviewer 2: Assoc Prof Dr Dao Thai Lai Reviewer 3: Dr Nguyen Huu Hau The thesis will be defended at the Boards of Examiners of Univeristy level, at Vinh University, No 182, Le Duan Street, Vinh City, Nghe An Province, Time: At , date month year 2020 This thesis can be found at: National Library of Vietnam The Information Center - Library of Nguyen Thuc Hao, Vinh University INTRODUCTION Rationale 1.1 By studying theoretical and practical teaching, we find that pre-university students master the knowledge and skills of mathematics Once they master the mathematics language system, they will be able to use this language system in the thought process, reasoning in solving math problems and putting them into practice In addition, language difficulties are a significant barrier to the acquisition and application of scientific and technical knowledge, especially for highly abstract scientific fields such as mathematics The results of the grassroots research topics that the author had done in 2009, 2013, 2015, 2016 and 2018 showed that pre-university students still have many limitations of expression when solving the problem 1.2 Flexibly understanding and applying concepts, theorems, consequences, properties, to solve math issues successfully is not an easy task But how to present the theoretical content briefly, concisely and highlight content to facilitate the use of them in mathematical reasoning is much more difficult 1.3 The Math curriculum for pre-university students not have content specifically to introduce and teach knowledge related to mathematical language The knowledge is introduced in an implicit manner in teaching process, in accordance with the students' level of knowledge in order to serve mathematical reasoning as well as apply it to other science subjects This shows that teachers have to pay attention to fostering self-studying skills for pre-university students so that these skills can be used as a means to serve the thinking and reasoning process 1.4 The mountainous areas in our country in general and the Central Highlands in particular are places where socio-economic conditions are still facing many difficulties There are still many children of ethnic minorities with low educational levels and uneven knowledge Through the teaching process at the pre-university Department of Tay Nguyen University, we found that the pre-university students in the Central Highlands are mainly ethnic minority people with many different languages, rituals and customs In general, they have many difficulties in learning subjects in general, and Maths in particular The lecturers teaching mathematics always try to let students know how to interpret the definitions, theorems and problems, from ordinary language to mathematics language and vice versa for the purpose of consolidation and applying knowledge However, in fact many pre-university students in the Central Highlands are still confused and encountered many mistakes when performing the above tasks This greatly influences the acquisition of knowledge, mathematical reasoning and the development of logical thinking 1.5 The task of the pre-university training system is to help students consolidate, systematize and better understand the basic knowledge of the high school program, build learning methods and self-study methods In order to help preuniversity training students confidently study Maths at the University and College levels later, it is necessary to practice and develop mathematical language during the studying period at pre-university From that awareness, the proposal of pedagogical measures in teaching to develop the language of mathematics in learning Maths is meaningful and practical work The study of this issue contributes to improving the learning results of Mathematics for pre-university students in the Central Highlands in particular and pre-university students in general Start from the above reasons we study the thesis “Contributing to the developing mathematical language for pre-university students in the Central Highlands” Research purposes Based on theoretical and practical research related to issues of language, mathematical language, thinking, the relationship between language and thinking, mathematical language and mathematical thinking, we propose some measures for developing mathematical language to contribute to improving the quality of teaching for pre-university students in the Central Highlands Subjects and scope of the research 3.1 Research subjects: Measures to develop mathematical language for pre-university students in the Central Highlands 3.2 Scope of the research Scope of time: The Doctoral thesis collects data on students in two courses K2016 and K2017 of pre-university Department of Tay Nguyen University Experiments on pre-university classes of blocks A and B, two courses of K2017 and K2018 of pre-university Department of Tay Nguyen University Scope of space: The Central Highlands Scope of content: Mathematical language in the curriculum of Mathematics which is used for pre-university students Research topic - Theoretical study of language, mathematical language, thinking, mathematical thinking, the relationship between language and thinking, the relationship between mathematical language and mathematical thinking, development mathematical language - Research content and curriculum of Mathematics using for pre-university students - Researching the development of thinking and language of pre-university students in the Central Highlands - Studying on the situation of the use of mathematical language in teaching mathematics at the pre-university - Proposing a number of pedagogical measures to develop mathematical language for pre-university students in the Central Highlands in teaching Maths - Pedagogical experiment to test the effectiveness and feasibility of the proposed pedagogical measures Research method 5.1 Methods of theoretical research We use a combination of research methods: collecting information, documents, analyzing, synthesizing, etc to study the theories of: language, mathematical language, thinking, mathematical thinking of Pre-university students of blocks A, B At the same time researching Math content, programs and subjects of Maths which is used for pre-university students 5.2 Practical research methods Coordinating the practical research methods to clarify the situation and test the effectiveness and feasibility of the Doctoral thesis 5.3 Information processing method Using statistical methods to process data after investigating the situation, data of pedagogical experiment process Scientific hypothesis In teaching mathematics for pre-university students, if building and implementing a number of teaching methods such as: Fostering knowledge of syntax and semantics (namely consolidating vocabulary, semantics, syntax, internal conversion capacity training in one language, converting from one Math language to another); Practice using mathematical language in typical teaching situations (specifically in conceptual teaching - theorem, in teaching rules - methods and in teaching math solving); Practice mathematical communication skills (listening, speaking, reading and writing skills); Developing mathematical language through active teaching methods (problem-solving method, role-playing method, game method and group work method) will contribute to university pre-university students' development of mathematical language, through then improve the quality of teaching - learning Math for pre-university students in the Central Highlands The contributions of the Doctoral thesis Systematizing some theoretical issues about language, mathematical language, thinking, mathematical thinking, development of mathematical language Analyzing the problem of mathematical language in the content of the mathematical program for pre-university students Find out the situation of using the mathematical language of the pre-university students in the Central Highlands Proposing groups of measures to contribute to the development of mathematical language for pre-university students in the Central Highlands Supporting contents for Thesis - Concepts of language, mathematical language, thinking, mathematical thinking, development of mathematical language of pre-university students in the Central Highlands - Pedagogical measures to contribute to the development of mathematical language for pre-university students in the Central Highlands - The results of the pedagogical experiment The structure of the Thesis In addition to the Introduction, Conclusions and References, the Doctoral thesis is presented in three chapters: Chapter The theoretical and practical basis Chapter Developing mathematical language for pre-university students in the Central Highlands Chapter Pedagogical experiments CHAPTER THE THEORETICAL AND PRACTICAL BASIS 1.1 Theoretical basis 1.1.1 Overview of research issues 1.1.1.1 International studies In 1952, Hickerson studied the meaning of the arithmetic symbols formed during a student's math class In the 70s of the twentieth century, Jesse Douglas (1897 - 1965) focused on studying the relationship between the capacity of using mathematical language and students' thinking ability In 1986, Andrew Waywood studied the influence of mathematical language on junior high school students In 1986, Martin Hughes in the book "Children and Numbers" proposed a perspective on the early efforts of children to understand mathematics He describes the incredible knowledge of numbers that children know before they start class Understanding of pre-school numbers is an obstacle to learning mathematical knowledge in the classroom In 1988, in the works "Second international handbook of mathematics education", two mathematicians Stigler and Baranes mentioned the use of mathematical language of elementary students in Japan, Taiwan, South Korea and the United States Pimm (1987), Laborde (1990), Ervynck (1982) confirmed that the use of mathematical language of students in maths is a barrier because the mathematical language is much different from the daily use language In 1993, Diane L Miller concluded that developing mathematical language has a profound influence on the development of mathematical concepts [78] In 1995, Eula Ewing Monroe and Robert Panchyshyn studied the lexical problem of mathematical language, the need for vocabulary in the development of mathematical concepts In 2007, Chard Larson emphasized the role of mathematical vocabulary in the understanding and learning of junior high school students He believed that mathematics is a language and students who want to master it must be able to use and understand vocabulary By using vocabulary quizzes and vocabulary-related activities taken from math, students will better acquire an understanding of mathematical concepts [75] In 2008, Charlene Leaderhouse studied the mathematical language in the subject of Geometry He studied the mathematical language of 6th grade students in learning geometry and concluded that the ability to understand and correctly use mathematical terms will help them master the mathematical concept To study geometry well, children need to have many opportunities to discuss ideas and practice in teaching which uses mathematical language [80] In 2008, Bill Barton [74] concluded that everyday mathematical ideas were expressed differently in different languages Diversity occurs in the way language expresses numbers, the language that describes the position of numbers and the grammar of mathematical content expressions In 2009, Rheta N Rubenstein researched the issues of how to help teachers teach mathematics in high school to recognize the challenges that students often encounter with mathematical symbols to propose teaching strategies that can alleviate those difficulties The study proposed solutions to help teachers know how to use different symbols and identify common difficulties that students often encounter when they speak, read and write symbols; At the same time, he also provided teaching methods to avoid or overcome these difficulties [93] 1.1.1.2 Domestic studies In 1981, Pham Van Hoan, Nguyen Gia Coc and Tran Thuc Trinh affirmed that the correct expression of the relationship between “mathematical ideology content” and “mathematical language form” wais the basis of important methodology of mathematical education [30, p 93] In 1990, Ha Si Ho presented some concepts and characteristics of mathematical language Accordingly, the language of mathematics is primarily the language of using signs, not the language of "speech" as in the language of mathematics The major mathematical language is the "written" language, which is both tight and flexible [31, p 45] In 1992, Hoang Chung studied mathematics language and teaching mathematical notation in high school In 1998, authors Ha Si Ho, Do Dinh Hoan and Do Trung Hieu mentioned many aspects of mathematical language Accordingly, it is necessary to have a language suitable for expressing mathematical content, and at the same time overcome the disadvantages of mathematical language [32] In 2004, in the Thesis "Contributing to developing the capacity of logical thinking and correct use of mathematical language for high school students in algebra teaching", the author Nguyen Van Thuan proposed the pedagogical measures: Set students to express some definitions and theorems in different ways; Train students to use correct transformations; Practice using terms and symbols of mathematical logic to express mathematical propositions [57, p 82-135] Recently, there are many direct and indirect studies on languages in teaching high school mathematics, such as Tran Ngoc Bich [4], Vu Thi Binh [5], Thai Huy Vinh [63], pre-university students in the Central Highlands are mainly ethnic minority people in Ede In recent years, there have been many studies on Ede language from a linguistic perspective, such as: Malyo - Polynesian languages in Vietnam of Romal Del and Truong Van Sinh [21]; Doctoral thesis of Doan Van Phuc (2009) with the topic Phonetic of Ede language [46]; The doctoral thesis of Linguistics by Truong Thong Tuan on the subject of Comparative method in the customary language of Ede [61]; Doctoral thesis of Linguistics by Nguyen Minh Hoat (2012) with the subject of type nouns in the Ede language The doctoral thesis of Linguistics by Doan Thi Tam (2012) with the topic of the system of human words in Ede language However, these works are only studied from the perspective of the Ede language - the mother language of most of the preuniversity students in the Central Highlands C Generalization, specialty Generalization and specialty are two different thinking actions that are contrary Specialization is the presentation of specific cases, particular cases of the problem Generalization is also generalizing the problem from specific cases and particular cases d Comparison Comparing mathematical objects helps students identify similarities and differences of two or more objects Regularly comparing students will have a more comprehensive view of the problem We often perform comparisons such as: compare two concepts, compare two definitions, compare two issues, 1.1.5 The relationship between language and thinking, mathematical language and mathematical thinking 1.1.5.1 The relationships between language and thinking Language and thinking are a unified but not a consistent relationship The language exists in the form of material while thinking is the form of spirit Language is perceived by humans by senses such as pitch, field, tone, etc and thinking is the inner awareness of the human brain in a certain logical order The language is nationalistic (the product of the nation) while thinking is humankind (all countries have the same products of thinking about the problem: sovereignty, peace, education, health, ) [22] 1.1.5.2 The relationship between mathematical language and mathematical thinking Mathematical language is both a tool and a material shell of mathematical thinking Mathematical language and mathematical thinking are a unified but not consistent This is reflected in the fact that mathematical language exists in physical form, mathematical thinking exists in mental form Units of mathematical language are perceived by the senses and have physical properties such as pitch, intensity, etc And mathematical thinking is not perceived by such senses, there are no properties of matter such as mass, weight, taste, etc The activity of mathematical thinking requires rational and logical while the mathematical language operates according to 12 habit Units of mathematical thinking are not identical with the units of mathematical language The function of mathematical language for mathematical thinking is to express ideas and directly participate in the formation of ideas [28] 1.1.6 Communication skill and mathematical communication skills 1.1.6.1 Communication skills Communication skills are a set of rules, the art of how behavior, responses are molded through practical experiences, making effective communication and achieving the purpose of specific circumstances 1.1.6.2 Mathematical Communication Skills Math communication skill is the ability to understand mathematical problems through communication, speaking, reading and writing It is the ability to effectively use mathematical language in a close relationship with the mathematical language for exchanging, presenting, explaining, arguing and proving mathematicians accurately, logically, clarifying mathematical ideas in particular contexts 1.1.7 Development and development of mathematical language 1.1.7.1 Development concept According to the Vietnam Encyclopedia "Development is a philosophical category that indicates the nature of the changes taking place in the world Development is an attribute of matter All things and phenomena of reality not exist in a different state from appearance to death, the source of development is unity and struggle between opposites ”[62] 1.1.7.2 Developing mathematical language a Develop competency in using mathematical language Competence in using mathematical language includes: * The ability to receive and understand knowledge and skills about mathematical language * The ability to create and apply effectively mathematical language in communication as well as thinking * The ability to select and convert languages in learning and in practice b Capacity development of mathematical performances 13 * Conventional performances and non-conventional performances * Internal performance and external performance c Develop mathematical communication competence 1.1.7.3 The scale of assessing development level of mathematical language for pre-university students in the Central Highlands Table 1.4: A scale for assessing Boleslaw's levels of thinking Thinking level Identification Level Students remember the basic concepts, can state or recognize them when required Students remember basic concepts and can apply them when they Understanding are presented in ways similar to the way that teachers teach or as typical examples of them in the classroom Students can understand the concept of a higher level of Operation "understanding", creating logical links between fundamental (Low Level) concepts and being able to use them to reorganize the information that is presented as similar to a teacher's lecture or in Textbooks Students can use the concepts of subject-topic to solve new Operation problems, unlike those learned or presented in textbooks but it is appropriate to be solved with the skills and knowledge taught at (High Level) the this perception These are the same problems that students will encounter in society Based on the rating scale of Boleslaw's thinking levels, in this thesis, we propose the following levels of mathematical language development for university preparatory students in the Central Highlands as follows: 14 Table 1.5: Scale for evaluating mathematical language development levels for pre-students in the Central Highlands Development Indicator level Students remember symbols, mathematical terms and grasp the Level syntax of mathematical language Students read the correct names, recognize symbols, mathematical terms and correctly use mathematical symbols and terms in a single form Students use correctly and accurately mathematical symbols and Level terms; Correctly associates mathematical symbols in simple form Initial reading, understanding mathematical content through drawings, diagrams, visual images Students use correctly and accurately mathematical symbols in Level complex forms; Initially, knowing the mathematical content through drawings, diagrams, visual images Students know: Reading and understanding correctly the mathematical contents presented in written language or diagrams, Level drawings; using mathematical language to present math problems in written language in a coherent, logical and accurate manner Using mathematical language to listen and understand what others have to say and present mathematical problems Thus, in order to achieve the above levels, it is necessary to have a system of measures to help pre-university students develop the mathematical language in teaching Maths 15 1.2 Practical basis 1.2.1 Mathematical program for pre-university students [2] 1.2.1.1 Goal, request a Target b Knowledge c Skills 1.2.1.2 content Table 1.6: Distribution table of Mathematical curriculum for pre-university students Algebra Number of periods SQN Chapter Name of chapter Total Theory Exercises, Review 1 Combinations and probability 25 12 13 2 Equations, systems of equations, inequalities 45 22 23 3 Trigonometric 15 4 Derivative and application 30 16 14 5 Primitive and integrals 18 10 6 Complex numbers Total 140 69 71 Geometry Number of periods SQN Chapter Name of chapter Total Theory Exercises, Review 1 Vector 2 Straight lines and planes in space 29 14 15 3 Polyhedron blocks - Spherical surface - Cylindrical surface - Cone surface 11 4 Method of coordinates in the plane 15 5 Method of coordinates in space 21 12 84 44 40 Total 16 1.2.2 Review of the mathematical program of pre-university rank A Advantages B Limitations C Proposals 1.2.3 Characteristics of pre-university students 1.2.4 Surveying the status of mathematical language development of preuniversity students 1.2.4.1 Survey purpose 1.2.4.2 Survey object 1.2.4.3 Survey content 1.2.4.5 Survey results 1.2.4.6 Cause of the situation 1.2.5 Conclusion of the situation of mathematical language development in pre-university students 17 Conclusion of chapter In Chapter 1, we investigated and clarified the following present, analyze and clarify a number of issues related to language, mathematical language, thinking, mathematical thinking, the relationship between language and thinking, between mathematical language and mathematical thinking, communicative skills, mathematical communicative skills, development and development of mathematical language Presents an overview of the concept, function, nature, characteristics of language as well as the relationships between language and thinking Introducing the Maths program for pre-university students Thereby analyzing the characteristics of the program as well as raising some notes when teaching Maths for pre-university students Finding out the situation of developing the mathematics language for the preuniversity students, thereby knowing the situation and seeing the necessary to train and develop the mathematics language for the pre-university students in the Central Highlands The above-mentioned content is the basis for which we propose the following issues and also new points of the thesis - Clarify and analyze mathematical language of pre-university students - Finding out and surveying the status of the mathematical language development of the pre-university students in Central Highlands at the current - Proposing some teaching measures to develop mathematical language for preuniversity students in the Central Highlands 18 Chapter DEVELOPMENT OF MATHEMATICAL LANGUAGE FOR PRE-UNIVERSITY STUDENTS IN THE CENTRAL HIGHLANDS 2.1 Some principles in formulating and implementing measures In order to develop mathematical language for pre-university students, we set up a number of teaching measures, which must ensure the principles: 2.1.1 Consistent with the characteristics of teaching Maths in the pre-university program 2.1.2 Consistent with the principle of teaching Maths in the pre-university program 2.1.3 Consistent with the psychology of pre-university students and special characteristics of ethnic minority students 2.1.4 Ensuring the feasibility in the current practical conditions of teaching mathematics at pre-university schools 2.2 A number of orientations in developing and implementing measures 2.2.1 Organize learning activities to enable students to realize the role of Maths in the pre-university Program 2.2.2 Exploiting thoroughly the knowledge, experiment and experience of students as a basis for creating new knowledge 2.2.3 Build a positive collaborative learning environment, always encouraging students to exchange, discuss, explore, discover and solve problems 2.2.4 Focus on helping students to create a connection between theoretical content, applying theory with practice 2.3 Some measures for the development of mathematical languages for preuniversity students in the Central Highlands 2.3.1 Measure 1: Reinforce the mathematical language knowledge and fostering language transformation capacity for students 2.3.1.1 Measure 1.1: Reinforce vocabulary and semantics of mathematical language for students 2.3.1.2 Measure 1.2 Reinforce the syntax of mathematical language for students 19 2.3.1.3 Measure 1.3: Develop mathematical language through fostering the internal transformation capacity of a language 2.3.1.4 Measure 1.4: Developing mathematical language through fostering the ability to convert from one mathematical language to another 2.3.2 Measure 2: Develop mathematical language through practice used in typical teaching situations 2.3.2.1 Measure 2.1: Developing mathematical language through practice used in teaching concepts and theorems 2.3.2.2 Measure 2.2: Developing mathematical language through practice used in teaching rules and methods 2.3.2.3 Measure 2.3: Developing mathematical language through practice used in teaching maths 2.3.3 Group of measures 3: development of mathematical language through training of mathematical communication skills (listening, speaking, reading and writing) 2.3.3.1 Measure 3.1: Development of mathematical language through training of listening skills in mathematics 2.3.3.2 Measure 3.2: Development of mathematical language through training speaking skills in mathematics 2.3.3.3 Measure 3.3: Development of mathematical language through training of reading skills in mathematics 2.3.3.4 Measure 3.4: Development of mathematical language through training in writing skills in mathematics 2.3.4 Group Measure 4: Development of mathematical language through aggressive teaching methods 2.3.4.1 Measure 4.1: Development of mathematical language through the organization of problem solving methodology 2.3.4.2 Measure 4.2: Development of mathematical language through the roleplaying organization 2.3.4.3 Measure 4.3: Development of mathematical language through a gamerelated teaching organization 2.3.4.4 Measure 4.4: Development of mathematical language through teaching organization by teamwork method 20 Conclusion of chapter Based on the theoretical and practical studies presented in Chapter and Chapter 2, we focus on researching and proposing measures to develop mathematical language for pre-university students in the Central Highlands Based on the principles and orientations, we have built measures to foster and develop mathematical language for students, including 15 specific measures in groups of measures: 1) Measure 1: Developing mathematical language through strengthening knowledge of mathematical language (4 measures) Implementing this group of measures helps students consolidate their knowledge of mathematical language, understand and master mathematical symbols and terms, semantics and syntax of mathematical language; Know how to convert internally a language (synthetic geometry language, vector language, ); Know how to convert from one language to another (synthetic geometry language into vector language, synthetic geometry language to coordinate language, ) 2) Measure 2: Develop mathematical language through training to use in teaching situations (3 measures) Implementing this group of measures will train students to use mathematical language in teaching formation, reinforcing concepts, teaching rules and methods, teaching solving math problems; 3) Measure 3: Develop mathematical language through practicing communication skills (4 measures) Implementing this group of measures will develop communication skills (listening, speaking, reading and writing) in mathematical language for students; 4) Measure 4: Develop mathematical language through active teaching methods (4 measures) Implementing this measure group will develop mathematical language through organizing non- traditional teaching activities (problem-solving method, roleplaying method, game method, working method group) In each measure, we propose suggestions and guide teachers to organize activities for students in the process of teaching Mathematical content in the pre-university program issued by the Ministry of Education and Training in the year 2012 [2] 21 The proposed measures are also always considered to ensure the scientific, practical, regional and specialized elements of the subjects of pre-university students Measures indicate the development according to the rating scale which are proposed in Chapter To confirm the feasibility and effectiveness of the proposed measures, we conduct pedagogical experiments 22 Chapter PEDAGOGICAL EXPERIMENTS 3.1 Experimental purposes Pedagogical experiments are conducted for the purpose of testing the feasibility and effectiveness of the pedagogical measures which are proposed in Chapter 3.2 Experimental organization and content 3.2.1 Experimental organization The experiment was conducted in two phases: Phase 1: Conducted from January 2018 to April 2018 Experiment at pre-university classes K2017A, K2017B, Pre-university Department of Tay Nguyen University - Experimental class is pre-university K2017A; Teacher: Tran Quynh Mai - The control class is pre-university K2017B; Teacher: Tran Quynh Mai Phase 2: Conducted from January 2019 to April 2019 Experiment at pre-university classes K2018A, K2018B, pre-university Department of Tay Nguyen University - Experimental class is pre-university K2018A; Teacher: Tran Quynh Mai - The control class is pre-university K2018B; Teacher: Tran Quynh Mai 3.2.2 Experimental content Phase 1: The experiment was conducted in 15 periods with the content of Coordinate Method in the plane of Chapter IV [35] Phase 2: The experiment was conducted in 20 periods with the contents of Equations, Inequalities, and Equations system of Chapter II [34] 3.3 Evaluate experimental results 3.3.1 Qualitative evaluation 3.3.2 Quantitative evaluation Conclusion Chapter This chapter presents the purpose, content and key outcomes of the experimental batches The pedagogical experiment aims to test the scientific hypothesis of the thesis through teaching practices and the feasibility test and the feasibility of the proposed pedagogical measures Pedagogical experiments have been conducted two times at pre-university classes of K2017A, K2017B, K2018A and K2018B, preuniversity Department of Tay Nguyen University 23 CONCLUSIONS AND RECOMMENDATIONS The thesis has completed the research contents and tasks, building the pedagogical measures to develop the mathematics language for the pre-university students in the Central Highlands The thesis obtained the following main results: Overview of language, mathematical language, thinking, mathematical thinking, the relationship between language and thinking, between mathematical language and mathematical thinking To give an overview of the communicative skills, mathematical skills, development and development of mathematical language Researching the current situation of studying Maths, situation of mathematical language development of pre-university students, clearly analyzing the causes as a basis for proposing measures to develop mathematical language Identify the four principles for developing and implementing measures for developing mathematical language Specifically, the measures must be suitable to the characteristics of teaching Maths; in accordance with the principle of teaching Maths; suitable with the psychology of pre-university students and special characteristics of ethnic minority students; ensure feasibility in the current practical conditions of teaching mathematics in pre-university schools Identify the four orientation to construct and implement the mathematical language development measures for the pre-university students Specifically, the measures must be built in the direction of: Organizing learning activities to create conditions for students to realize the role of Maths in the pre-university program; Fully exploit the knowledge, experiment, experience of students as the basis for creating new knowledge; Building a positive collaborative learning environment, which always encourages students to exchange, discuss, explore, discover and solve problems; Focusing on helping students create the relationship between the theoretical content, applying theory and practice On the basis of principles and orientations, we proposed 15 specific measures (belonging to four groups) to develop mathematical language For each measure, there are five parts: objectives, content, steps of implementation, examples 24 and notes for implementation The 15 proposed measures are as follows: Measure group 1: Consolidating mathematical linguistic knowledge for preuniversity students, including two measures: Consolidating vocabulary and semantics; Reinforcing the syntax of mathematical language for students; Helping students convert within a language (synthetic geometry language, vector language, ); Knowing how to convert from one language to another (synthetic geometry language into vector language, synthetic geometry language to coordinate language, ) Measure group 2: Developing mathematical language through practice using in teaching situations, consisting of three measures: development of mathematical language through practising, using in teaching concepts and theorems; in teaching rules and methods; in teaching maths Measure group 3: Developing mathematical language through training mathematical communication skills (listening, speaking, reading and writing), including four measures: Developing mathematical language through training listening skills; through practicing speaking skills; through practicing reading skills; through practicing writing skills in learning Maths Measure group 4: Developing mathematical language through active teaching methods, including four measures: Developing mathematical language through organization of problem-solving teaching; following the role play method; according to the game method; follow the teamwork method Organize experimental teaching to illustrate the feasibility and effectiveness of the proposed pedagogical measures Based on the research results, it is possible to confirm the research purpose of the thesis has been achieved, the research task has been completed and the scientific hypothesis is acceptable The dissertation's research confirms that measures to develop mathematical language are effective and feasible, improve Math learning results, develop logical thinking ability and develop mathematical language for preuniversity students in the Central Highlands 25 LIST OF PUBLISHED WORKS Nguyen Thanh Hung, Kieu Manh Hung (2014), “Some common errors of students when solving problems in spatial geometry”, Journal of Education, No 331, April 2014, p 47-50 Nguyen Thanh Hung, Kieu Manh Hung (2014), “Contributing to practicing thinking manipulations when solving in high school”, Journal of Education, Special issue, May 2014, p 163-165 Nguyen Thanh Hung, Kieu Manh Hung (2015), “Teaching mathematics in the pre-university rank towards building capacity for students”, Journal of Education and Society, Spring issue of the Year of the Goat, February 2015, p 10-14 Nguyen Thanh Hung, Kieu Manh Hung, Phan Phi Công (2015), “Contribute to the practicing of logical thinking when teaching Maths in high schools”, Journal of Education, Special issue, May 2015, p 150-153 Nguyen Thanh Hung, Kieu Manh Hung (2015), “Training teachers in the direction of forming learners' competencies in teaching mathematics”, Journal of Education and Society, No 56 (117), November 2015, p 22-26 Nguyen Thanh Hung, Kieu Manh Hung (2016), “Some solutions contributing to improving the quality of teaching mathematics for pre-university students”, Journal of Education and Society, No 63, June 2016, p 65-69 Kieu Manh Hung (2016), “The method of solving some forms of spatial geometry in the pre-university program”, Tay Nguyen Journal of Scientific, No 45, November 2016, p 34-37 Nguyen Thanh Hung, Kieu Manh Hung (2017), “Practising the skills of using mathematics for pre-university students”, Journal of Educational Science, No 136, January 2017, p 89-92 Kieu Manh Hung, Nguyen Thanh Hung (2018), “Teaching Maths in high school towards building capacity for students”, Journal of Educational Science, No March 2018, p 57-61 26 ... language Analyzing the problem of mathematical language in the content of the mathematical program for pre-university students Find out the situation of using the mathematical language of the pre-university. .. Supporting contents for Thesis - Concepts of language, mathematical language, thinking, mathematical thinking, development of mathematical language of pre-university students in the Central Highlands -... overcome the disadvantages of mathematical language [32] In 2004, in the Thesis "Contributing to developing the capacity of logical thinking and correct use of mathematical language for high school students