Dạy học hình học phẳng theo hướng phát triển năng lực sáng tạo cho học sinh chuyên toán trung học phổ thông TT TIENG ANH

MINISTRY OF EDUCATION AND TRAINING VIETNAM THE VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES NGUYEN XUAN QUYNH TEACHING PLANE GEOMETRY TOWARDS DEVELOPING CREATIVE COMPETENCY OF MATHEMATICALLY GIFTED HIGH SCHOOL STUDENTS Speciality: Theory and Methodology of Teaching Code: 14 01 11 SUMMARY OF DOCTORAL THESIS ON EDUCATION I, 2021 The thesis is completed at: THE VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES Instructors: Assoc Prof Dr Ton Than Assoc Prof Dr Dao Thai Lai Reviewer 1: Reviewer 2: Reviewer 3: The thesis will be examined by the Doctoral Review Committee of Vietnam National Institute of Educational Sciences at 101 Tran Hung Dao Street, Hoan Kiem District, Ha Noi On Date The thesis can be found at: - The National Library - The Library of Vietnam National Institute of Educational Sciences INTRODUCTION The thesis rationale The Fourth Industrial Revolution currently taking place is considered a great revolution of digital, internet of things, artificial intelligence and big data analytics The training of human resources to meet the requirements of the Industry 4.0 requires a breakthrough in education Instead of focusing on imparting knowledge, education and training needs to form and develop different types of competencies which can be applied to learners’ life, meeting the requirements of practicality, vocational guidance and development Teaching to develop learners’ competencies has become an urgent requirement and a common trend of education in many countries worldwide Studying the necessary competencies of humans in the 21st century, David Finegold and Alexis Spencer Notabartolo have proposed a list of 14 competencies in which creativity and innovation ranked at the top According to Beghetto (2005), the subject of creativity in education is not only an opportunity, but a pressing necessity Competency framework in the high school curriculum in many nations, namely: England, Australia, Singapore, Malaysia, Russia, the United States, Finland, Korea all affirm that creativity is one of the competencies that need to be achieved by learners The general curriculum issued together with Circular No 32/2018/TT-BGDDT dated December 26, 2018 of the Minister of Education and Training clearly states: Problem solving and innovation is one of the core competencies that high school students need to attain In high schools for the Gifted, students specializing in Mathematics are usually those with intelligence and quick perception; good memory; passion for learning; good self-study ability; good generalizability; distinct personality; are cooperative; industrious, patient learners with high adversity quotient and self-confidence; willing to face challenges - manifestations of creative competency Therefore, it can be seen that high school math students have a lot of potential, so teaching to develop their creative competency is essential In high school, Plane Geometry belongs to the Geometry and Measurement circuit of knowledge, an important component of Mathematics education This helps learners study about shape, size, properties, relative position of shapes on the plane, forming tools to describe objects and entities of the surrounding world Geometry helps students to form and develop good observation, imagination, judgment and intuition - the elements of creative competency Visual elements are also an advantage of geometry as visual images make students' thinking process faster and more logical Through teaching this content in high schools, especially in gifted high schools, teachers can train and develop these components, contributing to developing creative competency of students Due to the pressure of exams, educators have to teach a large amount of difficult knowledge in a short period Thus, today, teaching Plane Geometry in many high schools for the gifted is still basically an one-way impartation of knowledge and has yet to meet the requirements of forming and developing learners' competencies, especially creative one - as its inherent potential For the aforementioned reasons, the author chose the research topic of: “Teaching plane geometry towards developing creative competency of mathematically gifted high school students” Objective of the study To unravel the problems related to teaching to develop students’ competencies in general, and creative competency in particular Studying the process of teaching Plane Geometry in high schools for gifted students to see the current situation, potential and opportunities to implement creativity development-orientated education On that basis, propose some measures to teach Plane Geometry towards developing creative competency of Mathematically gifted high school students The research objects, subjects and scope - Research subjects: The process of teaching Plane Geometry content in high school for the gifted - Research objects: The process of teaching Plane Geometry to develop creative competency of Mathematically gifted high school students - Research scope: Contents of grade 10 Plane Geometry according to Mathematics Textbook 10 in Vietnam Scientific hypothesis If the basic characteristics of teaching towards developing creative competency for learners are identified, it is possible to propose appropriate pedagogical measures in teaching Plane Geometry for specialized Maths classes in gifted high schools This will, in turn, help teachers carry out such educational method, contributing to improving the efficiency of teaching Mathematics Research task - Problems related to competency-based education, especially creative competency to apply in teaching Plane Geometry at high schools for the gifted; - The opportunity and necessity of teaching Plane Geometry towards developing creative competency of Mathematically gifted high school students in our country; - The reality of teaching and learning Plane Geometry to develop creative competency in our country's high schools for the gifted; - Proposing measures to teach Plane Geometry to develop creative competency for high school Maths students in our country; - Illustrating teaching Plane Geometry towards developing creative competency for students through examples associated with teaching Plane Geometry in specialized Maths classes of gifted high schools; - Carrying out pedagogical experiments to test the feasibility and effectiveness of the proposed measures Methodology - Theoretical research methods - Practical research methods: observation, investigation - Methods: summaries of experience, professional solutions, case studies, product research methods, statistical methods, pedagogical experiments New contributions of the thesis In theory, the thesis has summarized a number of issues related to creative competency, in order for it to be applied in teaching 10th grade Plane Geometry in high schools for gifted students; Clarified the opportunity and necessity of teaching Plane Geometry towards developing creativity for high school Maths students in our country In practice, on the basis of understanding the reality of teaching and learning Plane Geometry to develop creative competency in some specialized high schools, the thesis has proposed some measures to teach Plane Geometry in such way for students in Mathematics major; Illustrated teaching Plane Geometry in the direction of creativity development for students through examples associated with Plane Geometry in gifted high schools; Conducted pedagogical experiments to initially test the feasibility of some measures Issues of protection - The opportunity and necessity of teaching Plane Geometry towards developing creative competency of Mathematically gifted high school students - Feasibility and effectiveness of the proposed pedagogical measures in teaching Plane Geometry towards developing creative competency of Mathematically gifted high school students Structure of the thesis In addition to the introduction, conclusion, appendices and list of references, the thesis consists of chapters: Chapter Theoretical and practical foundation Chapter Some methods of teaching Plane Geometry to develop creative competency of Mathematically gifted high school students Chapter Pedagogical experiments CHAPTER THEORETICAL AND PRACTICAL FOUNDATION 1.1 Competency-Based Education Competency-Based Education (CBE) is a specific model of outcome-oriented education There is a close coordination between methods of teaching and assessing students' learning outcomes through the demonstration of their knowledge, attitudes, values, skills and behaviors towards the requirements given at each level” Teaching from the perspective of competency development is a process in which learners focus on activating intellectual activities, training problem solving skills as well as practical situations, enhancing group learning, renewing the teacher-student relationship towards cooperation In the document "Teaching Mathematics at lower secondary tertiary towards developing students’ competencies" by author Pham Duc Quang (2018), the basic characteristics of teaching towards developing students’ competencies include: Teaching takes students' learning as the center; Flexible and active in approaching and forming competencies; Education meeting the requirements of practice, vocational guidance and development; Clearly identifying the necessary competencies of in learners These are considered as criterias for evaluating educational results Applying the above perspectives to teaching Plane Geometry toward learners’ creative competency development, teachers can approach and implement teaching in the following directions: First, form and train a number of skills in students towards the required competency, that is, to equip learners with tools in learning Geometry to achieve the purpose of Competency- based education Second, make students' learning more active by using open-ended questions, exercises, and Geometry topics so that students have the opportunity to explore, discover and practice Third, organize a variety of activities to learn, experience, explore and be entertained through Mathematics Geometry learning in order to create a teaching environment associated with real contexts, creating favorable conditions for learning and sharing, exchange, debate to nurture students' passion for the subject; Organize Plane Geometry teaching with the support of Information Technology to suit the trend of development, career guidance and meets the practical requirements 1.2 Teaching towards developing creative competency 1.2.1 The necessity of teaching towards developing creative competency Beghetto's research suggests that creativity and innovation in education is not merely an opportunity, but a necessity First, the emergence of new trends will entail drastic changes in learning strategies and pedagogical approaches (Redecker, 2008) Teachers must attract students' attention and attention in a new way, that is, to develop innovative approaches (Simplicio, 2000) Second, current and future generations of students are growing up surrounded by video games, smartphones and other digital media The ubiquity of these technologies offers a new understanding of communication, information retrieval, and learning The gap between the school environment and the digital environment of the family and society affects the expectations of students and their parents (Pedró, 2006), which raises the awareness of inadequacies of existing educational curricula with the practical demands (Selinger, Stewart-Weeks, Wynn, & Cevenini, 2008) Third, nowadays, creativity is considered a new form of knowledge generation (Craft, 2005) For the aforementioned reasons, teaching towards developing learners’ creative competency is an indispensable requirement of current and future education 1.2.2 The role of teachers in teaching towards developing creative competency From the characteristics of Competency-based Education, it can be seen that teaching towards developing creative competency requires highly active activities in learning Therefore the teacher will play the role of a designer, suggester, and supporter while learners are empowered to take control of their learning process 1.2.3 Teachers need to be supported and facilitated to apply teaching towards developing creative competency Teachers’ role is of utmost importance in teaching towards creative competency development They can either contribute to or inhibit the development of students' creativity First and foremost, teachers must be assisted to remove misconceptions about creativity, understand this trait, and find and nurture it (Runco, 1999; Sharp, 2004) Teachers need to be supported, trained or self-trained in creativity In other words, they must experience and be trained to acquire creative skills, techniques and methods Teachers need support in developing career skills (Esquivel, 1995; Ellis & Barr, 2008) Teachers need to clarify to students that innovation is always welcomed as well as acknowledge the equality between originality and value of creative products (Beghetto, 2007; Runco, 2007) Teaching towards learners’ creative competency development, teachers must be creative practitioners and need time outside work to experiment and explore while practicing innovation and creativity (Craft, 2005) 1.3 Some characteristics of gifted high school students and their creative potential Synthesizing a number of domestic and international studies, the traits of Mathematically gifted students can be identified as: Have a good memory; Care and appreciate the superiority of solutions; Pay attention to the reason and the effect of an action; Solve problems intuitively; Able to reverse the steps in the thinking process; Able to organize, arrange data and experience to discover new situations, new relationships; Able to improvise with scientific equipment and mathematical methods; Flexible in problem solving The above characteristics show that high school students specializing in Mathematics possess all the conditions as well as psychological and intellectual potentials to form and develop creative competency 1.4 Some components of creative competency and manifestations of creativity of Mathematically gifted students in learning Plane Geometry 1.4.1 Some components of creativity Inheriting the views on creativity of Vygotsky (2004), Davie (2000), Keegan (1996), Guilford (1973), Amabile (2012) and other scientists, through determining the components of students’ creative competency in learning activities and the specific characteristics of students specializing in Mathematics, we deem that the creative competency of Mathematics students in learning Planar geometry includes the following components: - Expertise, interdisciplinary knowledge and practical experience (Knowledge); - Imagination and Intuition; - Creative and Critical Thinking; - Creative Inspiration Figure Diagram of some components of creative competency Among these elements, knowledge can be considered the foundation, the "material" for imagination and intuition Next, “Imagination is more important than knowledge For knowledge is limited to all we now know and understand, while imagination embraces the entire world, ” - Albert Einstein Marx - Lenin said that intuition is the ability to acquire knowledge without recourse to conscious reasoning Intuition is the result of intellectual and knowledge repression, leading to an "explosion" Intuition is the product of talent and passion, perseverance and serious scientific work Thus, imagination and intuition are indispensable "catalysts" of creative competency In the creative process, to get the creative product, divergent thinking is not enough Convergent thinking helps us organize the details of an idea to make it a solution At this point, critical thinking is essential to reduce risks and find viable solutions Therefore, creative thinking and critical thinking are two unifying and essential sides to creative competency, like "two sides of a coin", inseparable Curiosity, thirst for discovery, passion, belief, creative inspiration are emotional states associated with creativity These are preconditions, "fire starters" that serve to "spark" the process of creativity Accordingly, the basic components of creative competence include: Professional knowledge, interdisciplinary and practical experience (Knowledge); Imagination and Intuition; Creative and Critical Thinking; Creative Emotion These elements converge together to help people become creative, spreading the wings of creativity to fly high (KITE) Figure Diagram of the relationship between the components of creative competency 1.4.2 Manifestations of creativity of Mathematically gifted students in learning Plane Geometry William Benn (2008) said that people with creative energy have the following characteristics: Always looking for more effective ways of doing things; Dare to break standards and limits to find something new; Stay curious by asking questions; There are many new and unique ideas; Dare to do, dare to take responsibility According to author Ton Than (1995), the student's manifestations of creativity in Maths are being able to look at the problem from a new perspective, many different angles and many different solutions; know how to hypothesize when having to explain a problem; know how to propose different solutions when dealing with a situation; feeling dissatisfied with the already existing solutions; not mechanically applying known rules and methods to new situations Thus, it can be seen that high school students specializing in Mathematics are students with intelligence, excellent results in Maths, and relatively comprehensive knowledge of disciplines and interdisciplinary subjects Most students possess all these expressions of creative ability in the process of learning Maths: eager to learn, passionate about Mathematics, curious, imaginative, flexible in thinking, able to find multiple solutions, able to generalize the problem, can propose new problems 1.4.3 Manifestations of creative ability of students majoring in Mathematics in learning Plane Geometry (1) Expertise, interdisciplinary knowledge and practical experience - Solid knowledge about the subject, with in-depth understanding of a number of issues - Relatively complete interdisciplinary knowledge Know the relationship between knowledge between related subjects, between raw knowledge and real life (2) Imagination and Intuition - Ability to observe and record information quickly Have a rich imagination Able to visualize static elements into dynamic ones and vice versa - Ability to express Geometry quickly and accurately, draw shapes with different situations and perspectives Know how to draw more shapes in multiple ways to exploit beneficial properties for problem solving - Have good Geometry intuition, often make correct predictions about the relationship and Geometry properties of objects Accept ambiguity (3) Creative thinking, critical thinking - Able to detect diverse relationships between objects, Geometry elements Able to isolate the objects needed to study or “embed” them into a larger, known problem Discover new elements from familiar things 11 aforementioned 70 lessons, in the grade 10 advanced Maths program, there are also 22 compulsory thematic lessons on Geometry: Calculation, constructions, proof, geometric locus, extremum problems More about displacement and similarity on the plane Introduction to inversion and its applications 1.6.2 Advanced Maths study material Advanced Geometry study material published by Vietnam Education Publishing House (2010) is used by most high schools for the gifted as the main reference book for students specializing in Mathematics This is a carefully compiled book series, including workbooks It has in-depth knowledge content, a rich system of exercises, many of which are selected from national and international excellent student contests Through the reality of teaching in high schools for the gifted, and consulting with teachers and students, we found that this material is of great value for students who specialize in Mathematics The book series basically meets the needs of accelerated students passionate about Geometry However, for most students, this is a difficult material, both in terms of theory and exercises The presentation is extremely "academic", with very little theoretical content and exercises related to practice Only a minority of students are able to understand and apply the lessons immediately According to a survey into the view of Maths students in some specialized high schools indicated that more than half of the students suggested: Analyze further into ways to find the solution; Presenting multiple ways to approach and solve problems; Systematizing exercises from basic to advanced; Instructing ways to imagine Geometry content so it can be easily understood, remembered and applied 1.6.3 Reality of teaching Whilst most teachers have a correct perception of creativity and innovation, others think that creative energy is innate and cannot be learned Teachers have yet to focus on instructing students about creative skills, which is important to develop creative competency for students Lectures and conversations are still common since the amount of knowledge in each topic requires a lot of time A big obstacle when advanced teaching is that many students not meet the subject requirements due to the difficulty of the knowledge (despite being in Maths major) Teachers must group students to assign tasks and the difference among these groups is enormous This, in turn, proves time-consuming for teachers to help each group According to senior teachers, the causes of the above problems are mainly: First, students in Maths classes are often required to solve many exercises in a short period, 12 so they rarely have the condition to deeply analyze or ponder to discover the beauty of Geometry and develop creative competency through the subject Second, few teachers in secondary and high schools favour teaching Geometry since teaching Algebra and Calculus appears easier Third, with the exception of students selected for Excellent Student Contests, other students spend little time studying Plane Geometry as this content appeared quite rarely with a low level of difficulty in the national high school exams these recent years Fourth, the higher level students reach, the clearer the link between Algebra and Geometry through coordination becomes, so they deem it unnecessary to delve deeper into pure Plane Geometry Fifth, Geometry problems often not have algorithms to follow like its counterparts Instead, each problem is a unique experience for students This also causes difficulties for students and even teachers to convey the content of the lesson Thus, in high schools for the gifted, basically only students in math teams learn in-depth about Plane Geometry and their main purpose is to participate in Excellent Student Contests This has failed to create interest in learning Geometry and developing qualities and abilities for students, especially creative energy as its inherent potential 1.7 Creative methods and techniques can be applied in teaching Plane Geometry 1.7.1 SCAMPER technique The seven techniques of the SCAMPER method include: (1) Substitute, (2) Combine, (3) Adapt, (4) Modify or Magnify , (5) Purpose, (6) Eliminate, (7) Rearrange or Reverse Applied to teaching Plane Geometry, teachers can guide students to use questions and suggestions according to SCAMPER to find answers, propose ideas or find new results related to solving the problem 1.7.2 Creative principle suggested by Altshuller Stemming from the idea of building a theory that helps any ordinary person to create inventions, he researched and proposed a system of 40 basic creative principles, mainly applied in science and technology Some of Altshuller's principles can be applied in teaching Plane Geometry: (1) "Segmentation" principle; (2) “Do It in Reverse” principle; (3) "Partial or Excessive Action" principle; (4) “Mediator” principle 1.7.3 Teaching in the direction of STEM education STEM is an abbreviation of Science, Technology, Engineering and Mathematics Discussing the relationship between STEM education and students' 13 creative competency, James Ogunleye (2018) said: The focus of STEM education is creativity, a material for innovation Creativity and innovation in STEM is basically supporting and encouraging students to not only know or understand "hard science", but also develop "the ability to look at situations from new and creative perspectives; the ability to express concepts and information clearly" Applying in teaching Plane Geometry, teachers can choose topics and teaching content associated with practice, including using elements of science, engineering and technology to solve learning tasks In the process of teaching in the direction of STEM education, students are always encouraged and given opportunities to create: from approaching, proposing ideas to choosing options, materials, completing products and improving products 1.7.4 Teaching Geometry in English According to Behzad Ghonsooly (2012), various recent studies have focused on and discovered important associations between bilingualism and creativity On the one hand, bilingualism enhances cognitive functions such as planning, cognitive flexibility, and working memory On the other hand, creativity is highly dependent on the extent of these functions Therefore, the more cognitive function improves, the greater the level of creativity will be achieved Studies also show that bilingual education significantly increases the four components of creative thinking, including: flexibility, proficiency, originality and meticulousness Teaching Geometry in English in particular and teaching Maths in English in general is a specific case of bilingual teaching Therefore, it has positive effects on students' creative competency CONCLUSION OF CHAPTER Coming from the reality of education, we are carrying out a fundamental and comprehensive renovation of education and training with the goal of developing the quality and ability of learners, meeting the requirements of human resources in the new era Hence, teaching towards developing learners’ creative competency is an urgent requirement for schools Among the competencies to be achieved by high school students, many countries worldwide, including Vietnam, believe that creative energy is one of the core competencies that students need to acquire In the view of most scientists, everyone has creative potential, that is, the ability to create something new that is unique and valuable, first and foremost, to themselves Creative is learned 14 and this confirms the role of teachers in education, the role of schools and society in creating an environment that encourages creativity Chapter of the thesis summarizes, inherits the views of some researchers on: Competency-Based Education, teaching towards developing creative competency, Some components of creative competency and manifestations of creativity of Mathematically gifted students in learning Plane Geometry From these, we see the opportunity to implement teaching towards developing creative competency for students Chapter also studies the current situation of teaching Plane Geometry towards developing creative competency for Mathematics students in specialized high schools in Vietnam to see the mismatch between the potential and the actual situation; researches theoretical and practical foundation to propose pedagogical measures in Chapter Some components of creative competency: Expertise, interdisciplinary knowledge and practical experience (Knowledge); Imagination and Intuition; Creative and Critical Thinking; Creative Inspiration On the basis of the components of creative competency, the manifestations of creative competency of students in learning Plane Geometry correspond to those elements, the thesis also points out the opportunity to implement teaching Plane Geometry towards developing creative competence for high school Mathematically gifted students CHAPTER SOME TEACHING MEASURES GEOLOGY OF CREATIVE CAPACITY DEVELOPMENT FOR HIGH SCHOOL MATHEMATICS STUDENTS 2.1 Orientation for construction and implementation of measures The proposed measures should aim to help teachers carry out the teaching of Plane Geometry towards creative competency development for students; Each measure should be implemented through some corresponding activities of students and teachers; The proposed measure must be feasible, suitable to the subject curricula and physical conditions of the high schools for the gifted 15 2.2 Some methods of teaching Plane Geometry towards developing creative competence for high school Mathematically gifted students 2.2.1 The first group of measures: Forming and training students skills to find new ideas and new solutions in learning Geometry The purpose of the group of measures The group of measures proposes application of some creative techniques of Altshuller, Polya, SCAMPER method to teaching Geometry in order to form and train students skills to find new ideas and new solutions; help students be creative in approaching and solving problems, can propose new ideas, problems and methods Steps to implement the group of measures The first step: Select appropriate techniques and methods that can be applied in teaching Geometry The second step: For each creative technique and method selected, conduct research on the content and some applications of that procedure in engineering and life sciences The third step: Find more illustrative examples for that creative technique and method The fourth step: Applying that technique and method in teaching plane geometry - Measure 1.1: Apply the "Segmentation" principle - Measure 1.2: Apply the “Do It in Reverse” principle - Measure 1.3: Apply the "Partial or Excessive Action" principle - Measure 1.4: Apply the “Mediator” principle - Measure 1.5: Apply the SCAMPER technique 2.2.2 The second group of measures: Using open-ended questions, exercises, and teaching topics for students to have the opportunity to explore, discover and learn The purpose of the group of measures This group of measures is designed to support teachers in selecting, building and using open situations in teaching to develop students' curiosity and imagination; create opportunities for students to approach problems from different perspectives to propose different ideas, to solve problems in different ways, to continue to expand and develop problems, to propose new solutions, new ideas, new problems Steps to implement the group of measures Teachers design and select questions, exercises and topics with diverse relationships, high applicability, and make natural and suggestive tasks Encourage students to approach, propose ideas and solve problems in various different ways 16 With each approach to problem solving, teachers need to organize for students to analyze and specify reasons and ways of thinking The teacher summarizes, allows students to comment and evaluate the advantages of each implemented option and encourages them to continue to explore and discover related issues - Measure 2.1: Organize teaching in the direction of STEM education - Measure 2.2: Use exercises with various different solutions - Measure 2.3: Use exercises that students can expand, generalize, and propose new problems 2.2.3 The third group of measures: Teaching plane geometry with the support of animation softwares; organizing a variety of learning, experiencing, discovering and entertaining Maths activities to nurture students' passion for the subject The purpose of the group of measures Teaching Plane Geometry with the support of animation software for students to have a visual observation, to support the development of their imagination, to provide them more tools in learning, discovery, and learning Steps to implement the group of measures Organize teaching Geometry with the support of computers, smart devices, using animation softwares such as GeoGebra, Sketchpad, Cabri Instruct students on how to construct shapes, predict Geometry properties before verifying with drawing software Organize games related to Mathematics, students propose techniques and strategies to get high scores and win Organize visits, model studies with Mathematical applications in real life within the scope of their knowledge, thereby proposing ideas to improve products or propose new applications related to Mathematical knowledge learned Organize Math club activities with lively and close-to-life topics, including challenges that require thinking and acting, thereby developing independent and group working skills - Measure 3.1: Teaching Plane Geometry with the support of animation softwares - Measure 3.2: Organizing a variety of learning, experiencing, discovering and entertaining Maths activities to nurture students' passion for the subject: Teaching Geometry in English; Organize for students to research, write and discuss topics on Plane Geometry; Guide students to participate in domestic and international forums on Plane Geometry; Organize club activities to experience games, challenges, to discover and be creative about Plane Geometry 17 CONCLUSION CHAPTER On the foundation of theoretical and practical research, Chapter of the thesis proposes three groups of measures to teach Plane Geometry towards developing creative competency of high school Mathematically gifted students The first group of measures: Forming and training students skills to find new ideas and new solutions in learning Geometry This group of measures is designed to help students answer the question: How to be creative? How to solve the problem in a creative way? In other words, this group of measures aims to equip students with "tools" to be able to create They affect students' creative thinking and critical thinking - an important component of creative competency Besides, students' knowledge, imagination and intuition, and creative inspiration also have the opportunity to be positively affected The main content of this group is based on the creative techniques of Altshuller, Polya; SCAMPER creative technique to apply to teaching Plane Geometry This is of utmost necessity so students develop various approaches, thoughts and solutions when faced with a problem, and form and practice creativity The second group of measures: Using open-ended teaching questions, exercises, and topics so that students have the opportunity to explore, discover and practice Openness is understood in the sense of being open in the way of asking, raising the problem, open in the choice of approach, the variety of ways to solve the problem, and open in developing the problem, applying creativity in different situations This group of measures aims to influence students' imagination, intuition, emotions and thinking Through this group of measures, teachers have made students' learning more active, affecting students' imagination, intuition, emotions and thinking, while students can practice problem solving in many different ways, expanding, developing and generalizing the problem, proposing new problems and applying knowledge of many subjects to solve specific problems in practice The third group of measures: Teaching Plane Geometry with the support of animation softwares; organizing a variety of learning, experiencing, discovering and entertaining Maths activities to nurture students' passion for the subject This group of measures is implemented by teachers in order to affect creative inspiration, imagination and thinking for students Stemming from the fact that the specialized program is quite heavy on knowledge for most students, many students feel tired and less passionate about the subject The flexible combination of Math education activities such as: Teaching Geometry in English; Organize for students to research, write and discuss topics on Plane Geometry; Guide students to participate in domestic and international forums on Plane Geometry; Organize club activities to experience games, challenges, to discover and be creative about Plane Geometry to help students reduce stress, find joy and passion in learning 18 CHAPTER PEDAGOGICAL EXPERIMENTS 3.1 Purpose and mission of pedagogical experiments 3.1.1 The purpose of experiments Conducting experiments to test the feasibility and effectiveness of some pedagogical measures proposed in the thesis, at the same time illustrating the correctness of the scientific hypothesis 3.1.2 Experimental tasks Discuss with teachers conducting experiments to clarify the purpose of pedagogical experiments, how to implement the measures proposed by the thesis; Class observation; Prepare teaching content and methods; Organize educational activities; Survey, test, evaluate; Process data and qualitative signs; Analyze the results and draw conclusions 3.2 Conduct pedagogical experiments 3.2.1 Process of pedagogical experiments Plan; Design experiment; Discuss with teachers and students about experimental purposes; Conduct model teaching; Carry out experimental teaching at selected classes; Observe the class; Interview students and teachers; Have students take a written test, question-and-answer or multiple-choice and then analyze the results 3.2.2 Sampling Experimental subjects: 73 students including: 35 students of grade 10 Mathematics major, Hung Vuong High School for the Gifted - Phu Tho; 38 students of class 10A (Mathematics major), Chu Van An high school - Lang Son Each class is divided into 02 smaller classes at random, each subclass is divided into 03 groups Teachers participating in teaching experiments: Pham Thi Thu Hien - Math group, Hung Vuong High School for the Gifted - Phu Tho; Bui Van Ngoc - Math Group, Chu Van An High School for the Gifted - Lang Son 3.2.3.Conduct pedagogical experiments - Experimental exploration: from September 2016 to May 2017 - Official experiment: from September 2017 to May 2018 3.2.4 Content of pedagogical experimental Due to the limited scope of the thesis and limited time, we only conducted experiments on the organization of teaching several Plane Geometry content for Grade 10 Mathematics specializing classes at two schools with the following 04 measures: 19 - Content 1: Experiment with measures 1.2: Applying the "Do It in Reverse" principle in teaching the lesson Practice: Vectors and vector operations - Content 2: Experimental measures 2.1 Organizing teaching in the direction of STEM education in the lesson Ellipse - Content 3: Experimental measures 2.3 Using exercises that students can expand, generalize and propose new problems in the content of The barycenter of the point system - Content 4: Experimental measures 3.2: Organizing a variety of learning, experiencing, discovering and entertaining Maths activities to nurture students' passion for the subject 3.2.5 Measures to evaluate experimental results 3.2.5.1 Qualitative assessment Qualitative assessment of students' manifestation of creative abilities through: - Expression in the learning process - Expression in student's work 3.2.5.2 Quantitative assessment Using datas on the manifestation of creative competency of students before and after experimental classes, especially for students who are studied in cases, to initially quantitatively assess the effectiveness of proposed measures 3.3 Evaluation of experimental results 3.3.1 Exploratory experiments Through exploratory experiments, we found that it is necessary to adjust and supplement some of the following contents: When dividing groups of activities, it is necessary to pay attention to the uniformity of students' academic performance in groups, to avoid low self-esteem for students It is quite time-consuming to implement the content and teaching intentions of the teacher, especially the content to be approached in different ways Experiencing math games is very attractive to students because they are both entertaining and challenging However, this activity needs to be done outside of regular school time and with the permission of the school since currently, many schools not allow students to bring cell phones into the classroom area 3.3.2 Formal experiments Teachers apply teaching methods towards developing creative energy for students as the thesis has proposed based on the lesson plans and teaching situations 20 that we have designed During class hours, students are encouraged to engage in activities such as: clearly defining the problem to be solved; anticipating, proposing, interpreting and developing ideas, making and implementing plans to solve problems; proactively presenting implementation results; learning to evaluate and self-evaluate solutions There is a significant increase in the number of students solving problems in diverse ways, including unique solutions; increase in the number of students who are able to generalize the problem Analyze the results of the case study Five students were observed, monitored and statisticized on the manifestation of creative competency during the teaching process Most of the children have more positive expressions after doing experiments The most obvious manifestations are: The number of ideas increases and learning becomes exciting These are signs that the pedagogical effects are significant CONCLUSION OF CHAPTER To test the feasibility and effectiveness of the proposed measures in chapter 2, the author conducted exploratory experiments, organized sample teaching and formal experiments in specialized Maths classes of 02 high schools for the gifted in the provinces of Phu Tho and Lang Son The sample teaching is done before the official experiment so that the teacher can observe the class, then discuss and agree on how to proceed The experimental teachers have performed well in the lessons as expected Through the process of implementing experiments; By observing, counting and from the opinions of teachers and students, we draw the following conclusions: Firstly, teachers and students are excited when conducting experiments, they hardly feel pressure in learning because they are often encouraged and motivated The ideas proposed by students are respected and recognized Secondly, schools have enough conditions to organize educational activities that the thesis has proposed Third, the quality and capacity of the teaching staff in the private schools meet the requirements for the implementation of the topic relatively well Experimental teachers have successfully completed the lessons as expected Students caught up quickly with the method of inquiry, discovery and active participation Their teamwork skills have also improved significantly Fourth, the measures proposed by the thesis are necessary, meaningful in theory and practice In the current context, education and training need to clearly define and balance the requirements of knowledge with the goals of students’ competency 21 development.Focusing solely on the amount of knowledge can come at the expense of the opportunity to develop competencies Fifth, due to the limitations of the thesis scope and time, we only conducted experiments with four measures out of 10 proposed measures as the representative of the three groups of measures mentioned above Each group of measures has been tested at least three times, from exploratory experiment, sample teaching to formal experiment The results show that the measures proposed by the thesis are initially feasible, can be deployed in specialized high schools and used to foster the Maths team, and students interested in Mathematics in other high schools Sixth, if the teachers of specialized high schools are well trained on teaching towards creative competence development, teachers’ pressure on achievement and students pressure on exams are reduced, then teaching towards developing creative competency will become more feasible The results of pedagogical experiments also show that students of experimental classes have shown progress in creative competence The appropriate implementation of the proposed measures will contribute to the formation, training and development of creative competency for students Besides, there are some issues that need attention such as: The implementation of teaching Plane Geometry towards creative competency development for students needs more time than the traditional teaching method Students' learning speed is different, so teachers need appropriate support Creating confidence in students about their creative potential is not easy and time-consuming Teachers must be creative people and always encourage creativity For classes that encourage creativity, students tend not to comply well with the school's regulations, such as: freedom, noisy, sometimes inattentive It is necessary to pay more attention to the assessment of the learning process and attitudes of students instead of only periodically evaluating them with grades CONCLUSIONS AND RECOMMENDATIONS Conclusions Through the process of researching for the thesis, we have obtained the following main results:In theory, the thesis has summarized a number of issues related to creative competency, in order for it to be applied in teaching 10th grade Plane Geometry in high schools for gifted students; Clarified the opportunity and necessity of teaching Plane Geometry towards developing creativity for high school Maths students in our country In practice, on the basis of understanding the reality of teaching and learning Plane Geometry to develop creative competency in some 22 specialized high schools, the thesis has proposed some measures to teach Plane Geometry in such way for students in Mathematics major; Illustrated teaching Plane Geometry in the direction of creativity development for students through examples associated with Plane Geometry in gifted high schools; Conducted pedagogical experiments to initially test the feasibility of some measures Chapter of the thesis summarizes, inherits the views of some researchers on: Competency-Based Education, teaching towards developing creative competency, Some components of creative competency and manifestations of creativity of Mathematically gifted students in learning Plane Geometry Thereby, teaching towards developing creative competency needs a pedagogical method in which learners are the center, learning isactive, personalized and individualized; creating a friendly and equal learning environment, encouraging cooperation; arouse interest, suitable for students’ Zone of Proximal Development; Students are empowered to take control of their own learning process; attach importance to the creative process rather than the creative product; focus on the experience of the games; nurture passion, inspiration, judgment and imagination for students when participating in learning activities In the process of teaching, teachers’ role is of utmost importance in teaching towards creative competency development They can either contribute to or inhibit the development of students' creativity To carry out teaching towards creativity development for students, teachers need to have a clear understanding of creativity; receive support, be trained or self-trained on creativity; be a creative practitioner in the teaching process; build confidence about creative ability for all students; never stop experimenting, discovering, practicing innovation and creativity Through the study of the current situation of teaching Plane Geometry towards developing creative competency for Mathematics students in specialized high schools in Vietnam to see the mismatch between the potential and the actual situation Based on the components of creative energy (Expertise, interdisciplinary knowledge and practical experience (Knowledge); Imagination and Intuition; Creative and Critical Thinking; Creative Inspiration), the manifestations of creative competency of students in learning Plane Geometry correspond to those elements, the thesis also points out the opportunity to implement teaching Plane Geometry towards developing creative competence for high school Mathematically gifted students, as a basis for proposing pedagogical measures in Chapter Chapter proposes three groups of measures The first group of measures: Forming and training students skills to find new ideas and new solutions in learning 23 Geometry This group of measures aims to equip students with "tools" to be able to create They affect students' creative thinking and critical thinking - an important component of creative competency Besides, students' knowledge, imagination and intuition, and creative inspiration also have the opportunity to be positively affected The main content of this group is based on the creative techniques of Altshuller, Polya; SCAMPER creative technique to apply to teaching Plane Geometry This is of utmost necessity so students develop various approaches, thoughts and solutions when faced with a problem, and form and practice creativity The second group of measures: Using open-ended teaching questions, exercises, and topics so that students have the opportunity to explore, discover and practice Through this group of measures, teachers have made students' learning more active, affecting students' imagination, intuition, emotions and thinking, while students can practice problem solving in many different ways, expanding, developing and generalizing the problem, proposing new problems and applying knowledge of many subjects to solve specific problems in practice The third group of measures: Teaching Plane Geometry with the support of animation softwares; organizing a variety of learning, experiencing, discovering and entertaining Maths activities to nurture students' passion for the subject Today, the application of Information Technology in teaching is mandatory for students to quickly acquire knowledge, master technology, develop competencies, and meet the requirements of practice The flexible combination of Math education activities such as: Teaching Geometry in English; Organize for students to research, write and discuss topics on Plane Geometry; Guide students to participate in domestic and international forums on Plane Geometry; Organize club activities to experience games, challenges, to discover and be creative about Plane Geometry to help students reduce stress, find joy and passion in learning In chapter three, due to the limitations of the thesis scope and time, we only conducted experiments with four measures out of 10 proposed measures as the representative of the three groups of measures mentioned above Each group of measures has been tested at least three times, from exploratory experiment, sample teaching to formal experiment The results show that the measures proposed by the thesis are initially feasible, can be deployed in specialized high schools and used to foster the Maths team, and students interested in Mathematics in other high schools From the above results, it can be affirmed: The thesis has identified the basic characteristics of teaching towards developing learners’ creative competency On that 24 basis, three groups of pedagogical measures in teaching Plane Geometry towards developing creative competency for high school Mathematically gifted students have been proposed At the same time, the feasibility of some proposed measures has been initially tested Thus, the scientific hypothesis of the thesis is acceptable, the research purpose of the thesis has been achieved, the research task has been completed Recommendations In order to meet the requirements of Competency-Based Education in general and teaching towards developing creative competency for high school Mathematically gifted students in particular, we propose some recommendations as follows: With the Ministry of Education and Training: - Prescribing the basic knowledge content that students majoring in Mathematics need to achieve, on that basis, limit the range of knowledge used in exams and tests Turning other advanced or in-depth content into reference content The Excellent Student Contests questions need to be close to practice, creating opportunities and encouraging students to be creative, putting less stress on knowledge and difficulty so that more students love the subject - Organize and compile a set of official textbooks for students specializing in Mathematics, which clearly shows the link of Mathematics to life, the role of Mathematics in other sciences, enhancing its applicability and practicability Enhance guiding students' thinking methods, encourage students to be creative For high schools for the gifted: - Facilitate and encourage teachers and students to approach, research and implement teaching and learning to develop learners' competencies, especially creative competency - Reduce pressure on exams and achievements for students - Assessing not only based on the academic score but also focus on evaluating the process to clearly see the progress of each student, encouraging students to continue to strive LIST OF PUBLISHED RESEARCH WORKS OF THE AUTHOR IS RELATED TO THE CONTENT OF THE THESIS [1] Nguyen Xuan Quynh, Developing Creativity for Mathematically Gifted Students in teaching Plane Geometry at the Hung Vuong High School for Gifted Students, Phu Tho Province, Proceedings of the International Scientific Conference: “Creativity Development and Opportunities for Business and Startup Ideas”, Hanoi National University Publishing House 2017, pp 188-209 [2] Nguyen Xuan Quynh, Applying some Altshuller’s creative principles in teaching Geometry towards Developing Creative competence for High School Mathematically Gifted Students, Journal of Educational Science, Vietnam Institute of Educational Sciences, 2019, Volume 15, Issue 3, pp 43-52 [3] Nguyen Xuan Quynh, Applying some Altshuller’s creative principles: “Division”, “Inversion” and “Excessive or partial action” in teaching geometry towards developing creative competence for high school mathematically gifted students, HNUE Journal of Science Educational Sciences, 2019, Volume 64, Issue 7, pp 159-171 ... comply well with the school's regulations, such as: freedom, noisy, sometimes inattentive It is necessary to pay more attention to the assessment of the learning process and attitudes of students... learning strategies and pedagogical approaches (Redecker, 2008) Teachers must attract students' attention and attention in a new way, that is, to develop innovative approaches (Simplicio, 2000)... students, this is a difficult material, both in terms of theory and exercises The presentation is extremely "academic", with very little theoretical content and exercises related to practice Only