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MINISTRY OF EDUCATION AND TRAINING VIETNAM INSTITUTE OF EDUCATIONAL SCIENCES - - TEACHING GEOMETRY AT SECONDARY SCHOOLS IN THE DIRECTION OF APPLYING MULTIPLE INTELLIGENCE THEORY Major: Theory and methods of teaching Maths subjects Code: 9.14.01.11 SUMMARY OF DOCTOR’S THESIS IN EDUCATION HÀ NỘI - 2019 The work was completed at: Vietnam Institute of Educational Sciences Science supervisor: Assoc Prof Dr Ton Than Dr Dang Thi Thu Thuy Reviewer 1: Reviewer 2: Reviewer 3: The thesis will be defended in front of the Institute's Thesis Evaluation Council, conducted at Vietnam Institute of Educational Sciences, 101 Tran Hung Dao, Hanoi At day month year The thesis can be found at: - National Library - Library of Vietnam Institute of Educational Sciences LIST OF RESEARCH WORKS PUBLISHED RELATED TO THE THESIS OF THE AUTHOR Nguyen Trung Thanh (2014), Helping students to develop spatial imagination through teaching some geometry exercises at junior high school, Journal of Education, Ministry of Education and Training, ISSN 21896 0866 7476 , No 330- Term 2, 3/2014, p.47 Nguyen Trung Thanh (2014), Orientation of learning method for junior high school students based on MI theory through teaching geometry at the senior level, Journal of Education, ISSN 2354 0753, No 345- Term 1, November 2014, p.46 Nguyen Trung Thanh (2016), Some theoretical issues about teaching according to MI theory, Journal of Education, ISSN 2354 0753, No 378- Term 2, 3/2016, p.16 Nguyen Trung Thanh (2016), teaching according to the approach of MI theory: The concept, principles and process of organizing a lesson, Journal of Educational Science, Vietnam Institute of of Educational Sciences, ISSN 0868 - 3662, No 131, 8/2016, p.41 Nguyen Trung Thanh (2017), Training and developing logical / mathematical intelligence for students through teaching geometry at junior high schools, Journal of Educational Sciences, Vietnam Institute of Educational Sciences, ISSN 0868 - 3662, No 143, 8/2017, p.61 Nguyen Trung Thanh (2015), Some theoretical issues on Mathematics teaching in MI at SS, Proceedings of Scientific Workshop of PhD Students 2015,Volume 2, Vietnam Institute of Educational Sciences , December 2015 PREFACE The reason for choosing a topic In recent years, the application of the achievements of modern psychology to teaching mathematics has always been of interest to mathematic education researchers, including Multiple Intelligence (MI) theory of American psychologist Howard Gardner This theory holds that each person has eight forms of intelligence,including: Logical Mathematical Intelligence; Language Intelligence; Space Intelligence; Body - Movement intelligence; Musical Intelligence; Spiritual Intelligence (introvert); Communication Intelligence (extrovert); Natural intelligence Current teaching practice in schools often focuses on developing linguistic and logical / mathematical intelligence The teaching process ignores the learning strengths through other forms of intelligence such as spatial intelligence, communication intelligence, inner intelligence, natural learning, etc of students Many students would be able to learn better if they were promoted their outstanding intellectual forms in learning activities MI theory expresses the viewpoint of human education and the necessity in teaching, each type of intelligence is important and each student has more or less his or her own learning strengths Therefore, asking the school, teachers need to help, stimulate the potential and create conditions for students to learn according to their strengths in the learning process The undertakings and policies on education and training in our country set the goal "To educate the Vietnamese people to develop comprehensively and uphold the best potential and creative ability of each individual" The 8th Central Conference of the 11th Session on Comprehensive Renovation of Education and Training clearly stated the viewpoint "To strongly shift the educational process from primarily equipping knowledge to fully developing capacity and quality of learners ", and the specific goal for general education is to focus on intellectual and physical development; forming citizens' qualities and capacities; detecting and fostering talents and orienting students’ future career Improving the quality of comprehensive education, focusing on ideal education, tradition, ethics, lifestyle, foreign languages, information technology, competence and practical skills, applying knowledge into practice Develop creativity, self-study, encourage lifelong learning Ensure students with lower secondary education (grade 9) with basic general knowledge, meet the requirements of strong level classification after students graduate from junior high school Accordingly, the trend of applying MI theory to teaching innovation in general education is necessary, helping learners develop comprehensively in both quality and competency; harmony of virtue, mind, body and beauty; best promoting the potential of each individual learner; orienting students to choose suitable career in the future In fact, there have been many changes in teaching methods of teaching Math in general and teaching Geometry at SS in particular However, many teachers are still teaching in terms of explanation, presentations, applying the same way of teaching, the same content, the same exercises, the same questions to all students in the same class This teaching method leads to many students who are passive in learning, less developing their own competence and forte; outstanding intellectual forms of students also have few opportunities to be promoted Therefore, teachers must help students know how to use outstanding forms of intelligence to search, discover and solve learning problems, through which they can improve the quality of teaching in general, teaching Math in particular Stemming from the above reasons, we choose the research topic of the thesis, "Teaching Geometry at secondary schools in the direction of applying Multiple Intelligence theory" 2.Purpose of the research Proposing some methods of teaching geometry at the secondary schools in the direction of applying MI theory, contributing to improving the effectiveness of teaching Maths at the Secondary Schools (SS) Object and subject of the research - Object of research: The process of teaching mathematics at at the SS in the direction of applying MI theory - Subject of research: Methods of teaching Geometry at SS in the direction of applying MI theory Scientific hypotheses If some pedagogical measures are built and implemented appropriately in teaching Geometry at SS in the direction of applying MI theory, it can contribute to improving the quality of teaching mathematics Scope of research - The topic focuses on teaching Geometry in grades and in the direction of applying MI theory - Experiments were conducted at Secondary schools in Thanh Hoa province - Experimental period: in academic years 2015 - 2016; 2016 - 2017 Research method Focusing on using a combination of a number of methods such as: theoretical research method; practical research methods; experimental pedagogy method; case study method; professional method; Mathematical statistical method New contributions of the thesis * As for the theory: 1) The concept of teaching Geometry at SS in the direction of applying MI theory 2) Method of teaching geometry at SS in the direction of applying MI theory 3) Some methods of teaching Geometry at SS in the direction of applying MI theory * As for the practice: The thesis can be used as a reference for Math teachers or students of Mathematics pedagogy Thesis defensive points 1) Some theoretical and practical issues of teaching Geometry at SS in the direction of applying MI theory 2) The feasibility and effectiveness of some geometric teaching methods at SS in the direction of applying MI theory The structure of the thesis In addition to the Introduction, Conclusions, Recommendations and Recommendations, List of tables and List of references, the thesis consists of three chapters CHAPTER 1: RATIONALE AND PRACTICE 1.1 Overview of research situation in the field of the topic 1.1.1 Some general issues about Multiple Intelligence 1.1.1.1 Terminology related to intellect In Vietnamese some terms such as wisdom, cleverness and intelligence are often used to refer to the ability of human thinking and understanding However, However, according to the psychological approach, these terms, which have their own nuances, are used in certain contexts These terms have similarities but they are not homogeneous, they are all related to mental activity but they are defined in different manifestations Howard Gardner, an American psychologist, took advantage of advances in medicine, based on an analysis of the ability of the human nervous system, initially to identify seven distinct types of intelligence: Logical Mathematical Intelligence; Language Intelligence; Space Intelligence; Body - Movement intelligence; Musical Intelligence; Spiritual Intelligence (introvert); Communication Intelligence (extrovert) In 1999, he announced two more types of intelligence: natural intelligence, survival intelligence However, he still does not have enough evidence to conclude that survival intelligence is a separate form of intelligence 1.1.1.3 Some basic characteristics of MI theory MI theory has some basic characteristics as following: 1) Differences: Howard Gardner argues that each person possesses eight forms of intelligence and these forms of intelligence are not the same combination, at different degrees in each person 2) Practicality: Howard Gardner considers that intelligence is the ability of solving problems in the reality of certain individuals, also the ability of producing or creating effective products suitable for social needs 3) Inspiration: No matter how much the individual possesses forms of intelligence, he or she can discover, train and develop it The level of development of personal intelligence is high or low depending on the pedagogical influence of teachers 4) Integration: When solving a problem, not only one or two types of intelligence are based but many different types of intelligence must be combined 1.1.2 Research situation of teaching in the direction of applying MI theory in the world and in Vietnam The MI theory was published (1983) Until now, it has been studied and applied in teaching by scientists in the world and in Vietnam In the world, there are a number of research works on teaching in the direction of applying MI theory, typically: 1) The work "Multiple Intelligence in the classroom" by Thomas Armstrong (1994a, 1994b, 2000), this work focuses on the curriculum, learning environment, learning strategies, ways of managing, evaluating and designing teaching plans for Multiple Intelligence; 2) Lirde Campbell's authors, Bruce Campbell & Dee Dickinson, have been studying "Teaching and learning according to the Multiple Intelligence theory" This work, the authors point out that the traditional education method only takes care of linguistic and logical / mathematical intelligence, the six types of non-traditional intelligence are often overlooked However, if teaching can develop according to multiple intelligence, it will promote the students' ability of learning; create a less passive teaching environment, in which each student will have different talents and always have a suitable place to develop In order to implement teaching according to the theory of Multiple Intelligence, teachers base on the actual outstanding intellectual forms of students manifested in the class from which to divide the group into corresponding groups; However, if teaching develops in the direction of multi-intellectual theory, it will increase the students' ability to succeed; create a less passive teaching environment, in which each student with different talents will always be created favorable conditions for development In order to implement teaching in the direction of MI theory, teachers base on the actual outstanding intellectual forms of students manifested in the class, from which the teachers divide the class into corresponding groups; 3) Regarding teaching mathematics in the direction of applying MI theory, there have been some works in the world such as: Mark Wahl (1997) "Math for everyone": Teaching mathematics in seven types of intelligence; Hope Martin (1999), MI and Standards - Basic Mathematics; The results of Mark Wahl's study not explicitly explain the teaching of geometry according to the theory of MI But in terms of inner meaning, we can understand how to create favorable conditions for the intellectual forms to be promoted in geometric learning activities such as: students who are lack of calculation ability (lack of logical / mathematical intelligence); lack of vision image and visual capacity (spatial intelligence); excel in language and communication (linguistic intelligence and communication intelligence); are instructed by teachers to use language to read, write documents, exchange and discuss with their friends and teacher on Geometry object Similarly, students who excel in logic / math should create conditions for them to analyze, compare, synthesize, infer and prove; Students who excel in spatial intelligence are allowed to promote their competence in recognizing and observing geometric characteristics, reading and understanding maps and recognizing images from different positions; creating two-dimensional or three-dimensional symbols, drawing homogeneous shapes, drawing symmetrical shapes; 1.1.2.2 Research in Vietnam With the characteristics of teaching in Vietnam nowadays, there have also been theses, dissertations and articles relating to the application of MI theory in teaching However, these studies have not clarified the theoretical basis, practical basis and feasibility of teaching mathematics in general and geometry teaching in the direction of applying MI theory in particular Therefore, the study of Geometry teaching at SS in the direction of applying MI theory is extremely necessary 1.1.2.3 Thesis issues to be studied The thesis studies some specific contents as following: - Research the theoretical basis of teaching Mathematics at SS in general and Teaching Geometry at SS in particular in the direction of applying MI theory In which, focusing on clarifying how to implement geometry teaching at SS in the direction of applying MI theory - Research the situation of geometric teaching at SS in the direction of applying MI theory - Research and propose some geometric teaching methods at SS in the direction of applying MI theory 1.2 Innovating method of teaching mathematics at SS in our country nowadays One of the highlights of comprehensive education reform in our country is the innovation of teaching method from focusing on content and knowledge to the approach of developing learners' competencies, which means changing from teaching what students have to know to guiding and orienting what students should know and in different situations and contexts This approach also requires students to master basic knowledge and skills but also focuses on the requirements of applying knowledge and skills to practice, solves the real situations in schooling and life; The quality and result of activities also depend heavily on the learners' interests, beliefs, morals, etc The fundamental innovation in this approach will dominate and require the innovation in teaching method towards the development of students' competence and quality ; The fundamental innovation in this approach will dominate and obligate to renovate teaching methods towards developing students' competences and qualities; develop the key qualities and common competences that every student needs, and develop the qualities and competences of each student; focus on how to teach and learn The innovation of teaching methods of mathematics at SS in the direction of capacity development shows that the study and application of MI theory in teaching mathematics in high schools in our country are completely appropriate and meet the requirements of renovating the teaching methods 1.3 Some geometric teaching issues at SS in the direction of applying MI theory 1.3.1 Characteristics of teaching Geometry at Secondary Schools Geometry as a subject of Math is highly abstract and universal practical, meaning that mathematics has more and more applications in life The goal of teaching geometry at secondary schools contributes to the formation and development of students the main qualities specified in the overall general education program such as: Self-study, disciplined, hard-working, diligent, persistent, proactive, flexible and creative; Common capacities include: self-reliance and self-study capacity, communication and cooperation capacity, problem-solving and creative capacity; specific capacities such as: calculation capacity, linguistic capacity, computer science capacity In teaching geometry, logical / mathematical intelligence is a form of intelligence with many outstanding advantages to form and develop However, the process of teaching geometry at the secondary school through combining mathematical education activities with experiential activities, as well as integrated teaching and differentiated teaching, the types of intelligence such as: Linguistic, spatial, communicative, personal, and natural intelligence, etc also have many opportunities for development 1.3.2 Characteristics of students at SS in learning Geometry 1.3.2.1 Psychological characteristics of students at SS in learning Psychological characteristics of junior high school students develop according to the uneven rule: Students at the same age, but their abilities and intellectual development are not the same, their ability, forte, learning method , are also different This difference creates a separate face in the psychological life of students In a classroom with 50 students, there are 50 differences All these characteristics show that the selection of geometric teaching methods at secondary schools in the direction of applying MI theory needs to create favorable conditions to attract and make students' learning activities more positive 1.3.2.2 Some manifestations of intellectual forms of secondary school students in learning Geometry MI theory has eight different intellectual forms However, in learning Geometry at SS,each type of intelligence has different characteristic manifestations For example: students who are interested in ways of learning through literacy, listening, and presentations often get linguistic intelligence ; students who are interested in learning activities that require calculation, reasoning and proof tend to own logical / mathematical intelligence, ; students who are interested in having lots of pictures, pictures, colors have spatial intelligence ; students with communicative intelligence are interested in learning in the form of teamwork, working in pairs, sharing tasks and learning experiences in groups, in class to solve tasks together; students with personal intelligence are interested in learning alone, show better results of working alone than working with others, expressing an independent sense, or strong personality; students with natural intelligence are interested in learning about nature, animals related to lessons, interested in extra-curricular lessons, visiting zoos or visiting botanical museums to search for samples figures, numbers and logic are the geometric objects in the natural environment; In fact, not every student fully manifests all eight types of intelligence, high or low level expressions depending on the teacher organizing the students' activities 1.3.3 The concept of teaching Geometry at SS in the direction of applying the theory of MI The trend of teaching research on human differences such as competence, forte, learning experience, etc is not a new trend that has existed for a long time in the world Therefore, the study of finding out the teaching method to suit the specific characteristics of students is given by many different educational scientists Teaching geometry at junior high school in the direction of applying MI theory is considered the next step and perfecting the teaching idea of focusing on the specific characteristics (differences in types of intelligence) of each student to have appropriate pedagogical effects, with which help students promote their outstanding intellectual forms in the learning process Therefore, we would like to mention the following concept in the dissertation: " Teaching geometry at SS in the direction of applying MI theory is to organize and conduct teaching activities basing on differences in students’ intellectual types to create the best learning results for each student " Geometry teaching at SS in the direction of applying MI theory is considered the following notes: - Create conditions for students to reveal outstanding intellectual forms - The expression of intellectual forms in teaching Geometry at SS is a premise to design and organize learning activities; to select content, design lessons with a series of learning activities / tasks, so that students who excel in any intellectual form are facilitated to promote the most in that intellectual form - Create a situation that students have the opportunity to use the dominant forms of intellect when they solve various problems to achieve their results better 1.3.4 Method of teaching Geometry at SS in the direction of applying the theory of Multiple Intelligence 1.3.3.1 The teaching objectives must be clearly defined Thomas Armstrong, a leading expert in studying the application of MI theory in the classroom, said that the goal of teaching in the direction of applying MI theory is to stimulate and promote the outstanding intellectual forms of each student Students 10 tutoring a weak student;) Math Web Design is a place to exchange among members of Math Club; - Teaching facilities include: round table, group exercises; board ; A4, A0 paper; v.Teaching techniques to help students promote internal intelligence -Organizing individual activities, stimulating activeness, self-discipline, selfmanagement, self-learning, self-exploration, discovery and knowledge discovery according to study materials; Learning by contract (voluntary, optional); Individual study project; Self-study assignment; Helping students develop their own learning plan for the day; studying plan for every week, every month, every year; - Teaching materials include: individualized curriculum; optional study materials; private study corner; The habit of thinking for a minute vi) Teaching techniques to help students promote the natural intelligence - Exploiting questions, examples, exercises, geometry content associated with the natural world life; - Take examples of animals and plants whose shapes have geometric applications 1.2.3.5 Use multiple ways to assess learning outcomes Any teaching goal can be taught in many different ways and every student must be assessed in those different ways Many assessment tools are also offered by many schools, such as: Record anecdotes; Audio tapes and discs; Video tape; Take a photo; Student magazine; Unofficial test; interview ; Standardized tests and assessments; Students record their learning and progress results by graphs (Student graphs); MI records; The tools and forms which are used to measure and evaluate students' learning results, must be diverse and flexible 1.4 The reality of teaching geometry at SS in the direction of applying the theory of Multiple Intelligence 1.4.1 Curriculum and textbooks of Math at SS (2002) with teaching in the direction of applying MI theory In order to have a practical basis for proposing measures as well as a basis for designing situations and lesson plans of Geometry teaching at SS in the direction of applying MI theory, it is necessary to clearly analyze the curriculum and textbooks of geometry subject at SS with teaching in the direction of applying MI theory; New curriculum geometry at SS ( 2018) has many advantages for teaching in the direction of applying MI theory 1.4.2 The reality of teaching and learning Geometry at SS in the direction of applying MI theory The surveys show that teachers initially realized that geometry teaching at SS in the direction of applying MI theory is to create opportunities for students to promote their outstanding intellectual forms; Create conditions for all students' subjects to 11 participate in learning activities; Teachers and students need to respect individual differences and needs Students are given the task of learning in accordance with their outstanding intellectual form However, some methods, organizational forms and teaching techniques can contribute to promoting the intellectual forms of students that have not been regularly paid attention to by teachers; eachers have not implemented teaching in-depth differentiation, questions and exercises give little application to real life; Teachers not organize teaching in the form of projects or groups Investigating and surveying students' opinions on geometric teaching in the direction of applying MI theory, most students said that during geometry lessons, students were rarely facilitated by teachers to promote their outstanding intellectual forms in learning activities The reason that the teachers are using teaching methods, form of teaching in each lesson is still monotonous, not suitable for many students' learning methods, not affecting the outstanding forms of intelligence, so only some students have excellent logic / mathematical intelligence to master the subject's knowledge and achieve high results, while other students with other types of intelligence will face many difficulties in learning Geometry, so their result has not been as expected CONCLUSION OF CHAPTER The research results in Chapter are the scientific basis for proposing geometric teaching methods at SS in the direction of applying MI theory -Analyzing and clarifying common problems of MI theory such as terms related to intelligence; general overview of MI theory and presentation of characteristics of MI theory; Overview of research history and issues related to the thesis topic in both domestic and foreign From the above , evaluate the results of geometric teaching at SS in the direction of applying MI theory At the same time we also explain the necessity of the thesis topic That is, through research and experimental works, many educators conclude that each subject is a certain ability in promoting students' intellectual forms if there is appropriate pedagogical impact In teaching geometry at SS there are many advantages for the development of logical / mathematical intelligence, linguistic intelligence, spatial intelligence, communication intelligence, personal intelligence, and natural intelligence learning under the influence of pedagogical measures -Analyzing the problem of renovating teaching mathematics at SS in the direction of developing capacity and applying MI theory to teaching in the current period is appropriate - Introducing the concept of teaching in the direction of applying MI theory; Method of teaching Geometry in the direction of applying MI theory Understanding and surveying the situation of teaching geometry at SS in the direction of applying MI theory is conducted by many different methods In this 12 chapter, there is an analysis and clarification of the advantages and limitations of the curriculum and textbooks at the current SS, the analysis of new points of the new mathematics program at SS, from which as a basis on designing content, situations and lesson plans of Geometry at SS in the direction of applying MI theory Through the results of the referendum, chat, interview, seminar, we found that the teachers' awareness about MI theory was still vague and general The problem of applying MI theory to teaching geometry at SS, many teachers think that there is a lack of theoretical basis and teaching documentation Therefore, in order to teach geometry at SS in the direction of using MI theory effectively, it is necessary to have an introduction document about teaching methods in the direction of applying MI theory The research results in theory and practice mentioned above will be the basis for us to conduct pedagogical measures in teaching geometry at SS in the direction of applying MI theory, which will be presented in the next chapter of the thesis CHAPTER SOME MEASURES OF TEACHING GEOMETRY AT SECONDARY SCHOOLS IN THE DIRECTION OF APPLYING MULTIPLE INTELLIGENCE THEORY 2.1 Orientation of construction and implementation of measures 2.1.1 Orientation 1: Ensuring the consistency between homogeneity and differentiation of teaching 2.1.2 Orientation 2: Ensuring to promote students' activeness, independence and creativity in learning 2.1.3 Orientation 3: Creating a teaching environment for students having conditions to discuss and exchange their ideas with friends and teachers 2.1.4 Orientation 4: Orienting the goal of comprehensive development for students, promoting outstanding intellectual forms and overcoming weaknesses in the intellectual forms which are missed by each student 2.1.5 Orientation 5: Ensure feasibility,be easy to apply for teachers and students 2.2 Proposing geometric teaching methods at SS in the direction of applying Multiple Intelligence theory 2.2.1 Measure 1: Assess students' outstanding intellectual forms 2.2.1.1 Purpose of the measure The purpose of the measure is to help teachers get the basic tools to investigate the intellectual forms, detect the outstanding intellectual forms of each student 13 2.2.1.2 Content and method of implementation In terms of teaching at present SS, there are many tools and means to measure the intellectual types of students, teachers can use methods such as using the Test Toolkit to evaluate the types of intelligence; observing; interviewing their teachers and parents; conducting questionnaire; using studying records to identify outstanding intellectual forms of students 2.2.2 Measure 2: Determining lesson objectives in the direction of applying MI theory 2.2.2.1 Purpose of the measure The purpose of the measure is to help teachers have more information on how to identify lesson objectives such as: determining the competencies that students need to achieve; content selecting content methods and forms of teaching to get the best results; identifying tasks of students; guiding students to learn and apply their knowledge and skills; determining the scope of education after each lesson 2.2.2.2 Content and method of implementation A lesson is not only based on the activities of teachers and students, using teaching methods and teaching aids , but it is essential that what each student is provided and what they can and apply after each lesson To determine the objectives of the lesson, on the basis of "knowledge", "skills", "attitude" of students after each lesson * Knowledge: To write the goal of theoretical lecture, teachers need to master levels of knowledge proposed by B J.Bloom as following: Identify, understand, apply, analyze, synthesize and evaluate * Skills: Teachers need to clearly identify what skills students gain after finishing the lesson Use verbs to describe the level of skills students need to achieve from simple to complex, know how to use verbs used to write goals about skills such as: Draw, observe, apply , know its application or use, use it correctly; calculate, know how to calculate, know how to transfer; perform, analyze; (linguistic intelligence, logical / mathematical intelligence, spatial intelligence) * Attitude: Teachers need to determine how students have the attitude after completing the lesson Phrases need to be used to describe such as: through the lesson, the formation of a virtue of carefulness, honesty, patience, a sense of responsibility, solidarity, awareness, respect, acceptance, approval, fascinating, criticizing, rejecting, cooperating, adjusting, comply, changing, consolidating, modifying, proposing, (linguistic intelligence, communication intelligence and internal intelligence) 2.2.3 Measure 3: Exploiting, selecting and designing content in the direction of applying Multiple Intelligence theory 2.2.3.1 Purpose of the measure The goal of this measure is based on the goals of the lesson that have been 14 identified, the teacher selects the content to convey, designing a system of questions and exercises that are suitable for each individual or group ( diverging questions and exercises), exploiting and adding a number of questions and exercises that are practical and interdisciplinary, with an impact on some outstanding forms of students 2.2.2.2 Content and method of implementation The content of this measure is implemented as following: (1) Exploiting and designing teaching content in the form of differentiation The first group: The general group (referring to the outstanding students in linguistic intelligence, spatial intelligence (gifted in Fine Arts), musical intellect, physical and kinetic intelligence, but on the level and speed of comprehending and solving the mathematical problem manifested at a normal or slow level) 1) Teachers exploit and design questions and exercises that only apply knowledge to simple change situations; 2) Teachers design questions, exercises, problems at a normal level, requiring a moderate level of thinking; 3) For difficult questions and exercises, teachers can break up the questions, exercises or re-set the problem, use language, visual words, explicit questions to re-do the exercises and questions, problems, shortening, reducing requirements thereby helping students to gradually realize how to solve each small part and adapt gradually to solving big, difficult and complex problems; The second group: The groups of students with outstanding logical / mathematical intelligence, in order to promote students' mathematical competence, teachers need: 1) Exploiting and using questions, exercises, and difficult problems to deal with three later levels of Bloom These are the levels that require skills of deduction, imagination and high-level association to develop the forte and mathematical ability 2) Adding requirements, change data, data to increase the difficulty level, complexity of exercises, questions, learning problems 3) Increasing the difficulty level, exploit deeply and detail problems while applying manipulations of thinking to analyze and infer the problems 2) Exploiting, supplementing and designing teaching content in the direction of practical and interdisciplinary application, having an impact on some types of intelligence such as: linguistic intelligence, logical / mathematical intelligence, nonintellect space, natural intelligence - Linguistic intelligence: Collecting stories about mathematics; historical stories about famous mathematicians, meaningful jokes to educate students who love Math; designing questions, crossword exercises; through learning content in this form helps students practice the language - Logical / mathematical intelligence: Supplementing questions and exercises with internal content of mathematics knowledge; content of interdisciplinary knowledge such as physics, chemistry, biology, art, - Spatial intelligence: Exploiting and adding questions, for example, exercises to 15 practice the skills of observation, measurement, drawing, modeling, cutting, joining, shifting and folding pictures; content containing pictures, art and fine arts; relating to architecture, construction; - Natural intelligence: Using questions, for example, exercises with content related to the nature of life; discover animals and plants; 2.2.4 Measure 4: Train students to use the dominant forms of intelligence in typical teaching situations 2.2.4.1 Purpose of the measure The purpose of this measure is to help students promote the characteristics of their outstanding intellectual forms in situations of conceptual teaching, theoretical teaching, teaching and solving math problems, thereby helping students occupy knowledge, solve Math problems in the best way 2.2.4.2 Content and method of implementation a) Training for students to use the intellectual forms in teaching concept With the purpose of training for students to effectively use the outstanding intellectual forms, while teaching the theorem of teachers can follow the "four steps" process as following: Step 1: Experiencing; Step 2: Formulating conceptual definition; Step 3: Consolidation; Step 4: Applying into practice b) Training for students to use the intellectual form in theorem teaching Teachers practice for students to use effectively outstanding forms of intelligence, when teaching theorem, teachers can follow the "four steps" process as follows: Step 1: Experiencing; Step 2: Formulating the theorem; Step 3: Consolidating theorems; Step 4: Applying c) Training for students to use the intellectual form in solving math problems Teachers can train students to develop intellectual forms in specific steps as follows: Step 1: Learning the content of the problem; Step 2: Finding a solution; Step 3: Presenting the solution; Step 4: Evaluating and research the solution Through teaching situations, including steps, each step has suggestions, leading the way to promote outstanding forms of intelligence such as: linguistic intelligence (fostering language in general, language of spoken mathematics in particular) Promote the ability to read and understand the requirements, to read and understand pictures, to use language and symbols to express and present solutions of problems, etc.Logical / mathematical intelligence (Solving problems requiring proof, students have to analyze, recall learned knowledge and reason logically, ), spatial intelligence (drawing pictures, observing drawings, drawing more auxiliary lines, auxiliary images, ), communicative intelligence (students are shared, exchanged and reflected their ideal and opinions while working in small groups, presenting their options The interaction, discussion and reflection of students help students understand the lesson, apply the knowledge they are learning, internal intelligence (independently solving exercises and answering questions, 16 teachers offer encouragement and guidance if necessary) However, it should be emphasized that in each teaching content (conceptual teaching, theoretical teaching or solving math problems) that the lesson has specific characteristics, it is only possible to describe each element (partial feature), characteristics of intellectual types that students can promote, directly related to certain learning content, so teachers should flexibly implement 2.2.5 Measure 5: Select and use teaching methods, teaching techniques and teaching facilities in the direction of applying Multiple Intelligence theory 2.2.5.1 Purpose of the measure The purpose of this measure requires teachers to select and coordinate flexibly the teaching methods, teaching techniques and various teaching methods in Math teaching, thereby teachers help students have the opportunity to learn the most with the most prominent forms of intelligence 2.2.5.2 Content and method of implementation Through the study of theory and practice of teaching in junior high schools today, there are many teaching methods, different teaching techniques that meet the requirements of teaching in the direction of applying MI such as: , corners teaching method, contract teaching method , project teaching method, topic teaching method and modern teaching techniques such as tablecloths, puzzle techniques, fish tanks, brainstorming; b) Applying the corners method and combining with the use of teaching aids While solving learning tasks at the corners, students can activate linguistic intelligence (using language to read and understand the content, express ideas, discuss with students in the same and different corners); logical / mathematical intelligence (analysis, calculation, logical thinking, reasoning, reasoning, ); spatial intelligence (observing images, paintings, colors, drawing mind maps, ); communication intelligence (collaborative learning at the corner, communicating with students in the other corners, ); you can design an angle with the following specific tasks: -The "Reading - understanding and analyzing" corner, including textbooks, reference materials, study cards The task is to ask students to read and study documents and answer the questions in the study sheet, analyzing and drawing knowledge in each lesson - The "Observing – practicing " corner includes computers, projectors, videos / clips, samples, practical items Students' task is to observe pictures, drawings, models, samples, films / videos / clips; perform measurement, drawing, folding, cutting, through these manipulations, students collect information, process information, and then discover and acquire their new knowledge - The “Applying” corner method , completing the exercises according to the learning card The task is to ask students to apply the basic knowledge of the lesson to the exercises Organizing for students to exercises to consolidate and deepen 17 knowledge; exercises to practice geometric thinking, logical thinking - The "Exploring, expanding and creating"corner method, the task of studying at this corner is to ask students to apply math knowledge into social life and other science subjects; to find ways to solve an exercise, to expand the exercise, and to recommend a new exercise The learning steps basing on the corner method Step 1: Prepare for learning with corner method - Stable organization; Arranging corner/ learning area being suitable for classroom space Do this before class to save time - Each corner has enough equipment, learning materials matching the task at each corner - Introducing corners and tasks in each corner, the maximum time to perform the task at the corners - Instructing students to study and choose the corners and how to move the corners and to avoid the situation of messy corner Step 2: Perform tasks with corner method (students work at each corner separately) - Teachers can coordinate with other teaching methods such as: problem-solving methods, small group teaching methods, etc with modern teaching techniques - Teachers should take notes: If the group activities are carried out at the corners, it is possible to use group learning techniques such as: Tablecloths; double cooperation; questioning in pairs During the learning process, teachers often observe and find out students' difficulties to guide them directly or have students use the support cards promptly Step 3: Report the results of tasks at the corners Requirements for students: The representative groups should report the results at the last corners (the gallery technique can be used to report the results), students visit the learning results of other groups; comment on reports of the other groups, state their opinions; The others listen, compare and make a respond; then make a agreement with common knowledge; finally record them Step 4: Assess/ Evaluate the learning process - Teachers focus on correcting and evaluating students' results obtained at the corners Teachers can also use different forms of assessment in the process of organizing student learning groups (self-correction, self-assessment, peer assessment, teacher feedback writing, random testing ) - Teachers must be flexible to evaluate to ensure time for the lesson b, Applying the project teaching method and combining with the use of teaching facilities Applying teaching methods and combining with the use of different teaching facilities has the advantage of stimulating learners' motivation; promoting self- 18 reliance and sense of responsibility (internal intelligence); developing skills of communication and cooperation (communication intelligence); skills of using IT such as: PowerPoint design, mind map design, computer manipulation, (spatial intelligence); developing capabilities of revealing and solving problem (logical / mathematical intelligence); developing skills of writing whole text (linguistic intelligence), developing capacity of acting and seeking knowledge in life and nature (natural intelligence) Specifically: * Planning - Select the project topic: Teachers and students propose ideas together, determine the project topic and purpose The content of the project may be in the scope of mathematics or interdisciplinary subjects, in the curriculum or in extracurricular activities - The next step is to build the outline as well as the tasks to be done; the expected product; the ways and time of implementing the project; * Project implementation - Gather information: Instruct students to use some technical devices such as computers, cameras, newspapers The computers are used to search information on the internet, use cameras for collecting images, make the content plentiful Use tools to measure length, width, height, etc (promoting linguistic, spatial, internal and communicative intelligence) -Processing information: Methods of using statistics, analysis, comparison, calculation, tabulation and charts are considered Thereby, students evaluate, comment, explain, draw conclusions (activating logical / mathematical intelligence, spatial and linguistic intelligence); - Discuss with the others: Exchange and discuss regularly, evaluate comments to share data, confirm opinions, solve problems, check progress (communication intelligence) - Exchanging, asking the teacher / instructor: Regular discussions with teachers to ensure the progress and direction of the project (communication intelligence).Teachers can guide students to implement projects, survey studying time, student's timetable During the survey, students use logical / mathematical intelligence to make statistics, calculate and analyze the data and statistics; use linguistic intelligence to make comments, assessments and comments from the existing data, from which teachers give solutions; spatial intelligence helps students make diagrams and tables, * Summary of results - Summary of results: Design project products according to the group's own way (content, structure, language and form) The final product is presented in many different forms: presentations, montages; report, or galleries (pictures, posters, real objects, models ), powerpoint, (activating language, logical / mathematical 19 intelligence, spatial intelligence) Evaluate products, including aspects such as: Content / criteria; knowledge, skills, attitudes, ; how to cooperate? what is infered after the lesson ?; What types of intelligence are developed ?, which types of intelligence should be promoted? , what need to be changed? 2.2.6 Measure 6: Assess student's progress in teaching Geometry in the direction of applying MI theory 2.2.6.1 Purpose of the measure The purpose of this measure is to provide some techniques to assess the progress of students Besides that, it helps student self-comment, self-study, self-adjust learning method; how to communicate, collaborate, be interested in learning and practice progress 2.2.6.2 Content and method of implementation There are many specific methods and equipments to assess students' progress according to MI theory such as homework, journaling, writing small projects, discussing with individuals ,checking notebooks, solving problems, learning cards, self- evaluating sheet to collect feedback in both qualitative and quantitative terms Here we use some of the following equipments: 1) Observing the learning process; 2) Interviewing; 3) Product reviews; 4) Assessing the learning records; 5) Evaluating with survey questionnaire; 6) Using multiple choice; 7) Method of self-assessment: CONCLUSION OF CHAPTER In chapter 2, the author has proposed orientations for constructing and implementing geometric teaching methods at SS in the direction of applying MI theory On the basis of theory and practice, the thesis proposes methods of teaching geometry in senior level of SS in the direction of applying MI theory, including: Measure 1: Assessing the intellectual forms of students Measure 2: Designing lesson objectives in the direction of applying MI theory Measure 3: Exploiting, selecting and designing teaching content in the direction of applying MI theory Measure 4: Training students to use the dominant forms of intelligence in typical teaching situations Measure 5: Selecting and using the teaching methods, teaching techniques and teaching aids in the direction of applying MI theory Measure 6: Assessing the students' progress in the direction of applying MI theory Each measure has a certain function and role in teaching process in the direction of applying MI theory At the same time, the measures have a dialectical relationship with each other, impact and support each other Implementing synchronously all measures will contribute to improving the effectiveness of teaching Mathematics in Secondary School The proposed pedagogical measures need to be pedagogically experienced to assess their effectiveness CHAPTER 20 PEDAGOGICAL EXPERIMENT 3.1 Purpose and mission of pedagogical experiment 3.1.1 Experimental purposes - Examining the correctness of the scientific hypothesis proposed in the thesis - Assessing the feasibility and effectiveness of geometric teaching methods at secondary schools in the direction of applying the MI theory proposed on the basis of analyzing qualitative and quantitative results objectively and scientifically 3.1.2 Experimental mission For the purpose , we have identified the following experimental tasks: - Selecting objects and places to organize experiments - Determining the content and experimental method - Preparing lesson plans, teaching facilities, and discussing with teachers who use experimental teaching methed in the direction of applying Multiple Intelligence theory about experimental lecture plans, evaluation tools, etc - Preparing a set of tools to assess students 'progress: Observation checklist, tests, teachers' questionnaires, product- evaluating sheets, students' questionnaires - Planning and conducting experiments according to the plan: A trial round aimed at exploring and drawing experience , then the official experiment is carried out - Processing the experimental results (qualitative, quantitative, case studies), drawing conclusions 3.2 Experimental organization and pedagogical experiment content -Select the experimental schools and the experimental objects Discuss with the teacher before teaching Organize experimental teaching - Organizing the first experiment: Conducted in the second semester, academic year 2015 - 2016 - Organizing the second experiment: Held in the first semester of the academic year 2016 - 2017 Experimental content: Conduct experiments of some geometric teaching methods at SS in the direction of applying MI theory, which is presented through geometry lessons at SS 3.3 Evaluate experimental results 3.3.1 Methods of evaluating experimental results Experimental assessment methods include: Observing in classroom; Interviewing, exchanging between with teachers and students; Researching products; Case studies; Statistical method used to process data 3.3.2 Results of pedagogical experiment 3.3.2.1 Analyze qualitative results By observing the lesson time, collecting opinions via questionnaires and interviewing 10 teachers in experimental schools, we found that: * In control class (normal teaching): The way to organize students to conduct learning activities is still very monotonous, has not created conditions for students to 21 promote outstanding intellectual forms, the students have not been active, selfactivating, self-gaining knowledge, they mainly perform activities according to inquiries and instructions of the teachers Students often learn passively, mainly listen to teachers and take notes; the teachers only try to convey all the content of knowledge in textbooks, the questions and exercises are very little extended or not even added to inculcate the knowledge Lesson content is not really integrated, interdisciplinary and practical Teachers have not created a learning environment yet, so that all students have the opportunity to develop their outstanding intellectual forms.the teachers only try to convey all the content of knowledge in textbooks *In the experimental class: Teachers apply teaching methods in the direction of MI theory shown in lesson plans that we have designed, organized orientation, adjusted, commented and assessed learning In teaching process, teachers flexibly apply teaching methods and techniques in accordance with the learning strengths of each student and each group In particular, teachers have specialized methods such as, offering exercises requiring high levels of thinking for students with outstanding logical / mathematical intelligence form and exercises requiring moderate thinking for general/ common students In addition, teachers give many questions, exercises to apply knowledge into real life, interdisciplinary knowledge, The process of operating the lesson, teachers have differentiated how to teach, how to suggest, subdivide the problem, use explicit questions, reinterpret the problem more easily to match the learning ability of the general students (group of students with non and less logical and mathematical ability) to help students solve each problem Teachers have different approaches for each case in the classroom For example: Students with outstanding linguistic intelligence promote the ability to use words to express thoughts, promote reading or presentating skills, ; Students who excel in spatial intelligence are encouraged to participate in activities of observating visual, models, diagrams, which contain information to be discovered 3.3.2.2 Analysis of quantitative results After each experimental phase, we conduct tests and assessments for students of experimental classes and control classes The average score of the test in the experimental class is always higher than that of the control class, which proves that the learning results of the experimental classes are better than that of the control classes, the experimental process has a positive impact on the results of experimental classes The results of both the experimental phases have initially confirmed the feasibility and effectiveness of the measures 3.3.2.3 Analyze the results on case studies With the criteria to select case studies as introduced above During the experiment, we selected students of grade 8A Dong Hoa at Junior High School, Dong Son district, Thanh Hoa province to make observation records, observe the students' intellectual 22 expression, as well as their outstanding types of intellect that participating in activities of learning The first step shows that students know how to promote their outstanding intellectual forms in each learning activity and their learning results are better For example, Nguyen Thi Tra M is a student with excellent linguistic and communication skills (level I) She is good at presenting and singing, she loves to join the Youth Union and the art activities of her class Tra M.'s ability of organizing public activities, which is very good, can attract her friends to actively participate in the activities of group her logical / mathematical intelligence manifests in Level II (7/10), in our interview, she thinks Geometry is a difficult and abstract subject, which requires a lot of reasoning and thinking Whenever she has a difficult exercise without solution, she does not know how to start During the experimental lessons, teachers always create opportunities for Tra M to develop her language skills, cooperate and exchange with her friends, and especially she is always practiced how to analyze difficult problems by using tricks such as: deducing in the right direction or the opposite direction or subdividing the problem to solve each part, especially training her to get a habit of groping, predicting solutions When we meet and discuss with her about the applied method during the lesson, she considers that her dominant intellectual forms have been promoted, the non-dominant intelligence types have been better, so she feels more interested in learning Math, her result of Math is much better CONCLUSION OF CHAPTER III Through the analysis of pedagogical experiment results, with the progress of students, the teachers who teach experiments have highly appreciated the proposed pedagogical measures and have considered that they can be applied well in the condition of current schools Experimental pedagogical results have confirmed the correctness, feasibility and effectiveness of methods of teaching Geometry at SS in the direction of applying MI theory CONCLUSIONS AND RECOMMENDATIONS Conclusion The thesis has done all the research tasks Through the research process, we have obtained some main results as follows: - Systematize the basic theories such as: clarifying some terms related to intelligence; According to MI Gard Howard's theory, each student has not only one but eight intelligence types but the intellectual level of each student is different Some manifestations in the intellectual form of this student are different from those of the other students Each type of intelligence can develop by practicing and educating Therefore, teachers must understand this difference to offer appropriate pedagogical impact - Clarifying the necessity of applying MI theory to geometry teaching at SS Analyzing clearly the purpose of teaching geometry at SS in the direction of applying 23 MI theory is based on the difference of intellectual types of students to use different ways of teaching, in order to create learning opportunities for every student, if this student does not have this opportunity, there will be other opportunities, thanks to which the students learn more interestingly , their results are better - Clarifying and identifying some characteristic manifestations of six types of intelligence: linguistic intelligence, logical / mathematical intelligence, spatial intelligence, communication intelligence, internal intelligence and natural intelligence at SS in learning Geometry, thereby teachers make a premise to design and organize learning activities such as: Finding (pointing out) opportunities to help students promote intellectual forms through teaching methods, MI teaching techniques - Analyzing the current curriculum and textbooks of Mathematics at SS and Geometry teaching program in the direction of developing capacity to see how the intellectual forms of students are promoted, and also show the opportunity to promote the intellectual forms of students at SS in Geometry teaching - Investigating, analyzing and drawing conclusions about the reality of geometric teaching at SS in the direction of applying MI theory in Vietnam - Proposing orientations for constructing and implementing geometric teaching methods at SS in the direction of applying MI theory -Proposing six pedagogical measures and the purpose of these measures instructs teachers how to implement geometric teaching at SS in the direction of applying MI theory + Assessing the intellectual forms of students This is the first stage, teachers must understand what types of intelligence each student owns + Designing lesson objectives in the direction of applying MI theory In fact, teachers present the required results of knowledge, skills, and attitudes in the goals of lesson, now teachers can change by behaviors with observation and evaluation levels ( behavior indicator) The goal should meet two requirements: (1) Identifying the students' behaviors to achieve the results stated in the goals (2) Through the activities (acts) of students, the types of intelligence will be gradually promoted + Exploiting, selecting and designing content in the direction of applying MI theory Measures to instruct how to design teaching content, exploit and build a system of questionnaires with differentiation for two groups of students: (1) The students with outstanding logical / mathematical intelligence; (2)The students excel in other types of intelligence that the ability of learning mathematics manifests itself at a normal level Exploiting questions, exercises with content associated with real life and interdisciplinary subjects + Training for students to use outstanding intellectual forms in typical teaching situations + Selecting and using the teaching methods, teaching techniques and teaching 24 facilities in the direction of applying MI theory Instructing how to apply teaching in corners and teaching project that create conditions for students to have the opportunity to promote outstanding intellectual forms + Assessing the students' progress in the direction of applying MI theory - Conducting pedagogical experiments at secondary schools with the participation of teachers teaching experiments Qualitative and quantitative results prove the feasibility and effectiveness of the proposed measures, and also demonstrating the innovation in teaching and learning, the evaluation of effective learning outcomes as well as confirming the correctness of the proposed scientific hypothesis.The content of the thesis can be used as a useful reference for mathematics teachers or students of mathematics pedagogy Recommendations Through the process of researching and experimenting on the topic of thesis, we have some recommendations as follows: - Research results can be implemented and applied in teaching mathematics at SS - Integrating teaching content and requirements in the direction of applying MI theory in the instruction of school year tasks, professional documents, training materials for teachers; - Needing to improve teachers' awareness about teaching in the direction of applying MI theory It is necessary to have important criteria to evaluate the teacher's periods, well- teaching competitions; - Trying to reduce the number of students in a class (no more than 40 students per class) to ensure teaching requirements in the direction of applying MI theory - Strengthening facilities for schools (subject classrooms, teaching aids, libraries, network connection, ), enabling teachers to implement teaching methods in the direction of applying MI theory, updating Information and innovating qualification ... 2014, p.46 Nguyen Trung Thanh (2016), Some theoretical issues about teaching according to MI theory, Journal of Education, ISSN 2354 0753, No 378- Term 2, 3/2016, p.16 Nguyen Trung Thanh (2016), teaching... applying MI theory -Analyzing and clarifying common problems of MI theory such as terms related to intelligence; general overview of MI theory and presentation of characteristics of MI theory; Overview... Vietnam Institute of Educational Sciences, ISSN 0868 - 3662, No 143, 8/2017, p.61 Nguyen Trung Thanh (2015), Some theoretical issues on Mathematics teaching in MI at SS, Proceedings of Scientific Workshop