Teaching geometry at secondary schools in the direction of applying multiple intelligence theory

nt. Students 8 who excel in any form of intelligence are promoted most of that kind of intelligence through learning activities. 1.3.3.2. Providing many approaches of teaching content The basic feature of the MI theory is to emphasize the differences between the intellectual forms manifested in certain field, in which the type of intelligence has developed significantly to achieve high results (in Mathematics, the logical / mathematical intelligence has the most chance of development), the expression is normal in the other fields. accordance with this distinctive feature in teaching process, teachers need to: Implement content flexibly, avoid applying rigidly and mechanically; Make a plan of teaching actively, adjust the content in the direction of basic, streamline and supplement the actual teaching content to suit each type of students; Focus on exploring and utilizing the content associated with students' experiences in daily real life; Select, organize and design "knowledge packages" that meet the needs of each individual or group. 1.3.4.3. Searching for (pointing out) opportunities to help students promote intellectual forms Opportunities for students to develop the intellectual forms in the process of teaching geometry, are done through typical teaching situations of Mathematics such as: teaching mathematical concepts, mathematical theorem, rules, methods of solving math exercises. The opportunities to promote the types of intelligence are realized through problematic teaching situations such as: forming new knowledge; exercising - practicing ; reviewing - testing. 1.3.4.4. Diversifying forms of teaching organization, flexible combination of group and individual activities, .. According to Campbell, B (1990) teaching basing on the theory of MI is the variety of different organizational forms of teaching, this diversity comes from the diversity of intellectual forms of students. Teaching methods such as individual teaching, group teaching, classroom teaching, experiential teaching, etc. In teaching process according to MI theory, teachers need to strengthen the organization of experiential activities. Because experiential learning emphasizes the active, positive and creative role of learners, as well as their personal experience and their interaction with the environment. 1.3.4.5. Using the techniques of Multiple Intelligence MI theory suggests: "There is no set of strategies that can work well for all students at all times. Every student has inherent bias in eight intellectual forms, so a specific strategy that is good for this group of students but not so good for other groups of students " and not all students learn the same way, teaching does not go into stereotyped and misleading learning bias, teachers need to apply flexibility and creating different teaching methods and techniques, thereby being able to reveal the characteristic manifestations of intellectual forms. Specifically: 9 i) Teaching techniques to help students promote linguistic intelligence - Use the teaching methods for presentation, lectures and conversations; brainstorming techniques; positive writing techniques (can be used after lessons to summarize the content learned); Organize activities to read lessons, read newspapers, read documents, read on the media, ... Organize activities to communicate and cooperate with others in the form of speaking and writing when they exchange, discuss , argue , explain and evaluate mathematical ideas and solutions and communicating with their friends and teachers; Train students how to master and convey content, knowledge in many different languages; Teaching materials include: textbooks, tapes, learning cards; writing notes, diaries, reading materials, using text editing software. ii) Teaching techniques help students promote logical / mathematical intelligence - Create a situation that gives students the opportunity to practice calculating skills; Practice predictive habits in problem solving. Apply logical knowledge to confirm or refute predictions; Practicing skills of forward and reverse reasoning while proving geometry; Exercise students know how to apply deductive methods and manipulations of analytical thinking, synthesis, comparison, analogy, generalization, specialization in problem solving; Teaching materials include: mathematical documents (math books, math reports, math exam questions), abacus, numerical tables, calculators, mathematical software, scientific equipment. iii) Teaching techniques to help students promote spatial intelligence - Using drawings, pictures, diagrams, tables, video clips, documentaries ... to convey or illustrate a content unit of mathematical knowledge; Expressing mathematical objects, expressing concepts, relationships, mathematical properties by drawing, maps, diagrams of thought to brief and summarize questions, exercises, knowledge ; Organizing for students to perform measurement, drawing, rendering, folding, cutting, creating shapes, .. helping students re-create spatial symbols, arrangement, construction, and moving from image to image in mind, ... to create new images, find new ideas.. Teaching materials include: Visual thinking exercises; geometry exercises; drawings, pictures, charts, graphics; camcorders, cameras, cameras; graphic software; use drawing software; Increase the use of visual media. iv) Teaching techniques to help students promote communication intelligence - Organizing activities in groups, teachers use cooperative teaching techniques such as teaching in pairs, teaching techniques of "tablecloths", teaching techniques of puzzle pieces, teaching according to angles, teaching according to group projects, brainstorming; Create conditions for students to help each other (good 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, self- management, 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 do 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 1 The research results in Chapter 1 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 2 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 do 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 6 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, non- intellect 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,