Summary of doctor’s thesis in education: Teaching Geometry at secondary schools in the direction of applying Multiple Intelligence theory

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).

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

At day month year

The thesis can be found at:

- National Library

- Library of Vietnam Institute of Educational Sciences

TO THE THESIS OF THE AUTHOR

1 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

2 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

3 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

4 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

5 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

6 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

1 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)

3 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

4 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

5 Scope of research

- The topic focuses on teaching Geometry in grades 8 and 9 in the direction of applying MI theory

- Experiments were conducted at 2 Secondary schools in Thanh Hoa province

- Experimental period: in 2 academic years 2015 - 2016; 2016 - 2017

6 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

7 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

8 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

9 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 do 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

do 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

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:

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

tutoring a weak student;) Math Web Design is a place to exchange among members

self 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