Dạy học hình học trung học cơ sở theo hướng vận dụng thuyết đa trí tuệ tt tiếng anh

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:
1. Assoc. Prof. Dr. Ton Than
2. 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
1.

2.

3.

4.

5.

6.

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 .


1
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


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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.


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* 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.


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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,

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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


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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


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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


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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:


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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

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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


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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


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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.

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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


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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


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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,


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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 do the exercises. Organizing for students to do exercises to consolidate and deepen


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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-

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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 2
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 6 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 6
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 3


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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 8 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 8 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
1. 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