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Tiêu đề A study on the teaching of mathematics in English at an 8th grade class at Doan Thi Diem private secondary school
Tác giả Tran Thi Thuy
Người hướng dẫn Dr. Mai Thi Loan
Trường học University of Languages and International Studies, Vietnam National University, Hanoi
Chuyên ngành English teaching methodology
Thể loại Thesis
Năm xuất bản 2015
Thành phố Hanoi
Định dạng
Số trang 75
Dung lượng 136,71 KB

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ACP: American Credit Program AAAS: Association of the Advancement of Science CLIC: Content and Language Tntegrated Tcarning DTD School: Doan Thi Diem private secondary school ELLs: Eng

Trang 1

NATEONAL UNIVERSITY OF ITANOL UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES

¥ACULTY OF POST-GRADUATE STUDEES

HARA RARER RIRR RARE

TRAN THI THUY

A STUDY ON THE TEACHING OF MATHEMATICS

IN ENGLISH AT AN 872 GRADE CLASS AT DOAN THI DIEM PRIVATE SECONDARY SCHOOL

NGHIEN CUU VIEC DAY TOAN BANG TIENG ANH TRONG MOT

LOP 8 TAT TRUONG TRUNG HOC CO SO DAN LAP BOAN THI DIEM

M.A MINOR PROGRAMME TIIESIS

Field: English Teaching Methodology Code: 60 140111

Supervisor: Dr Mai Thi Loan

HANOI - 2015

Trang 2

NATIONAL UNIVERSITY OF HANOI UNIVERSITY OF LANGUAGES AND INTERNATIONAL STUDIES

FACULTY OF POST-GRADUATE STUDIES,

TRAN THI THUY

A STUDY ON THE TEACHING OF MATHEMATICS

IN ENGLISH AT AN 8'" GRADE CLASS AT

DOAN THI DIEM PRIVATE SECONDARY SCHOOL

NGHIEN CUU VIEC DAY TOAN BANG TIENG ANH TRONG MOT

LGP & TAI TRUONG TRUNG HOC CO SG DAN LAP BOAN THI DIEM

M.A MINOR PROGRAMME THESIS

Field: English caching Mcthodology Code: 60 140 111

Supervisor: Dr Mai Thi Loan

HANOT - 2015

Trang 3

DECLARATION:

I certify my authorship of the thesis:

A study on the teaching of Math in English al an 8 grade class

at Doan Thi Diem private secondary school

is the result of my own for the Degree of Master of Arts at College of Foreign Languages, Hanoi National University, and this thesis has not boon submitted for

any degree at any other university or institution

Hanoi, 2015

Signature

Tran Thi Thay

Trang 4

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 5

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 6

1 Recapitulation .ccssncunencnninnaeineneinnnenieinenianenieieninenieane

2 Limitations of the study

3.Recommendations for further studies .0 :c:cccesseesssssssenseneneteeesessssnescanvaneiees

LIST OF ABBREVIATIONS

vi

45

4 46

Trang 7

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 8

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 9

Jarcelt’s and Kersaint’s stralogics in leaching Math in Bnglish lo FLLs 11

Learning environment in the classtoomt 0c0.ccccc cc ceeees sects eee ees › ⁄20

Teachers instructional strategies in the classroom 2 Students’ leaning strategies in the classroom sa 23 'Teacherˆs teaching siratepies in the cÏassroom 26 Students’ challenges of studying Math in English 2?

Students’ suggeslions lo make the program better 29

'Yypes and frequency of work for studenfs 3] Teacher monitoring in the classroom - 2

Teachcr”s mstruclidral toola mi the classroom - 24

Teacher`s assessment in the classroom se hoc,

Students’ benefits of studying Math in English - S28

vit

Trang 10

1 Recapitulation .ccssncunencnninnaeineneinnnenieinenianenieieninenieane

2 Limitations of the study

3.Recommendations for further studies .0 :c:cccesseesssssssenseneneteeesessssnescanvaneiees

LIST OF ABBREVIATIONS

vi

45

4 46

Trang 11

List of abbreviations sesenenneenmetnneaestne siemens hi

4, Scope of the Sh1ổy su 0n HH Hư HH0 re

7 Design of the study

PART B: DEVELOPMENT

CHAPTER 1: THEORETICAT BACKGROUND

1.1 Teaching Math in English to Fl

17 15/.1.:, 7n eee cee

1.2 Teaching Math iu Bnglish —a CLI approach coe

1,3 Implementations of teaching Math in Unglish sssnsmnenensnenemnenieD 1.3.1 History of teaching Math in English in Asia cone

1.3.2 Situation of teaching Math in English in Viein att women rienrneneien8 1.3.3 Benefits of teaching Math in English recognised by scholars 9

iv

Trang 12

ABSTRACT

Math, Science and Literature have been taught to ELLs in parts of the word

This research studies on the subject of Math because il is universal Lo people more

than any others: its aims arc to examine whether teaching Math in English is beneficial or not, the teaching methods used by the Math teacher, the challenges of

teaching Math in English in 8M al DTD School and to find out the

secommendations to improve the situation of teaching Math in English in the future

To fulfill these targets, three instruments employed to collect data were the

classroom observations, the questionnaire for the students and the interview for the Math teacher

The study was carried out and involved an American teacher of Math and 16

Vietnamese students in grade 8 at DID School Statistical analysis revealed that most of the students initially struggled with mathematical vocabulary, cultural dilTerences in icachers’ leaching methods and students’ leaming styles and especially, their English limited proficiency Gradually, they had improvement in

their English competence and mathematical knowledge thanks to the Math teacher’s

yolatively well-plarmed lessons Several stralogics which are recommended to deat with the found challenges inchie differentiating specific instructions, teaching

mathematical vocabulary properly, applying technology, enhancing

communications among students, parents, teacher and school and holding more

Math competitions to encourage students to study Math in Iénglish

ii

Trang 13

Jarcelt’s and Kersaint’s stralogics in leaching Math in Bnglish lo FLLs 11

Learning environment in the classtoomt 0c0.ccccc cc ceeees sects eee ees › ⁄20

Teachers instructional strategies in the classroom 2 Students’ leaning strategies in the classroom sa 23 'Teacherˆs teaching siratepies in the cÏassroom 26 Students’ challenges of studying Math in English 2?

Students’ suggeslions lo make the program better 29

'Yypes and frequency of work for studenfs 3] Teacher monitoring in the classroom - 2

Teachcr”s mstruclidral toola mi the classroom - 24

Teacher`s assessment in the classroom se hoc,

Students’ benefits of studying Math in English - S28

vit

Trang 14

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 15

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 16

Jarcelt’s and Kersaint’s stralogics in leaching Math in Bnglish lo FLLs 11

Learning environment in the classtoomt 0c0.ccccc cc ceeees sects eee ees › ⁄20

Teachers instructional strategies in the classroom 2 Students’ leaning strategies in the classroom sa 23 'Teacherˆs teaching siratepies in the cÏassroom 26 Students’ challenges of studying Math in English 2?

Students’ suggeslions lo make the program better 29

'Yypes and frequency of work for studenfs 3] Teacher monitoring in the classroom - 2

Teachcr”s mstruclidral toola mi the classroom - 24

Teacher`s assessment in the classroom se hoc,

Students’ benefits of studying Math in English - S28

vit

Trang 17

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 18

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 19

List of abbreviations sesenenneenmetnneaestne siemens hi

4, Scope of the Sh1ổy su 0n HH Hư HH0 re

7 Design of the study

PART B: DEVELOPMENT

CHAPTER 1: THEORETICAT BACKGROUND

1.1 Teaching Math in English to Fl

17 15/.1.:, 7n eee cee

1.2 Teaching Math iu Bnglish —a CLI approach coe

1,3 Implementations of teaching Math in Unglish sssnsmnenensnenemnenieD 1.3.1 History of teaching Math in English in Asia cone

1.3.2 Situation of teaching Math in English in Viein att women rienrneneien8 1.3.3 Benefits of teaching Math in English recognised by scholars 9

iv

Trang 20

List of abbreviations sesenenneenmetnneaestne siemens hi

4, Scope of the Sh1ổy su 0n HH Hư HH0 re

7 Design of the study

PART B: DEVELOPMENT

CHAPTER 1: THEORETICAT BACKGROUND

1.1 Teaching Math in English to Fl

17 15/.1.:, 7n eee cee

1.2 Teaching Math iu Bnglish —a CLI approach coe

1,3 Implementations of teaching Math in Unglish sssnsmnenensnenemnenieD 1.3.1 History of teaching Math in English in Asia cone

1.3.2 Situation of teaching Math in English in Viein att women rienrneneien8 1.3.3 Benefits of teaching Math in English recognised by scholars 9

iv

Trang 21

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 22

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 23

ABSTRACT

Math, Science and Literature have been taught to ELLs in parts of the word

This research studies on the subject of Math because il is universal Lo people more

than any others: its aims arc to examine whether teaching Math in English is beneficial or not, the teaching methods used by the Math teacher, the challenges of

teaching Math in English in 8M al DTD School and to find out the

secommendations to improve the situation of teaching Math in English in the future

To fulfill these targets, three instruments employed to collect data were the

classroom observations, the questionnaire for the students and the interview for the Math teacher

The study was carried out and involved an American teacher of Math and 16

Vietnamese students in grade 8 at DID School Statistical analysis revealed that most of the students initially struggled with mathematical vocabulary, cultural dilTerences in icachers’ leaching methods and students’ leaming styles and especially, their English limited proficiency Gradually, they had improvement in

their English competence and mathematical knowledge thanks to the Math teacher’s

yolatively well-plarmed lessons Several stralogics which are recommended to deat with the found challenges inchie differentiating specific instructions, teaching

mathematical vocabulary properly, applying technology, enhancing

communications among students, parents, teacher and school and holding more

Math competitions to encourage students to study Math in Iénglish

ii

Trang 24

ABSTRACT

Math, Science and Literature have been taught to ELLs in parts of the word

This research studies on the subject of Math because il is universal Lo people more

than any others: its aims arc to examine whether teaching Math in English is beneficial or not, the teaching methods used by the Math teacher, the challenges of

teaching Math in English in 8M al DTD School and to find out the

secommendations to improve the situation of teaching Math in English in the future

To fulfill these targets, three instruments employed to collect data were the

classroom observations, the questionnaire for the students and the interview for the Math teacher

The study was carried out and involved an American teacher of Math and 16

Vietnamese students in grade 8 at DID School Statistical analysis revealed that most of the students initially struggled with mathematical vocabulary, cultural dilTerences in icachers’ leaching methods and students’ leaming styles and especially, their English limited proficiency Gradually, they had improvement in

their English competence and mathematical knowledge thanks to the Math teacher’s

yolatively well-plarmed lessons Several stralogics which are recommended to deat with the found challenges inchie differentiating specific instructions, teaching

mathematical vocabulary properly, applying technology, enhancing

communications among students, parents, teacher and school and holding more

Math competitions to encourage students to study Math in Iénglish

ii

Trang 25

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 26

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 27

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 28

Jarcelt’s and Kersaint’s stralogics in leaching Math in Bnglish lo FLLs 11

Learning environment in the classtoomt 0c0.ccccc cc ceeees sects eee ees › ⁄20

Teachers instructional strategies in the classroom 2 Students’ leaning strategies in the classroom sa 23 'Teacherˆs teaching siratepies in the cÏassroom 26 Students’ challenges of studying Math in English 2?

Students’ suggeslions lo make the program better 29

'Yypes and frequency of work for studenfs 3] Teacher monitoring in the classroom - 2

Teachcr”s mstruclidral toola mi the classroom - 24

Teacher`s assessment in the classroom se hoc,

Students’ benefits of studying Math in English - S28

vit

Trang 29

1 Recapitulation .ccssncunencnninnaeineneinnnenieinenianenieieninenieane

2 Limitations of the study

3.Recommendations for further studies .0 :c:cccesseesssssssenseneneteeesessssnescanvaneiees

LIST OF ABBREVIATIONS

vi

45

4 46

Trang 30

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 31

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 32

ACP: American Credit Program

AAAS: Association of the Advancement of Science

CLIC: Content and Language Tntegrated Tcarning

DTD School: Doan Thi Diem private secondary school

ELLs: English Language Leamers

NCTM: National Council of Teachers of Mathematics

Math: Mathematics

OKCD: the Organizations for Kconomic Co-operation and Development

PISA: Programme for Tnterralional Student Assessment

SCS: Salomon Christian School

TESOL; Teachers of English to Speakers of Other Languages

vii

Trang 33

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

Trang 34

ABSTRACT

Math, Science and Literature have been taught to ELLs in parts of the word

This research studies on the subject of Math because il is universal Lo people more

than any others: its aims arc to examine whether teaching Math in English is beneficial or not, the teaching methods used by the Math teacher, the challenges of

teaching Math in English in 8M al DTD School and to find out the

secommendations to improve the situation of teaching Math in English in the future

To fulfill these targets, three instruments employed to collect data were the

classroom observations, the questionnaire for the students and the interview for the Math teacher

The study was carried out and involved an American teacher of Math and 16

Vietnamese students in grade 8 at DID School Statistical analysis revealed that most of the students initially struggled with mathematical vocabulary, cultural dilTerences in icachers’ leaching methods and students’ leaming styles and especially, their English limited proficiency Gradually, they had improvement in

their English competence and mathematical knowledge thanks to the Math teacher’s

yolatively well-plarmed lessons Several stralogics which are recommended to deat with the found challenges inchie differentiating specific instructions, teaching

mathematical vocabulary properly, applying technology, enhancing

communications among students, parents, teacher and school and holding more

Math competitions to encourage students to study Math in Iénglish

ii

Trang 35

1.3.4, Factors affecting Ells’ success in studing Matf, sec 1.35 Challenges for Math teachers and learners 10

1.3.6 Strategies for Math teachers and learners

1.4 Review of previous stucies related lo teaching Math in English 13 1.5, Summary

CHAPTER 2: METUODOLOGY

2.1L The current situation of teaching and learning at ITD School 1S

2.1.2 Material description cece cesses issn LS

3.3, Summary

PARTE C: CONCLUSION

Trang 36

1 Recapitulation .ccssncunencnninnaeineneinnnenieinenianenieieninenieane

2 Limitations of the study

3.Recommendations for further studies .0 :c:cccesseesssssssenseneneteeesessssnescanvaneiees

LIST OF ABBREVIATIONS

vi

45

4 46

Trang 37

ACKNOWLEDGEMENTS

From the bottom of my heart, I thank all people who have supported and

encouraged me Unrough the process T completed this thesis

First of all, I would like to send my most sincere and deepest gratitude to my

supervisor, Dr Mai Thi Loan for her wholchearled imsiruclions, precious

suggestions and knowledgeable advice to my study Without her enthusiasm, this

work would never have been accomplished

Next, I sincerely would like to acknowledge other teachers at the Department

of Post-Graduate Studies for providing me numerous interesting, valuable lectures

and guidance

Thave profound regards for Mr David Devine, an excellent Math leacher and

for all 8M students, at Doan Thi Diem private socondary school who spent their

precious time answering my survey questions Owing to their cooperation, my

thesis has been succes

Lully completed

Last but not least, I owe my life to my family and close friends for their incessant cnvouragemionls which have raised ue up a lot lo finish any Uesis.

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