thiết kế tình huống dạy học hình học ở trường trung học phổ thông theo hướng giúp học sinh kiến tạo tri thức bản tóm tắt tiếng anh

HANOI UNIVERSITY OF EDUCATION NGUYEN TIEN TRUNG DESIGNING GEOMETRY TEACHING SITUATIONS AT HIGH SCHOOL FOR HELPING STUDENTS CONSTRUCT NEW KNOWLEDGE Major: Theory and methods of teachi

HANOI UNIVERSITY OF EDUCATION

NGUYEN TIEN TRUNG

DESIGNING GEOMETRY TEACHING SITUATIONS

AT HIGH SCHOOL FOR HELPING STUDENTS

CONSTRUCT NEW KNOWLEDGE

Major: Theory and methods of teaching Mathematics

Code: 62 14 01 11

SUMMARY OF PEDAGOGICS DOCTORAL THESIS

HA NOI – 2013

Science instructor: Prof, Dr BUI VAN NGHI

Judge 1: Prof, Dr of Sci NGUYEN BA KIM , Dr

Judge 2: ASS.P Assoc Prof, Dr NGO HUU DUNG Vu Duong Judge 3: Dr Ngu Assoc Prof, Dr TRAN VUI n Van Thuan

Thesis will be defended in front of Council at University:

Hanoi University of Education, date:………

Thesis can be seen at National Library and Library of Hanoi National

University of Education

2 Nguyen Tien Trung (2011), Adidactic situation and mathematics teaching situation,

National Scientific conference of young teacher in pedagogical universities, the first

2011, Hanoi National Univesity of Education, pp 588-593

3 Nguyen Tien Trung (2011), Designing teaching situation: Developing formula to calculate distance from a point to a line (Geometry for 10 th grade), Journal of

7 Bui Van Nghi - Nguyen Tien Trung (2013), Some opinions on design the situation

of mathematic teaching in high school towards improving the positive student perceptions, Journal of Educational Science, No 312, pp 45-47; 50

8 Bui Van Nghi-Nguyen Tien Trung (2013), Designing a teaching situation: Developing formula to caculate the distance from a point to a plane in space (Geometry for 12 th grade, Chapter 3, Lesson 2), Journal of Science of Hnue,

Interdisciplinary Science, Vol 58, No 5, pp 47-52

3 Scientitic project

1 Nguyen Tien Trung, Designing some geometry teaching situations in high school,

No SPHN-10- 591NCS, Grade school Science project of Science and Technology, Hanoi National Univesity of Education, acceptance on 7/12/2012

INTRODUCTION

1.1 REASONS FOR CHOOSING TOPIC OF THE THESIS

* Approach in reasearch problems from published thesis The thesis

builds upon success of physiology, pedagogy and teaching methods applied by Vietnamese lecturers in 1960s of the 20th century There have been some well-known theories such as: theory of cognitive development by J.Piaget, theory of pschological activity; cultural historical theory of psychological development of high level psychology funtions by L.X Vygotsky, theory of didactical situation by

Guy Brousseau , …At that time, Vietnamese education scholars who had been experienced in teaching match made some innovations in teaching method One

of the most focused issues were how the theory of teaching method could be adapted to realities of teaching in Vietnam

Conducting research on view on action based teaching, professor Nguyen

Ba Kim was interested in action based learning , [50], [49], associate professor Trinh Thanh Hai had his opinion on how to apply action learning to technology training sessions at high school (2009)[35], doctor Nguyen Huu Hau (2012) focused on finding more actions, training students and facilitating their learning [40] Professor Nguyen Huu Chau who had dedicated himself to give insights into effective action learning emphasized the importance of enhancing students’motivated cognitive abilities [11] Professor Dao Tam who had taken interest in classification of learning activities conducted research on constructivist teaching in action, “hoạt động biến đổi đối tượng” and cognitive activities.… [83], [85], [86], [88]

With a view to study on theories of teaching and pschological theories of Maths teaching, there have been well- know researches such as constructivist approach in learning and teaching Maths conducted by professor Nguyen Huu Chau (1996) [12], application of constructivist view on geometry teaching at high school by doctor Cao Thi Ha (in teaching solid geometry) [13], [33] Theory of didactical situation had been main concern of many education scholars who employed it in teaching maths There have been some few more findings of application of theory of didactical situation to teaching for example researches done by Do Thi Chau (2008) [7] by Vu Dinh Phuong (2008) [72] From the best

of my knowledge, in order to make theory of didactical situation become practical applications in Vietnam, a number of considerable adaptation would be required

There has been a growing trend of application of teaching methods to math teaching The most common issues could be raised[103], interactive teaching method or collaborative teaching [23], [59], [60], …

* Research demand characteristics: The upcoming orientation of

education innovations in the 21st century includes: renewed teaching method, surmounting single impartion of information, improved critical thinking skills and applying advanced education method to teaching, enhanced self-study Geometry which plays the most part in high school level of Maths, provides students with the basis of plane geometry and solid geometry (including knowledge of the method of coordinates in the plane and the method

of coordinates in space) Moreover, geometry enables teacher to develop student’s logical thinking Consisting largely of abstract knowledge, geometry requires teacher to take an action based teaching which aims at inspires student’s positive thinking and enriches the lessons

After years of investigating issues, we have found that a lot of attempts have been made to apply active perspective as well as constructivism and theory of didactical situations to mathematic teaching at high school However, very few researches on teaching situations especially geometry teaching situations which we are searching for could be found

1.2 RESEARCH PROJECT

From the reasons above, we have chosen project “Designing geometry

teaching situations at high school for helping students construct new knowledge”

1.3 SCIENTIFIC HYPOTHESIS

If applying the active perspective, idea of constructivism and theory of situations (the theory of tidactical situations in mathematics), we can design teaching situations in geometry at high school in which student can construct their new knowledge

1.4 RESEARCH OBJECTIVE AND RESPONSIBILITY

Research objective: Designing some specific example of geometry

teaching situations at high school which inspire students and enable their constructivist learning THDH, teaching plan and designs of THDH based on constructivist learning would be recommended

Responsibilities:

+) Investigation of maths teaching and learning and practical teaching

+) Proving theoretical frame of math teaching situations in general and geometry teaching situations in particular at high school

+) Clarifying the viewpoint and design of geometry teaching situations based on contructivist learning at high school

+) Recommending plan to design geometry teaching situations at high school +) Designing and experimenting with some examples of geometry teaching situations, completing some geometry teaching situations at high school based

1.7 SCIENTIFIC VALUES AND FEASIBILITY

The thesis have recommeded several geometry teaching situations for helping students construct new knowlegde at high school The mentioned teaching situations that were practically designed and experimented would be possible for mathematic teachers to apply at high schools

In the thesis, author has showed his opinion on a teaching situations, plan and design of geometry teaching situations for helping students construct new knowlegde at high school Thus, the thesis highly supports teachers who are devoted to study and design geometry teaching situations particularly and mathematic teaching situations generally in the hope of producing higher teaching quality at high school

CHAPTER 2 THE SECOND RESEARCH RESULT

CHAPTER 3: THE THIRD RESEARCH RESULT

CHAPTER 4: THE FOURTH RESEARCH RESULT

CHAPTER 5: THE FIFTH RESEARCH RESULT

CONCLUSION AND RECOMMENDATION

2.2 HISTORY OF RESEARCH PROBLEMS

2.2.1 Reference and approach

(1) Lesson study: Lesson study is aimed at enhancing pedagogical profession

It requires that the joint research on teaching and learning in the certain classes has been done systematically to improve teaching and student’s critical thinking

We intended to design highly practical teaching situations approved by high school teachers As a result, we would be able to form theory as well as giving out suitable designs of identical teaching situations

(2) Constructivism and constructivist teaching: Based on viewpoint of constructivist teaching, student gains knowledge when they was immersed in an active learning environment where they find out their problems and solving them by applying given knowledge and experience to new situation

(3) Theory of didactical situations: Through document and knowlege gained at conference on theory of didactical situations and didactic Maths, we would like to apply the idea of a learning situation structure consisting of 3 basic situations: situation of action, situation of comunication and situation of

validation We were not to study on “adidactic” presented in theory of

didactical situations but to apply this kind of that situation to designing teaching situations

(4) Methods and teaching strategies: Based on suggestions of teaching strategies, teaching situations should be student centered learning which enables students to judge, to anticipate, to gain knowledge and to practise skills In teaching situations, we always anticipate, provide opportunities and support for students to solve the problem from the their knowledge and skills It also is a way

to improve the teaching situations

(5) Thesis on geometry teaching with different approaches: Some research papers which shared the same concern were conducted by professor Nguyen Huu Chau - Cao Thi Ha [33]; geometry teaching applied mathematics by professor Bui Van Nghi [63]; Development of logical thinking in elementary geometry teaching by associate professor Vu Quoc Chung [15] and application

of information technology to geometry teaching by associate professor Tran Vui [109], [110]; geometry skills building for 10th graders by professor Pham Duc Quang [75]; application of constructivism in geometry teaching by doctor Cao Thi Ha [12]

From the reasons mentioned above, it is a certain that our thesis is practical

2.2.2 Innovations of method of teaching mathematic

2.3 LITERATURE REVIEW

2.3.1 Active perspective

2.3.1.1 Phylosophy and pschology

2.2.1.2 Applying a ctive perspective in teaching

Active perspective in teaching means that teaching is done by actions from beginning to the end It also means students would be taught how to think and solve problems rather than learning theory only From that viewpoint, it is

highly recommened that teaching situation should be designed in the way that encourages cognitive development

2.2.2 Theory of constructivism

Jean Piaget (1896  1980) was a psychologist who collaborated to conduct

a well-known psychology theory named theory of constructivism His theory mentioning the development of cognitive process in children provided a solid foundation for child care and education

Two types of constructivism in teaching can be listed here: radical constructivism and social constructivism Individual constructivism emphasizes personal learning process Social constructivism focuses on how factors like culture, society influence on pernal development of knowledge

From conclusion and application of constructivism to teaching process, we deeply think that teachers should follow the model of learner centered teaching

in which students acts as information searchers through their activities (like signals, clauses, map and model, …) By this way, under the guidance of teachers, students can construct their knowledge

2.2.3 Theory of didactical situation

2.2.3.1 Concepts and definition of theory of didactical situation and applications to teaching process

a) Concepts

b) Four scientific hypothesise about theory of didactical situation c) Concepts of theory of didactical situation

d) Application of theory of didactical situation to teaching

Thanks to researches on theory of didactical situation and application of theory of didactical situation to teaching mentioned as [7]; [72]; [83]; [90]; [113],

we believe that, teacher needs to assign students challenging tasks which not only stimulate student’s thinking ability but also to improve their growing knowledge This type of teaching and learning requires both teacher’s creativity and student’s activeness

2.4 OTHER RELATED RESEARCH RESULTS

2.5 RESEARCH METHODS

2.5.1 Research methods

Theoretical studies method; method of summarizing educational experiences;

methods of observation; investigation methods; method of pedagogical experiment; methods of statistic

2.5.2 Pilot pedagogic stages

Teaching situations are designed following steps:

Figure II.3 Pedagogic experimentation stages

2.5.3 Purpose

Investigating the feasibility of designed teaching situations whether it would

be effective to students and whether it would be practical in Vietnam

teachers and put design of

teaching situation into use

at high school

Step 1’

2nd design of teaching situation by author

+ –

+) Number of high school surveyed: 22 high school from 8 provinces (Southern, Northern and Middle region)

+) Number of pedagogic experimentation training 04 high schools in Bac Giang, Quang Ninh, Ninh Bình, Ha Noi

2.5.7 Time of evaluation Time of pedagogic experimentation

2.5.7.1 Duration of evaluation

1st spell: April- May 2012; 2nd spell: November/2012 – February/ 2013

2.5.7.2 Time of pedagogic experimentation

2.5.8 Collecting and analyzing data

+) Design of teaching situation is referred to high school teacher to comments on ideas and feasibility High school teachers were asked to choose

at least three best teaching situations among eight designed teaching situations

We would like to ask for direct advice or comments from teachers

+) Class observation and pay document how actively and creatively students act during lesson, when students act as information searchers and the number of students benefit from new method All of the drafts and handouts returned to us would be considered as evidence of evaluation

+) Analyzing data: Making statistic table on students who construct completly knowledge Evaluation and testing hypotheses about the percentage of students who construct completely knowledge

RESEARCH RESULTS

Results presented in this part not only showed teaching stuations and pedagogic methods but also clarifying research process, pedagogic experimentation in each situation

This chapter shows the research results of design of teaching situations and pedagogic experimentation based on constructivist learning from general to particular (teaching cosine theorem in the triangle, Geometry 10th grade)

1.1 RESEARCH PROCESS

Process of designing the teaching situation: the cosine theorem in the triangle: Step 1: Investigating content overview, teaching objectives, anticipating advantages and disadvantages during lesson

(i) The cosine theorem in the triangle (Geometry for 10th grade) plays an important role in Math for 10th grade Therefore, we would like to inspire students by situations which stimulate their thinking ability and help them deeply memorize the lesson

(ii) Psychological and cognitive characteristics: One-way impartion of information (teacher centered teaching by presenting and explaining) gets students into the habit of inactive learning rather than selfstudy From my observation, students gain knowledge through specific examples

(iii) It is the fact that a considerable number of students in big cities, provinces take part in extra classes to learn ahead of schedule As a result, students are fully provided what they are supposed to search themselves

(iv) Surveying, interview and observation: We interviewed 300 10thgraders from Nguyen Tat Thanh high school a question: When it comes to lesson of cosine theorem, how many students already know it? Results: at least

3 students each class are taught the lesson ahead of schedule We asked 80 students who did not know the cosine theorem, have not read the textbook, in

two of the 10 classes above the following problem: “ ABC is triangle with

,

AC b AB  and angle A Determine the length of BC (BC c  )”a

Through observation we found that: all 80 students found the way to solve problem in general; there were no students who solved the problem from the

specific case of the corner A in order to generalize results problem in general;

there were no students who using knowledge of vectors as which is presented and suggested in the textbook

Step 2: Designing teaching situation: Our hypothesis is:After students identify

the length a (corner opposite A ) through the length and angle of the other two

sides in some special cases: A 30 ,0 A 60 ,0 A 1200 ., students can find the general formula, construct the cosine theorem in the triangle

Step 3: Ask for advice on designed teaching situation from mathematic teacher Step 4: Result statistic, reference to teachers and edit designed teaching plan

Step 5 If getting no more 80% of approval, return step 2, 3,4

1.2 RESULT

1.2.1 DESIGN OF TEACHING SITUATION

Activity 1: Warm-up:

Teacher: At 9th grade, students all know the

Pytago theorem in right triangle Presentation

and writing formulas of that theorem

Students: a2 b2  if ABC is rigth c2

triangle at A (squared length of the hypotenuse

of a right triangle is equal to the square of the

length of the two other side)

Teacher:What things will happen if ABC is

not a right triangle? Can you calculate the length of a term , b c and angles A or not?

would the formula look like?

Students: Yes, we can Because a triangle is completely determined when

we have two sides and one angle in between

Activity 2 Approach problem

Teacher: Divide the class into six groups, each of length a in the following

cases: A  600; A 30 ;0 A 1200 Teacher deliver worksheets to the groups Students: Solve the problem in each group’s worksheet

B

a c

b

Figure III.1. 1