APPLYING GRAPH THEORY IN TEACHING GENETICS FOR THE TWELVE GRADE PUPIL AT HIGH SCHOOL

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MINISTRY OF EDUCATION AND TRANING
HANOI NATIONAL UNIVERSITY OF EDUCATION
NGUYEN THI KHIEN
APPLYING GRAPH THEORY IN TEACHING GENETICS FOR
THE TWELVE GRADE PUPIL AT HIGH-SCHOOL
Specialism: Theory and methods in teaching Biology curriculum
Code: 62.14.10.11
THE ABSTRACT OF DOCTORAL THESIS IN PEDAGOGY
Hanoi, 2014
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This study is completed at Faculty of Biology,
Hanoi National University of Education

Academic supervisors: Assoc.Prof. Dr. Le Dinh Trung
Debater 1:Assoc.Prof. Dr. Nguyen Quang Vinh
Educational Science Institute Vietnam
Debater 2: Assoc.Prof. Dr. Nguyen Đinh Nham
Vinh University
Debater 3: Assoc.Prof. Dr. Nguyen Xuan Viet
Hanoi National University of Education
The thesis will be defended in front of the National Doctoral Examination
Board at Hanoi National University of Education at….
The thesis is also available at:
1. National Library of Vietnam
2. The library of Hanoi National University of Education
3. The library of Hai Duong university
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AUTHOR’ RELATED ARTICLES TO THE THESIS
1. Nguyen Thi Khien (2009), “Process questions using problem situations to
help pupils self-study textbooks for the teaching of evolution section - 12 high
school students” , Journal of Education (216/6), pp (47-49).
2. Nguyen Thi Khien (2011), “Classification graph and some graph learning
content Genetics Part 12 high school pupils”, Journal of Education (Special Edition /
12), pp 93-95.
3. Nguyen Thi Khien (2011), “Process up to graph and analyze the nature of the
relationship between the concept in the teaching of biological variation mutant
12”, Journal of Education (Special Edition Last year), pp 72 – 74.
4. Nguyen Thi Khien (2012), “Construction graph contents to teaching biology
Genetics Part 12”, Journal of Education (295/10), pp 43 – 45.
5. Nguyen Thi Khien (2012), “Research on construction graph teaching content
of part Genetics, Biology 12 - High School”, Scientific reports on research and
teaching Biology in Vietnam (National Scientific Conference for the first time,
HN), pp 832 – 839.
6. Nguyen Thi Khien (2013), “Applying graph theory to teach the laws of
genetics in biology program 12”, Journal of Education (318/9), pp 52 – 54.
7. Nguyen Thi Khien (2013), “Some of studies on the application of graph theory
to teach the world and in Vietnam”, Journal of Education (Special Edition /9), pp 110
– 112.
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INTRODUCTION
1. Reasons to select the subject
1.1. Starting from the current teaching purposes
The purpose of teaching is to make pupils know how to study properly.
This shows that they begin to get the idea in a way that the scientists create

product. The trainer must be wondering about the impact of their teaching on
pupil learning and how can firstly make they understand right? Resulted a way
that pupils learn as teachers' desire or not?
1.2. In pursuit of the policies, guidelines of the Party and Government
Goal of the innovation education in our country nowadays, where
innovative teaching methods are considered to be one of the strategic tasks.
These guidelines and solution were given through the leadership of the Party
and Government from the end of the twentieth century up to now as: Resolution
of the Second Congress of the Central Committee of the Communist Party of
Vietnam (National Assembly VIII , 1997) , the Ninth Congress of Party
(4/2001) and the development of education strategy 2001-2010; Resolution of
the 8th, the Central Executive Committee XI (Resolution No. 29-NQ/TW)
November 4, 2013 of radical innovations, comprehensive education and
trainingmeet, the requirements of industrialization and modernization in
economic conditions market the socialist-oriented and international integration.
Law on Education of Socialist Republic of Vietnam stipulates : "Educational
methods must be promote the positive, self-discipline, initiative, creative
thinking of students, fostering self-learning ability, passion for learning and the
will to strive".
1.3. Starting from the advantages of Graph in teaching
Graph is the mathematical scientific method which has high generality,
solid stability for encoding the relationships of the objects being studied.
Therefore using Graph in teaching genetics for pupils at high school will not
only help them master each separate element a discrete, isolated but also that a
system with interlaced networks of levels of life-organization and the existence
of levels of organization in the Biology world broadly, specific and more
intuitive. Studied Graph theory and apply it to ensure that teaching will improve
the quality of learning of knowledge optimally Genetics.
1.4. Starting from the basic characteristics of the Genetics grade (Biology 12-
high school)

From the Genetics part (Biology 12 - high school) studies structure and
function of the facilities at the life-organizational level and the relationship
between the levels of life-organization from the molecular level, cells, body and
populations. That is the concept of knowledge, the phenomenon, rules,
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mechanisms and biological processes of different life-organizational and its
practical applications.
So finding a way of teaching, learning content suitable for Genetic
knowledge is very important, ensure the student has acquired new knowledge
content, both systems are in a logic of knowledge and know how to tight the
mechanisms of their advocacy on breeding, practical production, cultivation
and human life. If using diagrams, tables, teaching Genetics section could be
advantageous in modeling, systems of knowledge. Graph has many strengths in
expressing relationships and hierarchical in Genetics. Therefore, using the
Graph in teaching genetics for high school pupils will help them not only see
each separate element a discrete, isolated but also see a system with interlaced
networks of levels organization of life and the existence of organizational levels
in biota broadly, specific and more intuitive.
Stemming from that reason, we chose the topic "Applycation of graph
theory in teaching part of Genetics ( Biology 12 – high school)”
2. Research purposes
Applying graph theory to structure content of Genetics section become
graph content logical system and use them in their learning process and as a
means, just as teaching methods turned to positive learning activities of students
to contribute to improving the quality and effectiveness of teaching and
learning part Genetics (Biology12 - High School).
3. Subject and the Object of study
3.1. The Subject of study

Research theory and Graph theory applied to teaching sections Genetics
(Biology 12 - high school).
3.2. The Object of study
The process of teaching Genetics (Biology 12 - at high school).
4. Scope of the Study
- Graph theory and its application in the teaching section of Genetics
(Biology 12 - high school).
- Experiments at some high schools in Hai Duong province and Hai
Phong city.
5. Scientific hypothesis
If the proposed process construction Graph content and built a system for
content Graph scientific and have methods reasonable use in teaching of
Genetics section (Biology 12 - high schools) both as a means and a method
appropriate to promote a positive, creative initiative to acquire knowledge and
skills of pupils learning under Graph theoretical approaches.
6. Research tasks
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6.1. Graph theory research and the application of graph theory in teaching
in general and teaching in part Genetics (Biology 12 - high school) particular;
6.2. Explore and use the graph in teaching Genetics (Biology 12 - high
school) of the current high school teachers;
6.3. Structured content Geneticist share as a basis for building Graph
contents by topic to facilitate the organization of the teaching process;
6.4. Elaboration of process content graph from which to build graph
contents by topic to teach part Genetics (Biology 12 - High School);
6.5. Construction process using and the proposed method use the graph to
the stages of the teaching process especially stitched teach new knowledge;
6.6. Identify the criteria for evaluating teaching effectiveness in graph

with some basic skills to develop thinking power of students;
6.7. Empirically pedagogy to proven effective use of teaching component
graph Genetics (Biology 12) according to the hypothesis proposed.
7. Research Methodology
7.1. Methods of theoretical studies
7.2. Pedagogical methods investigation
7.3. Professional method
7.4. Pedagogical Experimental Methods
7.5. Methods of data processing
7.6. Method of assessment
8. New contributions of the thesis
8.1. The system and supplemented, complete theoretical basis of graph
theory including: the quality graph, graph classification, characteristics and role
of graph in the organization types teaching lecture;
8.2. Proposed rules, building processes graph content to make molds for
shaping required to achieve the level of learners after each activity graph
teaching method;
8.3. Structured content section Genetics textbook as a basis for building a
general graph facilities, mechanism of genetic phenomena and variation in the
levels of organization from molecules to living populations; the regularity of
genetic phenomena; the application of genetics in production and life; human
genetics. Since then, build the graph content details for organizing learning
activities by the method of graph;
8.4. Build a System Graph part Genetics content and use them on the
stages of the teaching process contributes formation to the of student capacity
systems thinking logically about the content levels of organization of life, as a
basis favorable to help students get the system knowledge to learn all the
knowledge component of Ecology and Evolution;
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8.5. The thesis proposed rule, the process of using graph as a means, a
section teaching methods of the teaching process (especially new materials
research stages) in Genetics (Biology 12) contribute to improving the quality of
learning through practice the skills learned in Graph;
8.6. The thesis was initially confirmed the role of the teaching - both as a
graph by means of a teaching method facilitate students to form and develop
analytical thinking, synthesis, generalization path inductive and deductive
effectively contribute to improving pupils' learning capacity in Biology
teaching general and teaching particular sections of genetics in high school;
8.7. Developing lesson plans according research to experimental
development was initially confirmed a large role of the graph in teaching part of
Genetics (Biology 12 – high school) and made valuable references for the high
school teachers.
Chapter 1: THEORETICAL BASIS AND PRACTICAL APPLICATION
OF GRAPH THEORY IN TEACHING GENETICS (BIOLOGY 12 -
HIGH SCHOOLS)
1.1. History graph theory research on teaching applications
1.1.1. Research and teaching application graph in the world
Graph theory is a discipline of mathematics was born from his work on
the arithmetic problem “Seven Bridges in Konigsburg" author Leonhard Euler
(1707 - 1783), Swiss mathematician published in 1736.
Modern graph theory began to be published in the book “Graph theory
directed and undirected” author Comig, Lepzic published in 1936. In 1958 in
France author Claude Berge wrote the book “graph theory and its applications"
On the Internet, up to now, there are thousands of research articles on
graph theory and its application is published in journals such as Journal of
Graph Theory (Journal of combinatorial Theory, Series B); Review Graph
algorit and applications (Journal of Graph Algorith and Applications) and many
other popular magazines: “Graph theory”;

“Some graph
theory algorithm animations”; , Jonathan L Gross &
Jay Yellen, Topological Graph Theory, New York USA.
Currently, in the world there are many authors studied the converting
graph theory into numbers of different fields of science: research group
established by Prof. Dirk Janssens (University of synthetic Antrep - Belgium
(University of Antwerp); research group established by Professor Hartmut
Ehrig, Technical University of Berlin - Germany, professor Grzegorz
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Rozenberg University of Layden - the Netherlands; Presicce professor
Francesco Parisi University of Rome (Italy).
In the United States there are many authors have deep studied about
graph. The most prominent is the work of Jonathan L Gross (Columbia
University, New YOC) and Jay Yellen (University of Rolin, Florida). Two
authors have published many works on the graph as "manual graph theory";
"graph theory and its applications". Conclusion, the graph theory and its
applications have been studied for application in various fields, including the
field of education.
1.1.1.2. Applying graph theory to teach the world
In 1965-1966 , Russia LN Landa educators have conducted empirical
algorit transformation of mathematical methods into the teaching method
common to many scientific disciplines, since that time, many scientists Russia
(former USSR ), Germany, France, Switzerland In 1965 AMXokhor was the
first person who has implemented a number of theoretical perspectives oriented
graph to model a textbooks content about one concept, one law. In 1965, the
theorist teaching in Chemistry Mr. VX Poloxin based on the Mr. Xokhor’s
experience, visually describes the evolution of a teaching situation with the
sequence diagram of the actions teachers and students in a chemistry laboratory.

Other works also mention research on applications of graph as: Claudo
Becgo (1967) with "graph theory and applications"; RJ Wilson (1977) and
"Introduction to graph theory"; L.Iu Berezina (1997) with "Graph and its
Applications".
The increasing application of graph confirming the role of scientific
research and teaching in following subjects: Literature, Physics, Biology,
Education
1.1.2. Research and application of graph theory teaching courses
in Vietnam
1.1.2.1. Research and application of graph theory to teaching
Professor Nguyen Ngoc Quang the first person who study the application
of graph theory to teaching in general and teaching in chemistry particular. In
1972 he chose graph mathematical methods empirical objects, transform it into
a method of teaching Chemistry, in 1979 he launched to the readers a book
named "Theory of teaching - the science of mind-educate and teaching";
(1981), "graph methodology to solve Chemistry problem "1982, ; "the
transformation of scientific methods of teaching methods"; In 1984 Pham
Tu,“Using graph of lecture contents to teach and learn the chapter Nitrogen –
phosphorus, grade 10, High School”; In 1985, Nguyen Giang Tien "Concept
System and concept formation method in economic geography countries
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syllabus of class 10, 11 high schools”; In 1993, Hoang Viet Anh "Applying
graph diagram approach to teaching Geography for Primary Grades 6 and 8";
In 2004, Nguyen Thi Ban "Using the graph in teaching Vietnamese"; In 2002
Pham Minh Tam with his study "Using graph into teaching geography class
12, high school"…
1.1.2.2. Research use graph theory to teach high school biology
It is possible that the application of graph theory to teaching is not a new

problem for teaching in our country. However, the application of graph theory
to biology teaching only a few studies of Nguyen Phuc Chinh 1999 "Using
Graph to positive cognitive performance of students in the teaching of
ecology”; (2005), " Improving the efficiency of teaching human anatomy
physiology in junior high by applying graph method "; 2006, Tran Van Kien,
“Applying the problem-solving approach in teaching genetics in high school”
Thus, so far the teacher has to use Graph theory taught in many
disciplines and at all levels whether it is a means and a method of effective
teaching. However, with 12 high school Biology Genetics several MSc thesis
research on teaching Graph use in the beginning as a means of teaching, the
author does not go deep research systematically manipulating Graph theory in
teaching Biology Genetics part 12 high just as a means, just as the method.
1.2. Rationale of graph theory in teaching
1.2.1. Concept of graph
- According dictionary English – Vietnamese, Graph (noun) means:
charts, graphs, circuits, networks; Graph (verb) means: drawing diagrams,
graphs, illustrated by graphs; network drawn, draw the circuit; Graphic
(adjective) means: belonging to the diagram, graph belongs to, belongs to the
network circuit.
According to operator theory, graph as a discrete structure consisting of
vertices and edges connecting vertices which are described forms: G = (V, E).
V (Vertices) or (Nodes); E (Edges) or (arc). Edges can be oriented (arc) or
scalar. Graphs are usually drawn as a set of points (vertices) connected by
straight lines (edges). It is considered that E is the set of pairs (u, v) (u, v be two
vertices of V).
1.2.2 The nature of the graph
Graph is defined based on two sets: The set of vertices and set of edges
(arc). Thus, the conditions for the establishment of a graph must have two
elements: a set of vertices and set of edges. Each supply is composed of two
peaks related to each other, the two peaks are not correlated not made a

provision of the graph.
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1.2.3. Scientific basis of Graph classification
1.2.3.1. Sort by mathematical basis
- Graph undirected graph composed of single and multi-graph
- Graph directed graph composed of single and multi-graph
- Graph tree composed binary tree và multi-plant
1.2.3.2. Classification is based on the form and contents of the graph
- Classification according to the degree of perfection in knowledge graph
includes three categories: full graph, with graph, graph dumb
- Sort by content part lesson Genetics Biology includes 12 high schools in
the graph: Graph conceptual content; Graph mechanisms contents; graph process
content, content rule graph
1.2.3.3. Sort By teaching theories include: Graph Graph content and activities
1.2.4. Graph representation
1.2.4.1. Adjacency matrix (adjacency matrix)
Consider a graph G = (V, E) single graph is the number of vertices
(denoted | V |) is n, no loss of generality can be considered the top are
numbered 1,2,3, n. Then we can represent a graph with adjacency matrix
(square) A = [aij] of order n (nxn) has n rows corresponding to the initial vertex
and n columns corresponding to the top end.
1.2.4.2. List edge
In case the graph has n vertices, m edges, we can represent the graph as a
list of edges. In this representation, it lists all the edges of the graph in a list,
each element of the list is a pair (i, j) corresponds to an edge of the graph (in the
case of directed graph, each pair (i, j) corresponds to an arc, the top i, j is the
top end of the arc).
1.2.5. Characteristics of the graph in teaching

1.2.5.1. Systematic, generalized
1.2.5.2. Logica.
1.2.5.3. Intuitive
1.2.5.4. Stability and high transmission
1.2.6. Graph the instructional cycle
1.2.6.1. The Role of graph in instructional cycle
* Graph as a means
Graph means being teacher used to inculcate knowledge, specifying
exactly the content of the teaching process and students use the graph to learn,
to acquire knowledge, gain skills in the learning process. Can visualize the
interaction between teaching purposes and means of graph with teaching and
learning in the following diagram (Figure 1:27).
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Figure 1:27: The relationship between means and teaching purposes in the
teaching process
* Graph as a method
When teachers use the graph to teach, students using the graph to learn then
the graph is the means; also process teachers led student receive lesson content
knowledge, by gradually formed each vertex of the graph now graph characterized
by a method (graph operations).
* The role of the application graph into teaching
Graph helps build well organized lecture; Graph contribute to
improving the quality of teaching and learning in the classroom; Graph
reappear and help students comprehend lecture content better; Graph help
using textbooks effectively in teaching and learning; Graph help thinking
capacity training for students; Use graph student study guide.
1.2.6.2. Role of the graph in teaching genetics section (Biology 12 - High School)
Applying graph has a great role to help structured, codified knowledge

about genetic component facilities and function of the genetic apparatus in the
organizational level from molecules to populations of; building the kind of
knowledge graph concepts, systems of concepts, content graph mechanism,
process, system rules and processes, genetic rule very favorable for teaching,
the organization students are aware proactive, creative and effective.
1.2.7. Principles and conditions for the construction graph content
1.2.7.1. Principles graph construction part of teaching content Genetics( Biology
12 - high school)
1.2.7.2. Conditions constructed graph teaching biology content
1.3. Factual basis of the application of graph theory in teaching Genetics
Part (Biology 12 - high schools)
1.3.1. Survey of teachers teaching
1.3.1.1. Situation use of textbooks in teaching
From the data obtained showed that teachers mainly used textbook guides
students in the study 68.9% and summarize the knowledge content of 72.4%
rather than simple textbook used in decoding scheme; materials analysis,
content processing transform the textbook diagrams.
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Students
(school
activities)
Teachers
(teaching
activities)
Teaching purposes
(knowledge, skills, techniques)
Teaching facilities
(graph and other media)
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1.3.1.2. The utilization graph diagram in teaching biology teacher
Survey results show that the ability to apply graph GV on the processes of
teaching process is very low specific research new materials is 17.2%, 27.6%
reinforced stitching, sewing assessment 13.8%.
1.3.2. Results of student learning about the biology
Results showed that the majority of students just think biology as the
school's tasks (69.6%), student favorite subjects (23.2%), specially there is still
a considerable amount of student is not love favorite biology subject at all.
Percentage of student has moderate learning outcomes and weakness (37.6 %).
Especially student no study habits, knowledge of the system schematically.
Therefore, the analysis and synthesis problems on the basis of inference is weak
Chapter 2: CONSTRUCTION AND USE GRAPH TO ORGANIZATION
OPERATION OF TEACHING THE GENETIC (BIOLOGY 12 - HIGH
SCHOOL)
2.1. Building Graph content teaching section Genetics (Biology 12 - High
School)
2.1.1. Analysis of the structure and contents of the textbook program portion of
Genetics (Biology 12 - High School)
2.1.1.1. Program Content section of Genetics (Biology 12 – high school)
Part five - Genetics (Biology 12 - high school) were brought into the
beginning of first semester and also the first beginning of the second semester
of class 12. Consists of 5 chapters, 23 articles, information will be taught in 23
lessons divided into 5 chapters, presented specific in Table 2.1.
2.1.1.2. The content portion of Genetics (Biology 12 - High School)
Content genetic component, Biology 12 - High School are we structured
into the following graph (Figure 2.1-2.3). From the general graph that we have
the basis to build the graph content detail for each content of thethe lesson and
systematization all of the lesson, the content knowledge of genetics.
2.1.2. Construction graph component content Genetics
Although, graph containing what is the contents so set graph to the

contents part genetics (Biology 12 – high school) essentially consists of a
algorit includes the following basic steps (Figure 2.3).
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Step 1:
Step 2
Step 3: 
!"
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
$%&'(
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2.1.3. Construction graph content for some of knowledge Genetics (Biology
12 - high schools)
Applying graph construction process content to build content part
Genetics (Biology 12 - high school) including:
2.1.3.1. Develop conceptual graph content part genetics (Biology 12 –
high school)
2.1.3.2. Building graph content on mechanisms of biological processes
(Graph mechanisms and processes)
2.1.3.3. Building graph learning content genetic rules
2.1.3.4. Applying for building exercises graph genetic content
Process Common building graph Genetics solve follow 3 steps
Step 1: Analyze all contents (Identify the elements and factors to look
for); Step 2: Prepare the assignment graph; Step 3: Make a graph homework;
2.1.4. The number of graph content genetic section (Biology
- 12 high school) is built
Based on the graph content’s construction process of each knowledge of
genetic section (Biology 12 - high school), we have built some graphs content,
specifically presented in appendix 2. Specific numbers of each type are

presented in table 2.2.
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Table 2.2: Number of graphcontent types in the GENETIC
Orde
r
Group graph content
Numbe
r of
graph
formed
01 Graph
conceptual
content
Content Graph concept reflects the basic
structure of the genetic material at the
molecular level, cells
4
Graph concept reflects the content of signs,
biological phenomena
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Graph reflects conceptual content,
mechanisms and processes of genetic
phenomena and processing equipment, at
the molecular level, cellular level
9
02 Content
Graph
mechanism

s and
biological
processes
Content Graph mechanisms of biological
processes at the molecular level
6
Content Graph mechanisms of biological
processes at the cellular level
2
03 Graph
genetic
content rule
- Genetic rule of Menden 5
- Genetic rule on genes interactions 3
- Genetic rule of genes association 3
- Genetic rule sexual-association inheritance 2
- Genetic rule inherited through the
cytoplasm
2
04 Total 48
2.2. Use the graph to organize teaching activities Genetics sections
(Biology 12 - High school)
2.2.1. The principles used in teaching graph
Do not use a single graph or do not use separately; Avoid formality in the
preparation and use graph; Avoid abusive graph; Graph selectivity filter must
be scientific and objective to ensure pedagogy
2.2.2. Use the graph in teaching Genetics section (Biology 12 - high school)
2.2.2.1. Instruct HS the learning skills to follow the graph method
1. Reading the graph; 2. Translate graph; 3. Independently develop a
graph: This skill requires two small steps; a. Repeat the memory graph is given

by; b. Independently develop a graph content that students do not know its graph.
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* Method of learning in the classroom:
* Method of learning at home;
2.2.2.2. Using the graph method to teach new knowledge
* The level 1: GV organization offering content knowledge, teacher autonomy
graph content order logic of the lesson, students observe to learn how for the
graph to the teacher (Figure 2:13).
Figure 2:13: The process of teaching using graph method as the first level.
* The second level: The teachers develop partially "model" just for part of the
lecture, the rest of the lecture will be done by pupuils follow the model given by
teachs (Figure 2:14).
Figure 2.14: The process of teaching using graph method as level 2
* The third level: students graph established under the guidance of teachers
Step 1
Teachers: From the lesson’s
objectives and content -> GV
guides pupil how to structuralize
contents

Pupils: Studies materials then
find out the key knowledge, core
issue as per GV’s request (find out
vertices or fill contents to vertices
from uncompleted graph or dumb
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graph).

Step 2
Taechers: Monitors and redress
the results of the study group
students
Pupils: Continues to find the
relationship among the key
knowledge, core issues and develop
the assigned graph


Step 3
Teachers: Give comments,
modification recommendation,
supplement, and finalize the
graph.
Pupils: Pupils records the
finalized graph to their notebooks,
read and translate the graph.
Figure 2.16: The process of setting up the graph of students under the guidance
of teachers
* The fourth level: Student study textbooks and set graph content by himself
Step 1
Teachers: From the lesson’s objectives and content -> teacher request
pupils to study textbook, structuralize contents become graph

Step 2
Pupils: Self structuralizes contents, find out key knowledge, identify
vertices and its position, identify arc for each vertices and make graph

content

Step 3
Teacshers: Test the graph prepared by pupils, gives comments,
modification recommendation, supplement, and finalizes the graph.

Step 4
pupils: Finalize his graph as same as the graph given by teachers, read and
translate graph
Figure 2.18: Process deployment graph of students set graph content by himself in
the classroom
When the contents graph seted by himself students to a new study, the steps are as follows:
16
16
Preparaon
at home
Classroom acvies
)
Teachers: 
Students:*"
Teacher:$+","&
$%%-&./
17
+ Preparation;
+ Activity in class: Hours are as follows.
Process as follows (Figure 2:20)
2.2.2.3. Using a graph to review reinforce and improve knowledge
* The first level: GV request HS to read the graph has built-in learning
new knowledge, analyzing, explaining the contents of the vertices and the
relation between the vertices through the arcs to determine how cognitive

knowledge HS gained through the graph content.
* The second level: Teachers uses a graph that has been built in the new
teaching in the past, delete all vertices of the graph and request students to fill
again (graph dumb), or graph missing, ask students complete the missing
vertices, finalize the concept for each content knowledge needed revision.
* The third level: Teachers provide a messy vertices arrangement,
students is suggested to identify these vertices. Starting vertices, main vertices,
sub-vertices, branch-vertices, determine the relationship between the vertices
(means define arcs) from which students can form a graph.
* The fourth level: Develop a general graph from one lesson or some
lessons that the knowledge of closely related
2.2.2.4. Using the graph in checks – assessment
* Using the graph as a tool (means) to test – assessment
- Teachers offer a complete graph, ask students to read the content
contained in a specific path graph interpretation
- Use missing graph doing tests students to determine the missing vertices
and arcs
- Use dumb graph as test students to identify all the vertices, arcs of the
graph refers to a certain content of the lesson, chapter in textbooks.
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17
18
* Using the graph as a teaching method
- Teachers provide vertices extracted from a lesson’s knowledge,
students study and arrange the vertices, make the arcs to create a graph
reflecting the requested research issue
- Provide students content knowledge, request students to identify the
core knowledge, thereby determining the vertices become arcs from which
students should build graph using inductive way.
- From a content knowledge, teacher gives a graph has an inappropriate

number of vertices (vertices false name or false vertices position) students to
study repair to create a graph to bring exact content
* The form of check - evaluation by using graph
The first form: Based on the previous graph indicated the relationship
between knowledge,
The second form: Students replayed content acquired in the graph and
then use ordinary language, express document content textbooks
The third form: Teachers, based on the knowledge students have learned
to answer the following graph that summarizes the content
The fourth form: Ability to independently form a graph.
This form can be expressed in the following level:
The first level: Given a dumb graph, lacking graph. Students study the
textbook to structuralize the content then identify the vertices, the vertices
position and find the adequate words, phrases fit to complete the vertices.
The second level: Partially or fully provide content of lesson, depending
on the educational level of students. Students create structuralize content;
define arcs, the words and phrases appropriate to each vertices, form graph.
2.2.3. Develop criterias for evaluating the proficiency of the skills learned in Graph
2.2.3.1. Principles construction of criterias to evaluate the proficiency level of
students' skills in Graph
2.2.3.2. The criteria were developed to determine the proficiency of the skills
learned in Graph
Based on the Graph theory and general knowledge of biology and
genetics knowledge section in particular, we extract out the tasks associated
with identifiable skills, logical thinking of students in Graph includes basic 6
skills,each skill includes the criteria, each criterion represents a level of skill
achieved, denoted M1, M2, M3, M4. On the basis of these skills are built, we
have determined the criterias to be measured for each different specific skills
are presented in (Table 2.4).
2.3. Some experimental lesson

18
18
19
To deploy experimental pedagogy, learning outcomes assessment Graph
method we have designed some lesson plans in some of the articles of Chapter
1,2,3 genetics. The lesson plans prepared are designed for each level to train
cognitive skills each, from place students to familiarize with the vertex, the
supply of Graph, read Graph, Graph developed verbal and gradually built
vertices, edges, eventually the entire building is complete Graph. Specifically,
our lesson is presented in Appendix 3
CHAPTER 3: RESULTS OF EXPERIMENTAL
3.1. Purpose and principles experimentally
3.1.1. Practical purposes
Implement teaching using Graph as one means, one method to test the
feasibility of the hypothesis that
3.1.2. Experimental methods
- Choose experimental subjects: Choose the experiments; Choose
students experimental; Choose teachers taught experimental;
- Experimental layout: operate parallel the control group class (taught
under control method) and experimental class (taught under experimental
method) in the same school;
- Real-time experiment: Divided in 2 periods performed in 3 year (2010 –
2011; 2011 – 2012; 2012 – 2013).
3.2. Empirical content
Conducting lessons using graph in the research process new knowledge, review,
consolidate, complete knowledge and homework of Genetics, Biology 12 - high
school according to the level as outlined in Chapter 2 of the thesis.
- Experimental practice includes: Type of lessons to become familiar with
experimental methods mapped genetic knowledge; To develop Students’s
cognitive thinking and learning skill; For all experiments the ability to create

knowledge in a post, a program to help students learn how to systematize
knowledge after many lessons; Type experiments applications for all systems in
nature, review
- How to assess: Quantification out of 10 based on results presented
through the construction content graph obtained at the level of the evaluation
criteria and results are analyzed using Excel software to handle statistical
parameters ; m; s ; s
2
C(v%); t
d
; Results are presented from table 3.2 to table 3:14
and charts from Figure 3.1 and Figure 3.6; Qualitative analysis of learning results
achieved through tests to assess the perceived quality of knowledge, thinking power
and the ability to use knowledge after each lesson and reliable knowledge after
finishing some lesson are shown in the synthesis and generalize, systematize
knowledge; Assessment skills, including 6 skills: Skills structured textbook content;
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19
20
Skill determines the type graph of textbook content; Identify the top skills, the
provision of graph; Graph reading skills, according to the sign languages (review
and examination); Skills under the symbol graph translated into prose language
(interview test); Graph building skills content. Each skill is based on the assessment
criteria spread out over the different levels of awareness (M1, M2, M3, M4, ).
Also evaluated to acquire the ability of students through questionnaires
and surveys for students and teachers experiment; the opinion of the expert
ability to apply graph into teaching.
3.3. The experimental results
3.3.1. Learning results of students learn in Graph
3.3.1.1. Quantitative analysis of the experimental results

* Statistical results synthetic the 5 times test of the phase 1 (school year 2010-
2011)
Table 3.3: Distribution of frequency (% fi) - The number of students scoring xi
% of the experimental group class and the control group class synthetic 5 test
times phase 1 (school year 2010-2011)
Plan
x
i
n
3 4 5 6 7 8 9 10
Control 415 2,4
1
9,64 14,4
6
16,87 43,3
7
13,2
5
0
0
Empirical 420 0 7,62 7,14 14,29 40,0
0
29,0
5
1,9
0
0
* Statistical results synthetic the 5 times test of the phase 2 (school year 2011-2012)
Plan

x
i
n
3 4 5 6 7 8 9 10
Control 2100 1,6
7
2,3
8
8,8
1 33,1
39,5
2
14,5
2 0 0
Empirical 2095
0
1,6
7
3,5
8
28,6
4
44,1
5
17,1
8
4,3
0 0,48
20
20

21
* Statistical results synthetic the 5 times test of the phase 2 (school year 2012 – 2013)
Plan
x
i
n
3 4 5 6 7 8 9
10
Control
(ĐC)
2085 1,44 3,93 6,67 31,41 39,62 14,72 2,21 0
Empirical
(TN)
2100 0,67 1,90 3,57 15,91 39,86 30,43 6,09 1,57
* Comparative synthetic results of 3- year study experimental development
showed that:
Quantitative results obtained through the 3 years study of the two empirical
groups and control class, we use the statistical parameters to compare and
draw conclusions about the experimental results as follows (table 3:14).
Table 3.14 Comparison of statistical parameters specific middle class group
empirical class and group control over 2 period (3 years school from 2011 to
2013)
School year Plan N
x

±
m CV (%) d
TN - ĐC
t
d

2010 -2011
ĐC
TN
415
420
6,29
±
0,06
6,81
±
0,06
20,28
17,65
0,53 6,12
2011 – 2012
ĐC
TN
2100
2095
6,50
±
0,02
6,85
±
0,02
15,84
14,22
0,35 11,33
2012 - 2013
ĐC

TN
2085
2100
6,57
±
0,02
7,16
±
0,02
16,61
15,55
0,59 14,87
The results table 3:14 shows:
1 Offsets arithmetic mean (d
TN - ĐC
) between the empirical class and control class
groups of tests over 3 years school were positive specific (0.53, 0.35, 0.59),
suggesting that the empirical group class always achieved higher results
compared with control group class. Results of the 3rd year, the offsets d
TN - ĐC
higher than the before 2 years. This is most likely due to experience teaching
method graph of the participating teachers taught empirical increasingly mature
and improve.
- Arithmetic mean empirical group class increase from year 1 to year 3 in the
order: 6.81; 6.85; 7.16. This result is consistent with our assessment of on.
More later by Graph teaching has helped students with the general method of
thinking better, more accurate than conventional teaching methods. Control
group class, basically stable 6.29; 6.50; 6.57 does not have much difference.
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21

22
This increase may be largely due to the level of the students or teachers
involved teaching better empirical judgments on.
2. The variation (CV%) in grade empirical in 3 school years is always lower
than the grade controls (17.65, 14.22, 15.55). Demonstrate grade results in the
empirical is definitely stable.
3. Testing the reliability of the difference of two average values groups
between the empirical class and class control groups generous inspection td.
we see t
d
are larger than t(
α
)
= 0,05 and increases from 6,12; 11.33; 14.87.
Demonstrate the reliability of the difference of average values plus 2 of TN and
ĐC groups is meaningful.
4. The line frequency Convergence of empirical class groups is always on the
right side compared with control groups class, indicating a high score of more
empirical class groups compared to control.
3.3.1.2. Qualitative analysis (Some reviewers drawn from results of student learning
by graph
About the perceived quality of knowledge, thinking power (particularly systems
thinking) and the ability to apply knowledge: about the knowledge durability of
the students in empirical groups class than that class control groups shown in
the test results. Demonstrate ability to remember the knowledge longer, more
accurate, overall scores tend to stabilize special score pretty, good increase.
Also in control groups class, resulting in a test some knowledge you forget,
there are many errors, the score decreased significantly, particularly was pretty,
good low score; About excitement and the level of positive learning: Students
in empirical class, exciting academic atmosphere, they discussed and

exchanged very positive to learn new content, debate confidently defend their
opinions, even had they also offer questions for the group to solve research
problems still puzzling. In the process of taking steps building graph content,
student interest in learning, research, textbooks, maximize imagination, self-
learning capabilities, self-study. The textbook is an indispensable material in
the learning process.
3.3.2. The results evaluate the skills obtained from learned by graph of
students
* Summary of assessment of student skills by study the graph of the 3 school
year
Table 3:18: Summary of assessment of student skills by study the graph of the 3
school year
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22
23
#
The
skills
Content
criteria
Attai
nmen
t
results
school year
2010
-2011
2011
-
2012

2012 -
2013
1
Structur
ed
content
textbook
s
Read and
summarize the
key
knowledge
from textbook
content
M1
numbe
r of
420/
2505
3240/
12380
3518/
12498
(%) 16,77 26,17 28,15
Abstract part
textbook
(summary
missing some
content)
M2 numbe

r of
1940/
2505
9140/
12380
8980/
12498
(%) 77,44 73,83 71,85
Don’t Read
and
summarize the
content of
textbooks (not
derive key
knowledge
that is
presented as
the textbook)
M3
numbe
r of
145/
2505
0 0
(%) 5,79 0 0
02
Determi
ne the
type of
graph of

textbook
content
Identifying
the right type
of graph
M1
numbe
r of
2480/
2505
12290
12450
/1249
8
(%) 99,00 99,27 99,62
Identify the
wrong type of
graph
M2 numbe
r of
40/2505 90 79
(%) 1,00 0,73 0,45
Not determine
the types
graph
M3 numbe
r of
0/2505 0 0
(%) 0 0 0
03 Identify

the
vertices
Identify the
vertices and
edges of
M1
numbe
r of
420/
2505
2910/
12380
3065/
12498
(%) 16,77 23,51 24,52
23
23
24
#
The
skills
Content
criteria
Attai
nmen
t
results
school year
2010
-2011

2011
-
2012
2012 -
2013
and edges
of graph
graph
Identify the
verticesof the
graph but
misplaced
some vertices
M2 numbe
r of
1870/
2505
8580/
12380
8760/
12498
(%) 74,65 69,31 70,09
Identify
missing some
vertices and
some edges
M3 numbe
r of
175/
2505

890 673
(%) 6,99 7,19 5,38
Not be
determined
the vertices
and the
vertices
(defined
wrong and
missing)
M4 numbe
r of
40/2505 0 0
(%) 1,59 0 0
04
Read the
graph
accordin
g to the
sign
language
s
Accurate
reading graph
M1 numbe
r of
458/
560
2568/
2768

2710/
2780
(%) 81,43 92,77 97,48
Read incorrect
(missing or
incorrect and
provides a
number of
vertices)
M2 numbe
r of
106/560 200 70
(%) 18,57 7,23 2,52
Can not read
(or misread)
M3 numbe
r of
0/560 0 0
(%) 0 0 0
05
Translat
e under
the
symbol
Exactly
translate to
the language
graph
M1
numbe

r of
112/560
680/
2768
740/
2780
(%) 20,00 24,57 26,62
Accurately M2 numbe 302/560 1880/ 1830
24
24
25
#
The
skills
Content
criteria
Attai
nmen
t
results
school year
2010
-2011
2011
-
2012
2012 -
2013
graph
language

to prose
translate the
vertices but
service
lacking or
insufficient,
some of graph
vertices
r of 2768
(%) 53,93 67,92 65,83
Accurately
translate the
vertices but
logic
mistranslated
some vertices
content
M3
numbe
r of
146/560 208 210
(%) 26,07 7,51 7,55
No translation
graph
M4 numbe
r of
0 0 0
(%) 0 0 0
06
Skills

building
graph
content
Establish the
graph enough,
with the
vertices and
the edges
M1 numbe
r of
717/
3010
4960/
14980
5380/
15120
(%) 23,82 33,11 35,79
Established
incomplete
vertices, edges
of graph
M2
numbe
r of
1990/
3010
9860/
14980
9530/
15120

(%) 66,11 65,82 63,41
Establish the
wrong graph
(wrong
position
supply and
lack vertices)
M3 numbe
r of
303 160 120
(%) 10,07 1,07 0,8
The result of the skill level after 3 years of proved experience teaching in the
Graph just as a means, just as methods are developed logical thinking, positive
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