1
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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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)

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

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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”;

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

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

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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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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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

s and
biological
processes
Content Graph mechanisms of biological
processes at the molecular level
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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

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

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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* 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

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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

* 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


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* 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

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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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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#
The
skills
Content
criteria
Attai
nmen
t
results
school year
2010
-2011
2011
-
2012

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

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

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

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

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