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 1 1 2 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 2 2 3 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. 3 3 4 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, 4 4 5 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 5 5 6 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; 6 6 7 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: http://en.wikipedia.org/wiki/, “Graph theory”; http://www.students.ceid.upatras.gr/~papagel/project/contents/htm, “Some graph theory algorithm animations”; http://www.graphtheory.com, 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 7 7 8 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 8 8 9 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. 9 9 10 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). 10 10 [...]... wide to deploy teaching by using the graph as means and methods in all stages in the class in the Biology content other, contributing innovative teaching methods and fostering self-learning capability for high school students 2) In the case of Pedagogy note further training to students the basic skills on the processes build and used graph of the teaching process Especially stages teaching new knowledge... 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... 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. .. purposes of thesis and compare them with the task of research, theses have solved the basic problem: 1 The thesis focus on researching systematizing the rationale analysis concepts, nature, classification, characteristics and the role of mathematical graph to use in teaching - part genetics (Biology 12 - high school) 2 Results of the survey on the use of the Graph, perceived quality of knowledge in general... the part of Genetics (Biology 12 – high school) 4 The thesis also proposes principles, processes deployed graph on the classes according to the level used in the stages of the teaching process in detail: In the stage of learning new knowledge includes 4 levels; review and consolidate knowledge includes 4 complete levels, in the stage of checking evaluation includes 4 form Each level in each the stage... 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. .. present the process used to separate the role of teachers and students in finding knowledge and is implemented as a method for organizing teaching - part Genetics (Biology 12 – high school) towards developing positive thinking,student's creative follow the path inductive and deductive The process of using graph that thesis yet, allows the creation of a series of activities learning and skills to manipulate... 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. .. 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,... showed the effectiveness of using the Graph in teaching genetics section gives high results in student learning and work great in teaching teachers to facilitate the system cultural knowledge through diagrams For students demonstrated in the study results, the passion, excitement maximize learning capacity systems thinking, self-learning ability, self-study student CONCLUSIONS AND RECOMMENDATIONS 1 . 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. 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 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