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MINISTRY OF EDUCATION AND TRAINING HANOI NATIONAL UNIVERSITY OF EDUCATION NGUYEN THI TRUC MINH CONTRIBUTING TO THE DEVELOPMENT OF THE ARITHMETIC TEACHING COMPETENCE FOR ELEMENTARY PEDAGOGY STUDENTS AT UNIVERSITIES Major: Theory and Methodology of teaching Mathematics Code: 9.14.01.11 A SUMMARY OF DOCTORAL THESIS IN EDUCATIONAL SCIENCES HANOI – 2019 THE WORK WAS COMPLETED IN HANOI NATIONAL UNIVERSITY OF EDUCATION Supervisors: Dr Le Tuan Anh Assoc Prof Dr Tran Viet Cuong Reviewer 1: Assoc Prof Dr Cao Thi Ha Reviewer 2: Assoc Prof Dr Nguyen Trieu Son Reviewer 3: Assoc Prof Dr Tran Dien Hien The thesis will be defended before the university council at Hanoi National University of Education, No 136 Xuan Thuy, Cau Giay, Hanoi At 2019 The thesis can be found at: - National library of Vietnam - The library of Hanoi National University of Education LIST OF PUBLISHED PROJECTS OF THE AUTHOR RELATED TO THE THESIS Nguyen Thi Truc Minh, Training the skill in combining cooperative teaching method with teaching method of detecting and solving problems in instructing maths for students of elementary pedagogy, Journal of Education, volume 404, 2017 Nguyen Thi Truc Minh, The reality of developing arithmetic teaching competence for elementary pedagogy students, Journal of Education, volume 427, 2018 Nguyen Thi Truc Minh, Arithmetic teaching competence’s elements of elementary pedagogy students, Journal of Education, volume 429, 2018 Nguyen Thi Truc Minh, Le Tuan Anh, Developing preservice elementary teacher students’ understanding of arithmetic contents and explaining mathematical bases of arithmetic contents in elementary mathematics textbooks through teaching mathematical subjects, HNUE Journal of Science, volume 63, 2018 Nguyen Thi Truc Minh, Training designing skill and organizing arithmetic teaching activities for primary pedagogy students towards developing students’ competence, Vietnam Journal of Education, volume 05, 2018 Nguyen Thi Truc Minh, A number of measures to develop arithmetic teaching competence for elementary pedagogy students, Journal of Education, volume 450, 2019 INTRODUCTION Reason for choosing the topic of the thesis 1.1 Our country's education is in the process of fundamental and comprehensive innovation, transforming an education form imparting knowledge to developing both learners' quality and competence This has set up universities with many challenges to improve the content and teaching methods in the training strategy human resources to meet social needs In particular, improving the content and methods of training skills for students is a central and urgent task 1.2 With the requirement of reforming the education of our country today, teachers in general, elementary teachers in particular are facing difficulties and challenges with changing educational goals, teaching methods are changing from the type of teaching that focuses on the role of teachers and teaching activities focusing on the role of students and learning activities Newly graduated elementary teachers have not yet met the requirements on teaching and mathematics teaching competence is still limited Some teachers have not mastered the basic knowledge of mathematics in primary, even some teachers are not proficient in performing complex calculations and solving typical problems in grades and 1.3 In primary school subjects, mathematics is very important, it takes up most of the time in the teaching curriculum in primary school The knowledge and skills of elementary mathematics have many applications in life, which are essential for workers and for other subjects in primary and secondary education In the elementary mathematics curriculum, arithmetic knowledge play the mainstream role, is the basis for teaching the remaining knowledge circuits 1.4.Through finding out the literature, we find that there is a number of constructions focusing on studying of the training and developing of professional competence for elementary teachers However, these works focus on fostering and developing the teaching competence of elementary teachers rather than focusing on developing this competence for elementary pedagogy students in the training process In addition, there have been many works studying on training professional skills and developing mathematics teaching competence for students at teacher training schools, but most of them focus on developing teaching competence for mathematical pedagogy students at junior and senior high schools Until today, according to the literature we have known, no work has studied on developing arithmetic teaching competence for elementary pedagogy students Therefore, the researched results are not enough to meet the needs of society, the change of content and educational programs From the above reasons, we choose the problem: “Contributing to the development of the arithmetic teaching competence for prospective elementary teachers at universities” for our research topic Research target Determining arithmetic teaching competence’s elements need to develop for elementary pedagogy students and propose pedagogic measures to develop arithmetic teaching competence for elementary pedagogy students at universities, contribute to improve the quality of elementary teacher training Research task - Researching the theory on issues related to developing mathematics teaching competence and arithmetic teaching competence for elementary pedagogy students at universities - Researching the reality of developing mathematics teaching competence and arithmetic teaching competence for elementary pedagogy students at universities - Proposing measures to develop arithmetic teaching competence for elementary pedagogy students in the formal training process at universities - Pedagogy experiment to test the feasibility and effectiveness of the proposed measures Research subject and object - Research objects: Theory and reality of arithmetic teaching competence, the process of training teaching skills for students, the process of training elementary pedagogy students at universities - Research subjects: The process of developing arithmetic teaching competence for elementary pedagogy students at universities Scientific hypothesis If we clearly determine arithmetic teaching competence’s elements need to develop for elementary pedagogy students and propose, perform pedagogic measures to develop those competences, arithmetic teaching competence of elementary pedagogy students at universities will be developed Research method In order to carry out the above research tasks of the thesis, we use the following research methods: - Theoretical research method - Methods of observation, investigation - Pedagogy experimental method - Case study method The new contributions of thesis and scientific arguments will be presented - Determining arithmetic teaching competence’s elements need to develop for elementary pedagogy students at universities - Proposing pedagogy measures is feasible and effective in developing arithmetic teaching competence for elementary pedagogy students at universities The structure of the thesis Besides the introduction, conclusion, the thesis consists of three chapters: Chapter The theoretical and practical basis on developing arithmetic teaching competence for elementary pedagogy students at universities Chapter Pedagogy measures to develop arithmetic teaching competence for elementary pedagogy students at universities Chapter Pedagogy experiment Chapter THE THEORETICAL AND PRACTICAL BASIS ON DEVELOPING ARITHMETIC TEACHING COMPETENCE FOR ELEMENTARY PEDAGOGY STUDENTS AT UNIVERSITIES 1.1 Overview of Research Issues 1.1.1 Overseas research situation In the world, the issues of teaching skills and teaching competence have been studied for a long time Starting in the 20s of last century, in the Soviet Union and Eastern Europe countries had many works researching on teaching skills for pedagogy students By the 1960s, this problem was deeply studied and became a solid theoretical system By the 1970s, educational researchers in the Soviet Union and Eastern Europe continued to study on organizing scientific labor and optimizing the teaching process In the Western countries and other countries such as Canada, America, Australia and so on education researchers are especially interested in organizing to train teaching skills for students They based on the achievements of behavioral psychology and functional psychology to organize training for students these skills with the time of practicing is distributed more than that of theory For typical example such as the opinion of authors: J Watson (1926), A Pojoux (1926), F Skinner (1963), “The process of learning” of J.B Biggs and R Telfer (1987), “Beginning teaching” of K Barry and L King (1993) and so on In the United States, since the 1970s, Ohio National University had studies on constructing modules to train professional-technical teacher, the results had 600 skills to train technical-professional teacher were suggested At Stanford University, based on the basic American educational background, the research team of Phidenta Kapkar proposed five technical groups of teachers while teaching in the report "Science and art of training the teachers" Since the early 1930s, American educational researchers and managers have begun to study about the necessary competences of teachers to succeed in teaching and education with the work of authors such as O’Day, McDiarmid, Clevenger-Bright, Shulman and so on With the specificity of Mathematics, there were the knowledge models of the authors such as the model of teaching mathematics of Ball; at Cambridge University, researchers gave “The Knowledge Quartet”; Petrou and Goulding with “The knowledge model of teaching mathematics ” and so on In 2007, National Council of Teachers of Mathematics proposed seven specific standards of mathematics teachers In the Asia-Pacific countries, the role and task of forming pedagogy skills have also been identified in the workshop about "Workshop on renovation of the training and retraining of teachers of the Asia-Pacific countries" organized by APEID the in Seoul (Korea) The reports of the workshop identified the importance of forming knowledge and pedagogy skills for students in the training process The scientists confirmed that “Professional knowledge is the basis of pedagogical art but only presents in the system of pedagogy skills” 1.1.2 Domestics research situation Before 1975, the basic research on profession training for teachers had not yet, teachers' skills were only mentioned in psychology books and pedagogy books written based on the textbooks of the former Soviet Union Since 1975, improving quality teacher training have been interested more and more, many works studying on this issue have begun to appear From 1990s, research trends on teaching competence and teaching skills have become a matter of great concerned in our country There is a number of theses and topics of the authors such as Le Thi Nhat, Nghiem Thi Phien, Nguyen Canh Toan and so on At universities, studying on developing teaching competence and teaching skills for students were reflected in ministerial-level topics and theses of the authors such as Nguyen Huu Dung, Trinh Thi Quy, Tran Anh Tuan, Phan Thanh Long and so on These topics and theses relatively presented the system of related theoretical issues, found out the reality of forming pedagogy skills and training of teaching skills for pedagogy students From that they proposed, checked and took over measures and process training teaching skills for students to improve the quality of the forming and developing of suitable teaching skills for pedagogy students About Teaching Theory and Methodology of Mathematics, there were some theses studying on developing some teaching skills and teaching competence for students of authors such as Pham Van Trao, Nguyen Chien Thang, Tran Viet Cuong, Do Thi Trinh and so on The authors focused on to study theoretical and practical issues in developing teaching skills, job skills, teaching competence, and mathematics teaching competence for mathematics pedagogy students From that they proposed measures to develop teaching skills and teaching competence for those students through organizing to teach a subject at university, contributing to improve the quality of training high school mathematics teachers On training pedagogy profession and developing pedagogy competence for elementary pedagogy students, there were theses of authors such as Nguyen Thi Chau Giang, Pham Van Cuong, Do Thi Phuong Thao, Pham Thi Thanh Tu and so on In addition, there were many theses focused on studying to foster and develop teaching competence for elementary teachers of authors such as Nguyen Van Tan, Truong Thi Thu Yen, Hoang Cong Kien and so on These theses studied fostering and training for elementary teachers how and procedure to apply a new teaching method to teach at primary school to improve elementary teachers' teaching competence to improve the quality of teaching at primary school 1.2 The content arithmetic in elementary mathematics 1.2.1 Generalizing history of the formation and development of natural number set 1.2.2 Generalizing history of the formation and development of rational number set 1.2.3 The algebraic structure of number sets 1.2.4 Characteristics of the arithmetic content in elementary mathematics curriculum - Arithmetic content is arranged expanding and developing in accordance with number rounds, gradually increasing through each stage, knowledge in the former class is a premise to help students learning knowledge in the latter class - Arithmetic content in textbooks is built in combination between history and science - Arithmetic is the foundation for teaching other knowledge circuits and opposite - Arithmetic in elementary mathematics is inextricably linked with reality, with the development of elementary students' mathematics competence (mathematical thinking and arguments competence, mathematical modeling competence and so on) 1.2.5 The goal of teaching arithmetic in primary schools 1.3 Characteristics of mathematics teaching and learning in primary school 1.3.1 Cognitive characteristics of elementary students 1.3.2 Mathematics learning characteristics of elementary students - Thinking still depend on acting on objects and external events - Elementary students have ability to be aware of the invariant things and form preservation concept, can distinguish qualitatively and quantitatively - Elementary students of the later classes have progress in spatial awareness compared to students of the former classes - Elementary students initially have the ability to analyze, synthesize, abstract, generalize and simple forms of reasoning and judgment However, the development of these abilities is not evenly - Mathematical concepts are formed through abstraction, generalization but cannot only be based on perception because mathematical concepts are also the result of particular thinking manipulation - Elementary students often judge according to their own feelings so reasoning is often absolute In fact, it is difficult for them to accept assumption hypothesis 1.3.3 Characterictics of mathematics teaching in primary school - Elementary teachers need to master the development of students' thinking, correctly appreciate the existing ability and potential ability of students to have appropriate pedagogy measures - Although the psychological view is the mainstream view, it is necessary to realize the role of the logical view and the mathematical view - Can not teach mathematics but not master the characteristics of Mathematics, not master the basic and necessary mathematical knowledge related to the knowledge needed to teach - Limit the use of mathematical terms and symbols Abstract mathematical knowledge is presented through visual images and expressed in the way of children, not using mathematical terminology or symbols - Mathematical concepts are described by description and are not defined Mathematical properties are not proved rigorously and logically, are explained and illustrated with examples and reasoning - The knowledge and skills are formed mainly by practicing and are regularly reviewed, consolidated, developed and applied in daily life 1.3.4 Mathematical compentence of elementary students 11 each other Each component competence is described through criteria and evaluated in accordance with four levels from low to high The research results of theory and reality are an important premise to us to propose pedagogy measures to contribute developing elementary pedagogy students’ arithmetic teaching competence and improving the quality of training elementary teachers Chapter MEASURES DEVELOPING ARITHMETIC TEACHING COMPETENCE FOR ELEMENTARY PEDAGOGY STUDENTS AT UNIVERSITIES 2.1 Orientations to construct measures developing arithmetic teaching competence for elementary pedagogy students - Measures must be consistent with theory - Measures have to fit with reality and be feasible - Measures have to be in accordance with the requirements of the teacher career standards, orient towards the renovation of the curriculum and textbooks - Measures have to be in accordance with the component competences of the arithmetic teaching competence that thesis determined to develop for students 2.2 Pedagogy measures to develop arithmetic teaching competence for elementary pedagogy students 2.2.1 Measure group: Developing competence to understand issues related to arithmetic content in elementary mathematics 2.2.1.1 Base to propose the measure group 2.2.1.2 The purpose of the measure group 2.2.1.3 Measure Teaching the subject “Advanced Mathematics” orient towards connecting with arithmetic content in elementary mathematics textbooks In teaching advanced mathematics, lecturers can clarify the relationship between advanced mathematics content and arithmetic content in elementary mathematics textbooks through the following ways: - Indicating the representation of the concepts and properties of advanced mathematics in arithmetic content - Using the concepts of advanced mathematics to explain the constructing view and mathematics basis of arithmetic knowledge - Applying the knowledge of advanced mathematics to orient finding the answer of arithmetic problems - Using the knowledge of advanced mathematics to create new problems 12 2.2.1.2 Measure Organizing teaching the subject “Advanced Mathematics” by seminars focusing on contacting with arithmetic content Lecturers can organize teaching Advanced Mathematics for students by seminars according to the 4-step process as follows: Step Preparing The lecturer and students perform the following tasks: - Students self-divide into groups appropriately, then each group chooses a leader and a secretary - The lecturer gives seminar topics - The lecturer arranges for students to select topics, discuss contents that will be implemented (focus on establishing the relationship with arithmetic content in elementary mathematics textbooks) and set the working principle of the group - The lecturer suggests content structure and presentation form, supplies materials or guides students looking for materials - The lecturer gives evaluation criteria Step Writing presentation Each group of students performs the proposed tasks such as assigning tasks, making an outline, studying document, discussing, writing a presentation and so on in accordance with the working principle of the group Step Reporting, discussing The lecturer arranges for students reporting and discussing no more than periods per topic - Each group sends a representative to report the research results of the group - When the student completes the report, the lecturer organizes for students discussing and commenting - Finally, the lecturer comments the results, adds and expands as necessary, summarizes the knowledge gained (the knowledge of advanced mathematics) Step Evaluating Students' regular test scores is assessed through students' activities during the seminar about the aspects such as the research results of the group, the form of presentation, handling situations, answering questions from teachers and other groups, attitudes and so on 2.2.1.3 Measure Organizing small learning projects on the relationship between the knowledge of advanced mathematics and that of elementary arithmetic through teaching the subject “Advanced Mathematics” Lecturers can integrate small learning projects into the teaching process of advanced mathematics according to the following basic stages: 13 (1) Preparating stage: Preparation may take a week or more depending on the condition of the lecturer and students and necessary knowledge that students must have before the project starting The lecturer performs the following tasks: - Finding out students about aspects such as competence, attitude, learning awareness and so on - Dividing group: The lecturer need to study how to divide group scientifically and reasonably Each group should have from to 10 students Then, the lecturer instructs students dividing each member’ s task in the group in accordance with the competence and forte of them - Analyzing the relationship between advanced mathematics and elementary arithmetic to determine the topics of project and students' tasks - Anticipating facilities, materials, resources for learning - Building a plan to evaluate (2) The stage of planning and performing project The lecturer selects appropriate time, spend periods, before the evaluating stage about weeks The lecturer and students perform the following tasks: - The lecturer arranges for the groups selecting topics, defining objectives and content and planning to implement learning tasks - Students implement works in accordance with the plan in self-learning time (3) The stage of reporting product and evaluating project The lecturer spends from to periods before the end of advanced mathematics The lecturer and students perform the following tasks: - The groups submit their products to the lecturer - The lecturer arranges for students reporting the research results of each group, commenting, discussing and complementing each other - The lecturer comments the points need to be adjusted, revised, supplemented and finalized, evaluates the achieved results against the defined objective 2.2.1.4 The conclusion of the measure group 2.2.2 Measure group: Creating arithmetic teaching potential for students 2.2.2.1 Base to propose the measure group 2.2.2.2 The purpose of the measure group 2.2.2.3 Measure Training calculation teaching skills for students through teaching the subject “Mathematics Teaching Methods” The lecturer can spend periods in Mathematics Teaching Methods specific subjects to implement the following contents: (1) Training the teaching skills of mental calculation 14 The lecturer can spend periods to organize a seminar as follows:  Preparing seminar: The lecturer asks students listing mental calculated forms and corresponding calculated method in accordance with elementary students’ cognitive level in each stage  Performing seminar: The lecturer organizes students presenting the contents prepared With each type of mental calculation that students give, the lecturer organizes students discussing and drawing out the best mental calculated method and the best way to teach for elementary students (2) Training the teaching skills of calculated techniques The lecturer can spend periods to organize a seminar as follows:  Preparing seminar: - Students divide themselves into groups appropriately, then each group elects a group leader and a secretary - The lecturer introduces topics (addition, subtraction, multiplication and division in elementary mathematics teaching) In each topic, the lecture requires students to perform the following contents: presenting the decimal structure of natural numbers, the mathematical basis of the operation, explaining how to build and presenting the computational technique of the operation on natural numbers written in decimal system, the forms of calculations that elementary students often have trouble learning mathematics, selecting the lesson contains that forms to design teaching activities - The lecturer organizes a lottery for the group leaders choosing the topics - After selecting a topic, each group of students will discuss and perform tasks in their self-study time  Performing seminar: The lecturer arranges the groups presenting the contents prepared For each topic, the lecturer organizes discussing and commenting on the contents to draw out appropriate teaching methods for selected calculation forms 2.2.2.2 Measure Creating the teaching potential of solving arithmetic mathematics for students through the subject “Solving elementary mathematics” In this measure, the lecturer can spend periods in the subject “Solving elementary mathematics” to organize seminar the following contents: (1) Systematizing the forms of arithmetic problem  Preparing seminar: students perform the following tasks in their self-study time: - Classifying problem forms: Students rely on arithmetic problems in textbooks to identify, call the name of the problem form, and systematize problem forms - Describing the characteristic of problem forms: For each problem form, students describe its characteristics (conditions and requirements) or its general 15 problem, present how to solve it, present how to teach elementary students to solve it, systematize the common mistakes of elementary students when they solve it  Performing seminar: The lecturer arranges for students to present and discuss the contents prepared Then, the lecturer draws out the results of the problem forms (characteristics, solution, the common mistakes of elementary students when solving) (2) Arranging for students to find out the causes and correct the common mistakes of elementary students when solving arithmetic problem The lecturer arranges for students to find the causes and correct the common mistakes of elementary students when solving arithmetic problem by giving specific situations (or problems), asking students to discuss and find the causes and suggest how to correct the mistake of elementary students Example 2.8 When performing the calculation 396 + 25, there was an elementary student did as follows:  396 25 646 Finding the mistake and wrong cause of the elementary student and giving how to correct the mistake Students’ answer: - The elementary student placed the digits of the terms not in line and column leading to the wrong result - The wrong cause: The elementary student did not know how to arrange and perform calculations, did not understand number structure - Way to overcome: + Asking the elementary student to test the result of the calculation by performing a reverse calculation, so that he knows that he calculated wrong + Asking the elementary students to present the calculating rule of the addition The teacher can analyze (or ask him to analyze) the structure of numbers 396 and 25 to help him to understand number structure + Asking the elementary student to say the way he did so that he recognizes the cause of the mistake + Asking the elementary student to again the calculation in accordance with the stated above rule carefully + The teacher need attend to help elementary students having habit checking the results after calculating 16 2.2.2.2 Measure Arrange for students to design situations, questions, exercises in elementary arithmetic teaching through the subject “Training Pedagogic Professions” Through the subjects “Training Pedagogic Professions”, the lecturers arrange for students to practice the following contents: (1) Designing reality situations in arithmetic teaching The lecturer arrange for students to design reality situations in arithmetic teaching by giving specific contents and asking students to design reality situations to teach that Example 2.15 Asking students to design motivational situations for elementary students to learn the lesson “Reducing fractions” The designed situation as follows: An and Binh have the following comments: 10 An: “fraction and fraction are equal” 15 10 Binh: “fraction and fraction are not equal” 15 Finding out who are right? (2) Constructing and using questions in arithmetic teaching Before students are trained to construct and use questions in arithmetic teaching, students were equipped the knowledge of constructing and using questions in teaching The lecturer can organize seminars for students including the following steps: - Step The lecturer gives a situation (a situation can be a lesson, an exercise and so on), selects the type of question and asks students to design questions to teach the situation - Step Students design questions as required, the lecturer records the questions on the board - Step The lecturer and students comment and evaluate the above designed questions to choose the most appropriate question (3) Designing reality problems in arithmetic teaching With the characteristics of arithmetic content in elementary mathematics curriculum, we only train students to design reality problems to reinforce necessary calculation skills in daily life for elementary students  Introducing to students the practical problem designing process: - Step Defining the designing goal: Whom are the problems designed for? What knowledge or skills of elementary students will be reinforced? 17 - Step Selecting objects, context and data: The situation of the problem must be close to elementary students' daily life and relate to their need, their family, society, school and so on; the data must be consistent with reality - Step Presenting the problem - Step Solving the problem to check the result and adjust  Arranging for students to practice designing reality problems: The lecturer gives specific requirements and asks students to rely on the above process to design the problem Example 2.22 Designing a problem help elementary students to train adding skill, (no remember) subtracting skill in the range of 100 and help them to understand when addition and subtraction are used The implementing results of students: - Step Defining the designing goals: Designing a problem to help 1st grade students to train adding skill, (no remember) subtracting skill in the range of 100, help them to understand when addition and subtraction are used - Step Object: candies Data: numbers in the range of 100 Context: right in the classroom - Step Presenting the problem Lan has 23 candies, Hue has 56 candies Ask: a How many candies both of them have? b Who's more candies? How many are more? - Step The problem has data and context fit with the knowledge level of 1st grade students 2.2.2.4 The conclusion of measure group 2.2.3 Measures: Training students to apply the knowledge of teaching methods 2.2.3.1 Based on proposing group of measures 2.2.3.2 The purpose of the measure group 2.2.3.3 Measure Training students to design, organize arithmetic teaching activities through teaching the subjects of “Mathematics Teaching Methods” In this measure, with periods (2 periods in the subject Mathematics Teaching Methods, in the subject Training Pedagogic Professions), the lecturer can train students to design and organize arithmetic teaching activities oriented towards the development of learners’ competence as follows: (1) Providing necessary knowledge for students Before training, the lecturer provides materials for students to self-study and clarify the following issues: - Elementary Mathematics contributes to develop elementary students' 18 competence - The characteristics of designing lesson oriented towards the development of learners’ competence - Teaching methods are suitable with teaching oriented towards forming and developing learners' competence - The basic principles of mathematics teaching oriented towards the development of elementary students' competence (2) Training for students to design, organize arithmetic teaching activities oriented towards the development of elementary students’ competence i) The training process Step Researching the curriculum and contents of lesson, learners Students perform the following tasks: - Researching the content of elementary mathematics curriculum carefully, understanding the level of knowledge and skills of arithmetic content that elementary students must attain - Researching the content of the lesson will be taught, finding out the relation between its content and the content of the lesson before it and that of the lesson after it in the same topic, determining the quantity of knowledge elementary students must attain when they learn the lesson, determining the mathematical basis of teaching content and the intent of textbooks - Identifying the ability to meet cognitive tasks of elementary students: identifying their cognitive and psychological characteristics, identifying their attitudes, knowledge and skills, anticipating their difficulties and advantages when they learn the new knowledge Step Determining the aim of the lesson When defining the aim of the lesson to competence-developed teaching, the lecturer requires students not only identifying knowledge and skill goals, but also identifying competences which can be formed and developed for learners through the content of the lesson Step Selecting teaching methods, teaching means and teaching forms The lecturer guides students based on the content and objectives of the lesson, cognitive characteristics of elementary students, characteristics of teaching methods to choose teaching methods, teaching means and teaching forms appropriately Step Designing, organizing teaching activities The lecturer guides students to the following tasks: - Determining the logical sequence of the lesson to have idea to construct teaching activities 19 - Thinking how to form and develop the components of mathematical competence for elementary students through teaching activities - Focusing on learners' activities, elementary students' knowledge and skills to define necessary learning activities to get learning results as expected - Deploying specific teaching activities: Completing the design of small activities, the operations of both teachers and elementary students in each major teaching activity of the lesson Step Evaluating and adjusting - The lecturer arranges for students to present their research right in class The students of the class comment on the following criteria: + Accurateness, logicality, science, clarifying the main content of the lesson; + Compatibility between teachers' activities and elementary students' activities; + Elementary students have opportunity to experience in order to develop their necessary skills and competences; + The effectiveness of teaching activities - The lecturer comments the points need to be adjusted and revised, evaluates the results of teaching activities designed by students - Students revise their design based on the lecturer’s comments and other students’ comments, and then return it to the lecturer ii) Organizing the training The training is conducted after students have been learned the teaching method of specific contents and supplemented with the necessary knowledge The training is performed as follows: - Before students practicing, the lecturer guides students to design and organize the competence-developed teaching activities of an arithmetic lesson as a sample - The class is divided into four groups, each of which selects an arithmetic lesson to design and organize teaching activities of the lesson in accordance with the four steps 1st, 2nd, 3rd and 4th of the above process - Arranging for students to present their design results, then commenting and evaluating the results (the step 5th of the above process) 2.2.3.4 Measure Training the skill in combining teaching methods for students In the content of this thesis, we train the skill in combining the cooperative teaching method with the teaching method of detecting and solving problems in elementary arithmetic teaching for students The steps of combining the cooperative teaching method with the teaching method of detecting and solving problems in teaching: - Step Organizing to form groups: The teacher divides learning groups (each 20 group has from to learners) depending on the requirements of each group and the teacher’ s pedagogical ideas, and elects the group leader of each group - Step Creating problems: The teacher creates a problematic situation; learners detect the problem that need to be solved, state the problem and set goals to solve it - Step Discussing in group, solving the problem: The teacher determines tasks and guides how to work for each learning group The groups discuss, analyze the problem and unify solution to solve the problem Learners independently solve the problem in accordance with the solutions discussed and then converse together to unify the overall working results of the group The teacher observes and assists the groups when necessary - Step Conclusion: The groups report their result; the teacher evaluates and comments the results and then makes a general conclusion In the process of training pedagogical skills for students, after all students are trained teaching skills such as lesson preparing skills, lecture implementing skills and so on, the lecturer can train the skill in combining the cooperative teaching method with the teaching method of detecting and solving problems for students in accordance with stages as follows: a) Stage Preparing: - Arranging for students to understand and master the concepts, teaching process and related issues of the cooperative teaching method with the teaching method of detecting and solving problems (the lecturer can also integrate this understanding in the teaching process of the subject Mathematics Teaching Methods) - The teaching evaluation card: the lecturer designs the card in fields that are teaching skills and the content of teaching b) Stage Training additional skills In order to combine the cooperative teaching method with the teaching method of detecting and solving problems in teaching, students need have skills: forming group skill, the skill in organizing group activities, and so on At this stage, the lecturer trains students to help them to achieve these skills c) Stage 3: Training the skill in combining the cooperative teaching method with the teaching method of detecting and solving problems in teaching After completing the above phases, the lecturer arranges to train the skill in combining the cooperative teaching method with the teaching method of detecting and solving problems for students in the following steps: - Step Planning teaching: Arranging for students to choose the appropriate lesson through analyzing the content and requirements of each lesson and basing on 21 the characteristics of the teaching methods After that, the lecturer arranges for students to make teaching plans for the selected lessons in accordance with the steps presented above - Step Teaching: Students teach the lesson prepared The teaching take place with the participation of the lecture and other students, these students play a role both as participants and learners - Step Evaluating the results: The lecturer and other students analyze, discuss and evaluate the advantages and disadvantages of the teaching-student in accordance with the teaching evaluation card to draw out conclusion and appropriate behavior in order to teach more effective The lecturer need to guide the criteria for students clearly so that students only focus on the suggested criteria when assessing 2.2.3.5 Measure Arranging for students to converse, discuss on regular assessment situations in arithmetic teaching through the subject “Mathematics Teaching Method” The lecturer can spend periods in the subject “Mathematics Teaching Method” to perform the following contents: (1) Introducing to students the process of regular assessment in teaching - Step Determining the assessment content - Step Selecting assessment method and evaluating - Step Stating comments (2) Arranging for students to converse, discuss on regular assessment situations The lecturer arranges for students to converse and discuss on assessment situations as follows: asking students to identify the assessment content and anticipate the assessment method of the specific lesson selected; then the lecturer gives students to watch a video the teaching of the lesson and asks students to observe the progress of the teaching, record the teacher's assessment; lastly, the lecturer arranges for students to converse and analyze the teacher’s evaluating method to learn the teacher's experience THE CONCLUSION OF CHAPTER On the basis of theory and reality, in this chapter we clarified directions to propose pedagogy measures From that, we proposed 03 measures groups including specific pedagogy measures to develop arithmetic teaching competence for students For the purpose of developing arithmetic teaching competence for students, the proposed measures are closely linked and used in combination in the teaching process of the subjects on Mathematics and Mathematics Teaching Methods Each measure is implemented through one or two subjects in accordance with the teaching plan of the primary education program in universities 22 Chapter PEDAGOGY EXPERIMENT 3.1 The purposes of pedagogy experiments We organized the pedagogy experiments to aim the following basic purposes: - Testing the scientific hypotheses of the thesis through the teaching reality - Testing and evaluating the feasibility and effectiveness of the pedagogy measures were proposed 3.2 The content of pedagogy experiments We organized pedagogy experiments at Dong Thap University Based on the curriculum and content of the elementary pedagogy, we experimented the following contents: (1) Equipping the mathematics basis of the arithmetic content in elementary mathematics textbook for elementary pedagogy students through teaching the subjects “Basic Mathematics 1” and “Basic Mathematics 2” (2) Training students to systematize arithmetic problem forms and their solving methods in elementary mathematics, find out causes and how to overcome the difficulties and mistakes of elementary students in arithmetic learning (3) Training students to design, organize arithmetic teaching activities oriented towards the development of learners’ competence (4) Training students to create situations, questions, reality problems in elementary arithmetic teaching (5) Training students to evaluate the learning process of elementary students in elementary arithmetic teaching 3.3 Tools to evaluate the result of the pedagogy experiments We evaluated qualitative and quantitative the results of each pedagogy experiment as follows: - Qualitative assessment: We relied on observations, interviewed lecturers, elementary teachers and students and case-study to further clarify the research problem - Quantitative assessment: We used the T-Student test to evaluate the effectiveness of pedagogy experiments 3.4 The first experiment 3.4.1 Organizing experiment - The purposes of the experiment: Testing the feasibility and effectiveness of the measures 5th - The content of the experiment: the second content - The subject of the experiment: 70 second-year students (36 students in the experimental class and 34 students in the control class) - Organizing experiment: The experiment was performed on 12/2015 3.4.2 The result of the experiment 23 3.4.3 Analyzing the result of the experiment 3.5 The second experiment 3.5.1 Organizing experiment - The purposes of the experiment: Testing the feasibility and effectiveness of the measures 6th, 7th and 9th - The contents of the experiment: the contents 3rd, 4th, 5th - The subject of the experiment: We continued using the selected subjects in the second time - Organizing experiment: + From 02/2016 to 5/2016: experiment in the subject “Elementary mathematics teaching method B” + From 04/2016 to 06/2016: experiment in the subject “Training pedagogical Profession 2” 3.5.2 The result of the experiment 3.5.3 Analyzing the result of the experiment 3.6 The third experiment 3.6.1 Organizing experiment - The purposes of the experiment: Testing the effectiveness and feasibility of the measures 1st and 2nd - The content of the experiment: the first content - The subject of the experiment: 94 first-year students (47 students in the experimental class and 47 students in the control class) - Organizing experiment: + From 9/2016 to 12/2016: Experiment in the subject “Basic Mathematics 1” + From 02/2017 to 5/2017: Experiment in the subject “Basic Mathematics 2” 3.6.2 The result of the experiment 3.6.3 Analyzing the result of the experiment 3.7 Case study To provide a basis for the assessment of the effectiveness and feasibility of the proposed pedagogy measures, we selected 02 students in the experimental class to observe Students were selected were Nguyen Phan Thuy Quynh and Ca Thi Bich Tram THE CONCLUSION OF CHAPTER In Chapter 3, we presented some experiments to illustrate and verify the effectiveness and feasibility of some pedagogical measures proposed We were divided into experiment times, each time preformed different contents and were evaluated in both qualitative and quantitative aspects In addition, we also selected 02 24 students in the experimental class to conduct case-study The experiments achieved some positive results: - The results of the first experiment showed that students grasped the solution method of elementary arithmetic problem forms, had the necessary skills in mathematical problems solving teaching (the skill in solve problems, the skill in analyzing causes and arranging for elementary students to overcome mistakes when solving arithmetic problems) - The results of the second experiment showed that students known how to design practical situations, owned the knowledge of questions and known how to use questions in teaching appropriately Students understood the process of designing practical problem and known how to design practical problems to supplement into the system of exercises for elementary students Students could design and organize competence-developed teaching Students understood how to evaluate by comments and known making specific judgments attaching reasons and directions to support elementary students, known how to motivate and encourage elementary students - The results of the third experiment showed that the teaching method of the subjects Advanced Mathematics as proposed helps students to understand the viewpoint of producing arithmetic content in elementary mathematics curriculum and own the skill in determining mathematics base and program analyzing skills Thereby, we can conclude that the scientific hypothesis of the thesis has the scientific basis, the proposed measures are effective and feasible CONCLUSION AND RECOMMENDATIONS CONCLUSION Through the research process, the thesis had achieved the following main results: - Systematically mentioning the concepts, theoretical issues and previous studies related to the research direction of the thesis, clarifying the structure of teaching competence and elementary teachers’ mathematics teaching competence, clarifying the characteristics of teaching and learning arithmetic at primary - Clarifying elementary pedagogy students’ arithmetic teaching competence including component competences and giving some criteria to evaluate elementary pedagogy students’ arithmetic teaching competence - Conducting survey and analyzing to determine the reality of developing elementary pedagogy students’ arithmetic teaching competence at some universities - On the basis of theory and reality, the thesis clarified directions to propose pedagogy measures From that, we proposed 03 measures groups including specific 25 pedagogy measures to develop arithmetic teaching competence for students Examples were presented in the content of measures to illustrate how to implement pedagogy measures - Pedagogy experiments were conducted times for some proposed pedagogy measures Experimental results were evaluated in qualitative and quantitative methods, and at the same time, used the results of case-study to prove the correctness, rationality and feasibility of pedagogy measures The results of pedagogy experiment showed that the pedagogy measures affected the stages of the training process and created a favorable pedagogy environment to develop arithmetic teaching competence for elementary pedagogy students - There were some articles published in prestigious professional journals The content of the articles is closely related to the content of the thesis The above results initially proved that the scientific hypothesis of the thesis is acceptable, the purpose and mission of the thesis had been completed RECOMMENDATIONS Universities need to reasonably distribute the duration of the modules in the program of elementary education training, pay attention to increase the time to train professional skills for elementary pedagogy students, strengthen facilities, classrooms and practice rooms for the students, create a close relationship with primary schools because these are the best environments to develop teaching competence for the students and are the places that most clearly reflects the output result of the elementary education program Lecturers need to properly recognize the importance of developing arithmetic teaching competence for students, their own role and responsibility in the developing of the competence for students Besides training basic teaching skills for students, lecturers need to pay attention to train for students other skills such as the skill in determining mathematical basis, the skills in designing situations and practical exercises and so on Lecturers need to pay attention to contact the content of Advanced Math with that of elementary arithmetic Students must be properly aware of the importance of developing arithmetic teaching competence for themselves, understand the role and relationship of the modules of Mathematics and Mathematics Teaching Method with the development of developing arithmetic teaching competence Students must invest their effort and time to study and practice seriously, must take most of the time of pedagogy practice at the primary school to learn the experience of elementary teachers Students must be aware of self-training and self-fostering ... problems in grades and 1.3 In primary school subjects, mathematics is very important, it takes up most of the time in the teaching curriculum in primary school The knowledge and skills of elementary... for students at teacher training schools, but most of them focus on developing teaching competence for mathematical pedagogy students at junior and senior high schools Until today, according to... train teaching skills for students They based on the achievements of behavioral psychology and functional psychology to organize training for students these skills with the time of practicing