Improving the capacity of diagnosis for the students in primary education to satisfy with the requirement of renovation in teaching mathematics

MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY DO VAN HUNG IMPROVING THE CAPACITY OF DIAGNOSIS FOR THE STUDENTS IN PRIMARY EDUCATION TO SATISFY WITH THE REQUIREMENT OF RENOVATION IN TEACHING MATHEMATICS Specialized: Theory and Method Teaching of Mathematics Code No: 62.14.01.11 ABSTRACTS DISSERTATION DOCTORAL EDUCATION NGHE AN – 2013 The work is completed at Vinh University, Nghe An Province The Instructor: Associate Professor, Doctor Vu Quoc Chung Comment 1: Comment 2: Comment 3: The Thesis will be presented in front of University-level Thesis Evaluation Committee at … at … on … 2013/…/… More details can be found at Libraries: Vietnam National Library Center Information & Nguyen Thuc Hao Library, Vinh University INTRODUCTION Reason for choosing the title Nowadays, the development of knowledge development and process of globalization take place very strongly This process has also effect on the development of Education and Training The requirement on social development demands the department of Education and Training necessary to renovate the educational contents, a learner must change the style of studying, a teacher must change the style of teaching, so a learner who has the capacity must act, develop enthusiastically, independently, actively in the realistic activities 1.1 The target of Training Program on Primary Teacher is to satisfy with the requirement on renovation of Primary Education in the period of industrialization, modernization Graduate student must have the capacity of teaching not only satisfied with the renovating requirement of Primary Education at present, but also it is able to research and self improvement in qualification, satisfied with the requirement of Primary Education in the next decade An orientation in renovating the teacher’s education and a change from the training in knowledge equipment, skills into the training in Capacity of Teaching and Education, “Training Program of Primary Teacher’s Framework ”, in addition to the training requirement of vocational capacity for students “Professional Standard on Primary Teacher” also put forward the requirement, criteria in the aspects that Primary Teacher has achieved These are the bases allow the pedagogy college to build the strategy, training target, improve the Primary Teacher to satisfy with the targets of Primary Education in each period 1.2 In order to satisfy with the requirement of teaching mathematics in Primary Level, Primary Teacher must have the capacity of specialty and capacity of profession A lot of scientists refer to the capacity of teaching has defined the capacity of anticipation is a capacity in an important role At a seminar “Improving on the training quality of Primary Teacher”, the authors called Nguyen Tri, Vu Quoc Chung, Nguyen Huu Dung engage in discussion on construction “Primary Teacher’s Training Program” propose that is necessary to take form, improve some basic capacity of teaching, in which including the capacity of diagnosis is a capacity has an important role As there is a proposal, “Preferred issues are to improve the educational quality”, author called Nguyen Huu Chau puts forward a basic capacity of teacher, it is necessary to have the capacity of diagnosis (Capacity of discovering and realizing enough, accurately, timely on the development of pupils, the requirement necessary to educate by the pupil) Author called Tran Ba Hoanh as presenting “Capacity groups of teacher” also defines the capacity of diagnosis on the requirement and features of teaching person is “…In the style of teaching “focused on the pupils and activity of learning” requires the respect of benefits, requirement of pupil and implement to teach the division this capacity is necessary to express…….Only when grasping through the objects, a teacher is able to control the process of teaching efficiently… ” In other words, teaching Mathematics in Primary Level is also different from the other levels of school due to that: object of teaching known as the pupils at the age of beginning the formation and quick development, variety in intelligence, character; a development in realization, the requirement on studying mathematics unequally; teaching contents though the primary mathematical knowledge, simple but not mean the preparation for building the mathematical knowledge in the following knowledge; …To satisfy with the requirement of teaching, carrying out successfully the task of teaching, it is necessary to have the capacity of diagnosis penetrated in the internal world of pupil, understand the features of personality and realization of pupils, realizing the occurrence of thoughts, sympathy, psychology of pupils is a key capacity 1.3 In fact, each of University students will teach in many years, many classes, in that time it is possible to change the contents methods of teaching Mathematics Therefore, a problem is put forward the Teacher should know what; it is possible to what? In order for teaching is satisfied with the request of expectation as there is a change in teaching mathematics in primary school In other words, teaching at present requires the teaching which is not only to communicate knowledge, but is necessary to organize the activities of looking for, argument, “encouragement”, understanding, suggesting the thought and instructing the pupils to overcome the difficulties, challenges in studying However, there are not few teachers who teach Mathematics in Primary School still show their restrictions (embarrassed, lack of self confidence, less decisive, less active, creative) as resolving the situations occur due to carry out the activities in estimation well in teaching This thing together with the fact research in training, improving the Primary Teacher show that process of training has a lot of deficiency, inadequate, without supplying with the teaching staff has enough capacity correspondently with the requirement and tasks in a new stage These restrictions, insufficiency are because of reasons, in which there is a formation, improvement of teaching ability Therefore, it is necessary to improve the students on the capacity of diagnosis in teaching mathematics and other capacities, so it is not only satisfied with the requirement of teaching at present, but also there is a modification, renewal on the targets, contents and methods of teaching mathematics in future 1.4 It is not currently colleges of pedagogy, scientists just look after the formation and improvement of teaching ability in Mathematics for the students, but there are a lot of researching works in improvement according to every aspect, levels, different facet However, until now there is not any private researching work on the formation and improvement of estimated capacity in teaching mathematics at primary level for the students From the reasons said above, it is possible to mention on the researching issues made and improving the capacity of diagnosis in teaching mathematics for the students that is necessary, urgently Therefore, the author chose the title of thesis: “Improving the capacity of diagnosis for the students in Primary Education to satisfy with the requirement of renovation in teaching Mathematics” Target of researching Proposal on some methods of improving the capacity of diagnosis in teaching Mathematics for the students in Primary Education in order to contribute the improvement of teaching ability in order to satisfy with the requirement of teaching at present and when there is a change on the target, contents, method of teaching Mathematics in Primary Level Scope of researching Proposal on some methods of improving the capacity of diagnosis in teaching Mathematics at primary level for the students throughout teaching Mathematics at basic level, method of teaching Mathematics at the primary level, regularly pedagogy professional practice in the pedagogy college and pedagogy organization for practice, pedagogy practice The research on certifying the knowledge sources, skills, existent experiences of pupils at each time and resolving the expression of specific limitation on the knowledge of pupils in fact to teach Mathematics in the primary school not in the scope of researching this title, due to the fact that Student in Primary Education does not really teach in class and less condition in learning about the teaching fact in primary school Tasks of researching Making clear about the conception of estimating, capacity of diagnosis in teaching Mathematics, role in estimation, capacity of diagnosis in teaching, showing the capacity of diagnosis in teaching Mathematics Presenting on the basis of formation and element of promoting the development in the capacity of diagnosis in teaching Mathematics Generalizing on the fact situation in setting up, improving the capacity of diagnosis teaching Mathematics for the students at some pedagogic colleges currently Defining the requirements on improving to satisfy with capacity of diagnosis in teaching Mathematics basically, method of teaching Mathematics, …at the pedagogic college Suggesting some methods of improving the capacity of diagnosis in teaching Mathematics for the students in Primary Education Testing the practicability, efficiency at the first step to carry out the method of improving the capacity of diagnosis in teaching Mathematics as mentioned Method of researching In order to carry out the project title, the author has used the methods of researching: argument researching, survey, investigating, researching the cases, pedagogy experiment Scientific assumption of the thesis If the organization of comprehensively implementation to the methods of improving the capacity of diagnosis in teaching Mathematics for students in the branch of primary education according to the proposal in the thesis, it will contribute to improve the quality, efficiency on training the primary teacher, overcome the restriction, inadequacy when teaching Mathematics by the Primary Teacher, satisfied with the request on teaching Mathematics Contributions of the thesis Extra contribution in teaching arguments at the University in the sphere of arguments on the formation and improvement in the capacity of teaching for the students, specifically on the development of teaching ability to the students in primary education Generalization in the fact situation of the formation and improvement in the capacity of teaching the students in primary education currently in the pedagogy colleges Proposal on the some methods of improving the capacity of teaching to the students in primary education satisfied with the request on teaching renovation on Mathematics Theoretical points raised on protection The way of conception about the estimation, the capacity of diagnosis in teaching Mathematics as a Thesis with the significance for arguments and practice in training the primary teachers The formation and improvement on the capacity of diagnosis for the students is an important training target in training the primary teacher in currently pedagogy colleges Methods of proposal on carrying out the improvement of diagnosis capacity in teaching Mathematics for the students in primary education feasibly and efficiently Structure of Thesis Thesis, in addition to the part of Introduction, Conclusion and Encouragement, Documents on reference, the content consists of chapters: Chapter1: Some bases of arguments and practice in improving the capacity, diagnosis in teaching Mathematics in the primary school Chapter 2: Some methods of improving the capacity of diagnosis in teaching Mathematics in Primary School for the students Chapter 3: Pedagogy Experiment Chapter 1: SOME BASES ON ARGUMENTS AND PRACTICE IN IMPROVING THE CAPACTIY OF DIAGNOSIS IN PRIMARY EDUCATION 1.1 Capacity, Capacity of diagnosis in teaching Mathematics In this section, Thesis has put forward a way of conception and made clear about the concepts of diagnosis, capacity of diagnosis in teaching Mathematics 1.1.1 Conception on capacity of teaching Mathematics Term of diagnosis is used popularly in medicine and psychology; recently it is used in the occupations, field of: economy, technique, military, education…, and any occupation in life, prior to make a decision or carry out such a thing (whether big or small, important or less important), in thought people carried out the activities of diagnosis at a certain level (if diagnosis is correct, the opportunity of success is high) According to Vietnamese dictionary, Diagnosis is to define the disease based on the symptoms and results of testing According to the pronoun in Vietnamese, Diagnosis is to search, remarks on the symptoms of disease by the means of hearing, looking at, acquiring, feeling pulse, and then decisive on the cause of disease mechanism and cure According to the conception of diagnosis in psychology, Diagnosis consists of the collection of all documents, information possible to achieve in practice, survey, explanation about the results of researching, testing, after that conclusion is final and estimated It is possible to understand broader, diagnosis on a thing; event is to look for, considerate, find out, judge, is a classification of characteristics and cause Diagnosis is often used to find out the connection between the cause and results or definition of cause is the symptom, problem and solution to the symptom, problem From the explanation about the term of diagnosis and conception of diagnosis as above, Thesis provides the conception: Diagnosis in teaching Mathematics is a process of income activity and dealing with the information on technique, skills and experiences of pupils at a certain time in relation to the contents of teaching, estimating the situation, capacity of occurrence in teaching process and put forward the way of solution, the way of teaching suitable to every cases, ability to happen according to the prediction in order to achieve the target in teaching Mathematics Therefore, Diagnosis in teaching Mathematics consists of supporting activities: Activity 1, Income and dealing with the information concerned with the contents of teaching (target, content, condition on teaching, characteristics of thought and requirement on knowledge of pupils); Activity 2, Prediction in the situations, the ability to take place in teaching (difficulties, problems, mistakes of pupils, … and causes, ability to mobilize, apply with technique, skills of pupils ); Activity 3, Putting forward the method of resolving, the method of teaching suitable to every situation, the capacity of occurrence Attention, Diagnosis in teaching Mathematics that is not stopped by the teacher looks for and collects to deal with the information certified the existence on the knowledge of pupils at a certain time that consists of the development of implicit problems, prediction on the ability to take place, tend to the development of knowledge of pupils, from which there is any action, expedient on resolving in accordance with every cases However, the contents of researching to resolve in the Thesis is not to put forward the request on the students must define accurately, full of technical source, skills in Mathematics and experiences in existence of each pupil at a certain time, because as we know in fact the student does not upgrade the class From the activities of component, Thesis on explanatory, definition on the main experiences that student must have as the implementation to the diagnosis in teaching Mathematics in primary and make clear about the relationship between diagnosis and prediction (judge) Thesis on putting forward examples of explanation about every activities in order to make clear about the conception in activities of diagnosis in teaching Mathematics at primary level For example 1.1: Diagnosis as teaching the pupils in class in the types of exercise: “Symbol of division into 2” (or 5;9;3) [Mathematics 4; page 94-99] For example 1.2: Diagnosis as guidance on the 4th grade pupil to key to the 5th grade Mathematics in [Mathematics 4, page 99] 1.1.2 Capacity of diagnosis in teaching Mathematics Vocational capacity is referred in the different aspects in the works of researching on the improvement for the capacity to the student, but till now rectangular there is not still authors who make a decision on the official definition Some scientists think that capacity of vocation is a correspondence between the features of psychology of each person with the requirements of vocational skills, the capacity of vocation is mainly formed throughout training and in the process of occupational activities Each of lines, each of different sectors demands it is necessary to have the core capacity and differentiate capacity suitable to the requirement of that lines, sector Capacity of teaching is shown in the capacity of organizing the implementation to the activities of teaching to obtain the target in quality, high efficiency Capacity of teaching is the general capacity of many types of capacity, mainly formed from the source of knowledge, skills equipped with the experience in teaching, as the product of training and practical process As referred on the problem of formation, improvement on some capacity of diagnosis to the teaching staff in the current periods, some authors have defined on the capacity of diagnosis has an important role in teaching, it is necessary to form, improve the teachers, but also the conception has not been raised on the capacity of diagnosis and like how is diagnosis, capacity of diagnosis in teaching The author called Nguyen Huu Chau showed that capacity of diagnosis is the capacity is found out and realized full, exactly, timely on the development of pupil, the requirement on the necessity to be educated by the pupil In here, the author thinks that capacity of diagnosis is only the capacity in relation to find out , realize on the development , requirement on education of pupils without putting forward the problems to find out the shortcomings, deviation and cause of them in order to find how to resolve, overcome From the conception of capacity as above, thesis puts forward the conception: Capacity of diagnosis in teaching Mathematics of students in Primary Education understood as the correspondence between the psychological features of each student to the requests of skills in carrying out the diagnosis in teaching Mathematics and showed on the correct diagnosis on the situation, capacity of appearance n the activity process of teaching Mathematics in primary school From the conception on the capacity of diagnosis in teaching Mathematics for the students as above, Thesis analyzes on defining the basics features of diagnosis capacity, capacities to develop the capacity of diagnosis and giving 03 examples of explaining about the activities of diagnosis, formation of diagnosis capacity for the students throughout teaching some contents For example 1.3, practicing the students to carry out the diagnosis as teaching on the contents of Formation of natural figures, For example 1.4: Practicing the students to carry out the diagnosis as teaching the contents The elements of geometry and For example 1.5 : Practicing the students to carry out the diagnosis as teaching the lesson “Area of Triangle” [Mathematics 5, page: 87] 1.2 Role pf diagnosis, capacity of diagnosis in the function of teaching operation Thesis is to make clear about an important role, realistic application of activities in diagnosis, capacity of diagnosis in teaching and giving 02 examples of explaining about the necessity to carry out the diagnosis and it is necessary to have the capacity of diagnosis in teaching Mathematics at primary level, For example 1.6: Organizing the students to acquire about the necessity of diagnosis in and necessity of diagnosis activities in teaching and making a plan to teach the lessons Plus two the fractions different from the denominator in [Mathematics 4; page 127] For example 1.7: Practicing the students to carry out the actives in teaching the 5th grade pupils who are excellent, good to find out how to solve the mathematical exercises “ It is assumed that triangle called ABC has the angle of A squared and length of the side of AB is cm, AC is cm Please calculating the area of square with the side equal to the side of BC “This mathematical exercise with the knowledge, skills in the possession of students are not difficult, because of only using the Pythagorean Theorem to calculate the side of BC immediately, from which it is possible to find out the area of square with its side of BC But the pupils of 5th grade pupils not study about Pythagorean Theorem, so the pupils can not calculate the side of BC directly In order to instruct the pupils who find out how to solve this mathematical exercise by the means correspondent with the pupils, the student must carry out the activity of diagnosis 1.3 Some of popular manifestations in the capacity of diagnosis on teaching Mathematics On the basis of question list on reference for the opinion of some lecturers and primary teachers to realize on the manifestation of diagnostic capacity in teaching Mathematics, Thesis provides 10 popular manifestations on the diagnostic capacity of students in teaching Mathematics 1.4 Levels of diagnostic capacity in teaching Mathematics in primary school of students Based on the manifestations of student (knowledge, activeness, independence, fluency, complexity, in own power as carrying out the activity of diagnosis) Thesis puts forward levels of diagnostic capacity in teaching Mathematics of the students 1.5 Some bases of taking form and element to promote the development of diagnostic capacity in teaching Mathematics in Primary School 1.5.1 Bases of taking form the diagnostic capacity in teaching Mathematics 1.5.1.1 Basis of Psychology 1.5.1.2 Base of Philosophy 1.5.2 Some elements to promote the development of diagnostic capacity in teaching Mathematics In this section, Thesis only refers to some mainly elements that lecturer of Mathematics with the condition and ability to affect directly the students by means of teaching elementary mathematics, Methods of teaching Mathematics in Primary School and training the pedagogic staff regularly: 1.5.2.1 Knowledge and skills of mathematics (1) Theoretical basis of set, mathematical logics (2) Some structures of basic algebra, figure sets (3) Basis of mathematics to take shape of mathematics at primary level 1.5.2.2 Knowledge and skills, method of teaching 1.5.2.3 Knowledge of psychology, education 1.5.2.4 Realistic experiences 1.6 Fact situation in improving the capacity of diagnosis in teaching Mathematics at primary school for the students In this section, Thesis has shown some restrictions in the knowledge of conception in relation to the activity of diagnosis in teaching, with regards to explore and organize the practice in carrying out the activities of diagnosis in the process of teaching elementary mathematics, methods of teaching mathematics in Primary School and training the pedagogic staff regularly and organize the pedagogic visit and teaching practice for the students 6) What should teacher pay attention to/ features of thinking development and cognition of students when teaching? 7) How students comprehend the knowledge and skills in this Maths lesson? 8) What trouble student encounter when comprehending the knowledge and skills? List those reasons and difficulties, methods of settlement? 9) When comprehending the knowledge and skills, what wrong can students make? List those reasons? Submit the ways of recognizing, repairing and preventing those defects? 10) Which settlement and teaching methods (organization form, teaching method, teaching tool, etc) should be chosen to fit each problem above to obtain desirable teaching target? 2.4.2 Measurement 2: Organize for students to train to implement diagnosis activity in teaching Maths through exploiting to apply the knowledge and skills of basic Maths 2.4.2.1 Scientific basis of measurements: Train for student to exploit to apply the knowledge and skills of basic Maths directly related to teaching content of primary math in training several skills of implementing diagnosis activity that helps students have ability to analysis, acknowledge, apply contents under different angles, different aspects, then gradually enhance diagnosis capacity in Maths teaching for students This is specific environment and condition, situation that facilitate students to train skills to implement diagnosis activity in teaching Maths 2.4.2.2 Purpose of measurements: Help students train skills to implement the diagnosis activity through exploit and apply the knowledge and skills in learned Maths into primary Maths , step by step to improve diagnosis capacity in Math teaching in primary level 2.4.2.3 Implementation of measurements: Thesis reported way of training some skills of diagnosis activity as teaching Maths under knowledge line At first, equip supplementation and systemization and mastering several knowledge and skills related directly to teaching contents of primary Maths as required More important, it is regular (in every cases) to integrate, mainstream to organize for students to diagnose each lesson content under procedure and answering the system of question Guiding the students to exploit and apply the knowledge and skills that have been learned to see clearly close relationship between the knowledge and skills of advanced Maths and the knowledge and skills of primary Maths, then gradually enhance diagnosis capacity in teaching Maths in primary level for students In each teaching lesson, thesis provides examples to demonstrate organization and implementation of measurements: a) Train to exploit, apply and implement diagnosis when teaching several knowledge and skills content related to set in Maths in primary level: the thesis provides Example 2.1 (Example 2.2): Training students to exploit, apply the knowledge and skills in set when teaching forming nonnegative integer (calculation in set when teaching forming of some calculus) in Maths in primary level and train students some skills of diagnosis activity when teaching set b) Train to exploit, apply and implement diagnosis when teaching several knowledge and skills content related to relationship in Maths in primary level: Thesis shows Example 2.3 to exploit and apply the knowledge and skills in relationship and practice several skill of diagnosis activity when teaching “ equal fraction” [Maths 4; page 111]; Example 2.4: Train students to exploit and apply the knowledge and skills in equivalent relationship and train them several skills of diagnosis activity when teaching forming addition (substraction) of two fractions with different denominator (in number) form: a c   ? [Maths; page 127, 130]; b d Example 2.5: Train students to exploit and apply the knowledge and skills on ordering relation and train some skills of diagnosis activity when guiding students of grade to arrange sequence (3581; 3158; 3518; 3185) under arisen sequencing (or contrary ); then show example 2.6: Train students some skills of diagnosis performing when guiding good upward students to explain task: “Demonstrate that in random nonnegative integer integers, if sum of any numbers is always greater sum of two remaining and 2012, all of these are also bigger than 2012” c) Train to exploit, apply and implement diagnosis when teaching the knowledge and skills related to mapping in Maths in primary level: Thesis reports some cases that apply the knowledge and skills in mapping in teaching Maths at primary level ( however this term is not used) to form symbols, consider relationships between addition and subtraction, multiply and dividing, use word for number, explain tasks in form” filling in blank with number or explain x and y” Or build conception on variable quantity, direct proportion, inverse proportion, expression contained word, calculating value of word contained expression, build general formula on the spirit of mapping d) Train to exploit, apply and implement diagnosis when teaching the knowledge and skills related to logical clauses in Maths in primary level: Thesis shows some examples to demonstrate training, exploiting and implementing diagnosis activity with each form of deduction used for teaching Maths at primary level Example 2.7: Train students to apply deduction and train some skills of implementing diagnosis when guiding students to answer task: “ A rectangular ABCD has circular equal to circular of square MNPQ with side 8cm As known length of rectangular is 6cm longer than it of square, please look for area of that rectangular” Example 2.8: Train students to exploit, apply, deduct and train them some skills to perform diagnosis activity in teaching practice “ criterion for divisible by 3” [Maths grade 4; page 97] Example 2.9: Train students to exploit, apply and incomplete inductive inference in Maths in primary level and train them some skills of implementing diagnosis in wrong number when using incomplete induction in teaching on multiplication, division of nonnegative integers (or fraction, decimal number) at primary level Example 2.10: Train students some skills to perform diagnosis for students with good study ability upward to explain maths tasks in looking for sum of terms “ Summing : 12+112+212+…+1912+2012” Example 2.11: Train students some skills to implement diagnosis when teaching “ Multiply a number with a sum [Grade Maths; page 66] Example 2.12: Train students to exploit, apply, deduce as in Math at primary level and train some skills to implement diagnosis when guiding students to answering: “ there are points, how many rectangular are there if connecting these points” after students answer “ there are points on a circle, how many rectangular are there if connecting these points” Example 2.13: Train student some skills of implementing diagnosis when teaching principle for answering Maths task “ Look for numbers when knowing sum and rate of those” [ grade math; page 147] Example 2.14: Train students to exploit, apply and incomplete inductive inference in primary Maths and train some skill to implement diagnosis when guiding grade student with good study ability upward to answer “ Look for numbers which contain numeral, as known that numeral of ten digit doubles numeral of unit digit” Example 2.15: Train grade students with good study ability upward some skills to implement diagnosis when guiding them to answer “ In a room, there are 25-40 chairs, as arranging seats, it is said that if it is arranged in seats or seats per row, no seat abandons Please look for how many chair in that room” Example 2.16: Train students to exploit, apply, deduce inversing in Math at primary level and train some skills to implement diagnosis to find formula of height calculation and formula of bottom side calculation of a triangular (inversing direction), after lesson of formula of triangular area calculation S= axh (forward direction) [Math 5; page 87] Example 2.17: Train student to exploit some form of inversing inference that often used and train them some skills to implement diagnosis in teaching Math at primary level Example 2.18: Train students some skills to implement diagnosis when guide grade student with good study ability upward to answer “ Look for nonnegative integer n as known: 1+2+3+….+n =2012” Example 2.19: Train students to exploit conflicting evidence inference in Maths at primary level and train grade student some skills to implement diagnosis when guiding them to answer “Demonstrate that there are always 4-5 Sundays” Example 2.20: Train students to exploit and apply extrapolation inference and train some skills to implement diagnosis when considering some rules in Maths at primary level Example 2.21: Train students some skills to implement diagnosis when reviewing on calculating circumference, area of a learned geometry [Maths 5; page 166-167] Example 2.22: Train students to exploit and apply method of analysis and integration in Maths at primary level and train some skills to implement difficult diagnosis of grade students when training, reviewing on appearance identification, quantity identification have been learned in drawing e) Practise to exploit, apply and implement diagnosis when teaching the knowledge and skills on several algebraic structures in Maths at primary level: Thesis reports some case that may train students to exploit and apply the knowledge and skills on several algebraic structures in Maths at primary level On set of numbers, addition and multiplication are close, they are always done, division and subtraction are not close, and they are possible to anytime Except for addition and multiplication, they are characteristics of commute, combination and delivery Or realize that set of nonnegative integer N and set of commensurable numbers Q+ is group of addition and multiplication, so it has unit ( for addition, for multiplication) Commensurable numbers Q+ have own inversing fraction (reversing element for multiplication), therefore, it is a multiplication group, etc f) Practise to exploit, apply and implement diagnosis when teaching the knowledge and skills on set of numbers in Maths at primary level: Thesis shows some examples to train student to exploit and apply the knowledge and skills in diagnosis in teaching Example 2.23: Train students to exploit and apply the knowledge and skills in reading number, writing nonnegative integer and train some skills to implement diagnosis in Maths at primary level Example 2.24: Train students some skills to implement diagnosis when answering “ How many number is common terms of two sequences: “3,8,13,18,….,93,98 and 4,7,10,13,…., 97,100” Example 2.25: Train student some skills to implement diagnosis when answering “Demonstrate that there is a fraction that is not only greater than also smaller than but 17 Please look for fraction with denominator as 30 and satisfy the 17 mentioned conditions, then arrange the fractions in lowest term with arisen sequencing” g) Train to exploit, apply and implement diagnosis when teaching Maths basis forming line of subject knowledge in Maths at primary level: Thesis shows some cases that may train students to exploit, apply Maths basis to implement diagnosis when teaching Maths basis forming line of subject knowledge in Maths at primary level: Maths basis forms numeric conceptions, numeric preparation, calculations, numeric sets, write nonnegative integers, word-contained expressions, expression used word instead of number, simple equation, direct proportion quantity, inversing proportion quantity, quantity and quantity measurements, etc h) Train to exploit, apply methods of abstracting, generalizing and implementing the knowledge and skills when teaching some contents in Maths at primary level: Thesis shows some cases that may train to exploit, apply methods of abstracting, generalizing and implementing the knowledge and skills when teaching some contents in Maths at primary level because this a key method to form object conceptions, events in Maths in general and in primary Maths in particular (conception on Maths object, relations, features, rules, formulas, etc when forming for primary students mostly cannot be defined, demonstrated closely, it is mainly used methods of abstracting, generalizing through guiding students to manipulate on object, observe, consider on some demonstrated pictures, specific examples because cognition still exists limitation and visual view) 2.4.3 Measurement 3: Organize for students to train to implement diagnosis in teaching Maths at primary level through exploiting and applying the knowledge and skills on Maths teaching methods at primary level 2.4.1.3 Scientific basis of measurement: It is impossible to teaching Maths at primary level when teacher does not mastering Maths cognition feature of students, the knowledge and skills on Maths teaching methods When students exploit, apply the knowledge and skills on Maths teaching methods, it is possible to predict exactly probable ability and situation in teaching, select correctly solving methods, provide suitable teaching method with cognition level of students Guide students to train some skills to implement diagnosis when teaching Maths teaching methods at primary level shall create opportunity for students to enhance their own diagnosis capacity 2.4.3.2: Purpose of measurements: Help students train to implement diagnosis when teaching some contents in Maths at primary level through exploiting, applying the knowledge and skills on Maths teaching method at primary level for enhance gradually diagnosis capacity in teaching Maths for students 2.4.3.3 Implementing measurement: At first, ask students to research to comprehend the knowledge and skills on Maths teaching method at primary level (to know how primary student is learning Maths?) What is purpose of Math teaching at primary level? What is content of primary Maths teaching? Which teaching method and organization form often used in primary Maths teaching? Etc) as basis to apply in training to implement diagnosis activity in Maths teaching Then train them to have awareness, habit of discovery, exploiting and applying the knowledge and skills on teaching methods to train to implement diagnosis when teaching some contents in primary Maths to gradually enhance diagnosis capacity in Maths teaching 1) On target, tasks of teaching Maths at primary level 2) Features on development of Maths thinking of students 3) On some teaching methods and organizational forms of Maths teaching 4) On some forms and methods of assessment 5) On teaching tool used in Maths teaching 6) On teaching under subject line of knowledge in Maths Teaching each content of knowledge in primary Maths teaching method for student must be mounted to exploitation and application in teaching primary Maths to help students has right view on opinion, thought, and method of building Maths knowledge at primary level When teaching, it must be organized activities, methods (assigned to self study, self research, exercise, group discussion, essay, etc) suitable for students to implement diagnosis activity in teaching Example 2.26: Train students to exploit, apply the knowledge, skills on primary Maths in diagnosis when teaching to form Maths knowledge (symbol, conception, calculation, rules, mmathematical formula, ) in Maths at primary level For example 2.27: Let Students execute diagnostic activities when teaching the lesson of formula formation (rules) to calculate area of trapezium [Maths 4; pp.93] For example 2.28: Practice of diagnostic activities for Students when teaching lesson types of informing conception on natural numbers with many digits at the 2nd, 3th, 4th grades 2.4.4 Measurement 4: Practise diagnostic activities for students in teaching Maths explanation at primary level by teaching practice of Maths explanation and instructing students to Maths 2.4.4.1 Scientific base of the measurement: Doing Maths in primary level requires student to connect in ideas, use, apply knowledge, mathematical concepts, teaching methods that have been learned under a flexible manner That is also consistent with features of awareness, requirements and qualifications of students in different grades Solving Maths and guiding students is convenient environment for students to use knowledge, mathematical concepts, learned teaching methods as well as support the implementation of diagnostic activities in the teaching of Maths at primary level When practical teaching to solve Maths in elementary level, it is necessary to practise diagnostic activities for students 2.4.4.2 Purpose of the measurement: Create conditions for students to practise and perform concepts diagnostic activities in Maths resolution teaching when exploiting Maths exercises and guiding students in elementary level to improve the quality of diagnostic quality in teaching Maths for students 2.4.4.3 Implementation of the measurement: Dissertation presents the requirements for organizing practice on concepts explaining Maths types at elementary level to students under the methods which are consistent with the level of awareness of the student to apply to perform diagnostic activities when guiding students on Maths explanation 1) Concept of single Maths exercises explanation at elementary level 2) Concept of applying Maths explanation process to explain mixed Maths exercises 3) Concept of typical Maths exercises explanation at elementary level 4) Concept of using of some normal Maths explanation methods and special ones to explain Maths exercises for excellent students Then give some examples for students to perform diagnostic activities through Maths explanation and guide to students Example 2.29: Practise diagnosis activities for students when students of the fifth grade explain Maths exercises "Distance from home to school is 20km A student walks 5km then he goes by motorbike It takes 30 minutes to go to school by motorbike Ask if the student goes to school by motorbike from house to school, how long does it take? For example 2.30: Practise a diagnosis activities for students when teaching practice of Maths explanation, " Find two numbers when you know sum and subtraction them " [ Maths , page 47] Example 2.31: Practise a diagnosis activities for students when teaching practice of Maths explanation: "Find two numbers when you know subtraction and ratio of them " [Maths , page 150] Example 2.32: Practise diagnosis activities for students when teaching difficult Maths exercises: “The rectangle ABCD and M, N are respectively midpoint of line segments AB, CD Connecting DM, BN AC respectively cuts in I and K Demonstrate that: AI = IK = KC.” Example 2.32: Practise diagnosis activities for students on difficulties and operations of students when the fifth grade students explain Maths: “The trapezium ABCD, AC cuts BD at I That the area of the triangle AIB, CID, AID, BID 2cm2, 2cm2, 5cm2, 3cm2, 3cm2 respectively, the ratio of AB and CD of the trapezium” For example 2.34 Practise to student diagnose difficulties and thoughts of students when explaining Maths for the fourth grade student: "Give a natural number with four digits and the last is 5.Know that if you remove the last digit of this number, the new number is 2012 smaller than the old number Find that number?” For example 2.35: Practise to student diagnose difficulties and thoughts of students when explaining Maths for the fifth grade student: “Three water limes flow into a tank If water lime I and II flow, it takes 7,5 hours to fill the tank If water lime II and III flow, it takes 10 2/7 hours to fill the tank If water lime I and III flow, it takes hours to fill the tank Ask if all three water limes flow, how long does it take to fill the tank?” 2.4.5 Measurement 5: Practise diagnostic activities for students in fact through regular pedagogy professional practice and listening in for practice of pedagogy and pedagogy practice 2.4.5.1 Scientific base of the measurement: Developing the ideal of organization and execution of regular pedagogy professional practice, listening in for practice of pedagogy and pedagogy practice of some pedagogy universities (very popular for universities besides pedagogy ones), creating conditions for students to access to teaching in fact at primary school so that students can learn and exploit information of vocational concepts meeting teaching requirements for Maths in fact Meanwhile, students are able to plan practice of some diagnostic activity skills For improving diagnostic capacity of Maths at primary level is very necessary and effective 2.4.5.2 Purposes of the measurement: Facilitating students to access and learn teaching in fact at Primary Schools by themselves early to practise execution skills of diagnosis; improve diagnostic capacity step by step 2.4.5.3 Execution of the measurement: Execution of regular pedagogy professional practice and listening in for practice of pedagogy and pedagogy practice for students of primary education includes many activities relating to many subjects with management and taking part in of my subjects Time of regular pedagogy professional practice is only for Maths (1 credit) therefore practice for all students are not met It is necessary to concentrate on preparation of students, teaching practices under groups with students are objects at class Under the author, the teacher of teaching methods can mix, integrate some typical exercises of Maths for primary class to let students research, exploit, and analyze, discuss under groups, answer questions system and practise diagnostic activities for teaching under the mentioned process [item 2.4.1.3] On the other hand, pedagogy universities need to give specific requirements, criterion (standard) that students need to archive so that the students know and practise by themselves in the process of training Meanwhile, it is necessary to require lectures of teaching methods subject who are responsible for guiding students on planning specifically, practicing skills of diagnostic activities for teaching Maths at primary level in the process of training Besides, pedagogy universities also need to facilitate students (contact with primary schools, create relationship, introduce students to primary schools) and guide tasks specifically so that students (student groups) contact with primary schools by themselves, choose time for listening in for practice from the second year (It is necessary to concentrate students on listening in for practice at the same time), pedagogy practice for the final year to execute tasks and requirements (including Maths at primary level) Then, coordinating with the units, specialized function parts (lecturers, teachers at primary level) to evaluate practice results of students under the criterion as require Conclusion of chapter Chapter 2, some measures of diagnostic capacity improvement for teaching Maths at primary level for students, the thesis shows some main contents: 1) The thesis shows orientations to build measures of diagnostic capacity improvement for teaching Maths at primary level for students of pedagogy universities: Respecting contents of the training program of the study branch and teaching principles of the subject; Matching qualification, demands and ability of awareness of students; Organizing and guiding students learning by themselves, major in practice; Matching teaching conditions in fact 2) The thesis analyzes contents of teaching Maths at primary level about structural characteristics of teaching contents, targets of teaching and some notices when teaching Maths at primary level 3) The thesis shows some overview improvement requirements meeting diagnostic capacity for teaching Maths at primary level 4) The thesis suggests five measurements of improving diagnostic capacity for teaching Maths at primary level for students of primary education branch through teaching basic Maths, teaching methods of Maths at primary level, regular pedagogy professional practice and listening in for practice of pedagogy and pedagogy practice at primary schools: Improving awareness of diagnostic activities, diagnostic capacity of Maths and guiding the process of diagnostic activities for teaching Maths; Practice of diagnostic activities for teaching Maths at primary level for students through exploiting and using knowledge , concepts of basic Maths at primary level by exploiting and using knowledge and concepts on Maths teaching methods; Practice of diagnostic activities in teaching Maths explanation at primary level through practice of Maths explanation, guiding for students; Organize diagnostic activities in teaching fact for students by regular pedagogy professional practice and listening in for practice of pedagogy and pedagogy practice Improvement to increase diagnostic capacity for teaching Maths requires a regular, continuous and long process of students Chapter PEDAGOGY EXPERIMENT 3.1 Purposes and tasks of the experiment 3.1.1 Purposes of the experiment Experiment on scientific assumption of the thesis in teaching fact about the feasibility and effectiveness at first, use of improvement measurements of diagnostic capacity of Maths 3.1.2 Tasks of the experiment Preparing conditions for executing the experiment: Analysis and process of experiment data to evaluate preliminary results in two respects: the feasibility and effectiveness of the measure 3.2 The experiment organization, some measures 3.2.1 Contents of the experiment The experiment improves awareness of diagnosis and diagnostic capacity and integration of practice for students to perform diagnosis for teaching Maths at primary level through exploiting and using knowledge, concepts of basic Maths when teaching basic Maths, Maths taeching medods at primary level 3.2.2 Time and methods of the experiment The experiment is carried out two periods in two terms: Period 1, the 1st term, Academic year 2011-2012, Period 2, the 2nd term, Academic year 2012-2013 For each basic Maths, Maths teaching methods at primary level in the training program of primary teachers, only choosing one experiment of one chapter or one topic and one experiment class, one class of the general of the same course, Faculty of Primary-Kindergarten, Dong Thap University, as follows: + Period 1, the 1st term, Academic year 2011-2012 - The basic subject, choosing the chapter “Logical Foundation of Maths” with the experiment class GDTH11A with 48 students and the general class GDTH11B with 46 students - Maths teaching methods at primary level, choosing the topic:“Some methods and organizational form of teaching Maths at primary level” with the experiment class GDTH10A with 47 students and the general class GDTH10B with 49 students - Basic Maths, choosing the chapter: “Maths Foundation of arithmetics” with the experiment class LT11A with 53 students and the general class LT11B with 51 students (connected system from college to university) + Period 2, the 2nd term, Academic year 2012-2013 - Basic Maths, choosing the chapter: “Natural numbers” with the experiment class GDTH11A and the general class GDTH11B - Maths teaching methods at primary level, choosing the topic:“Teaching numbers and how to count at primary school”, the experiment class GDTH10A and the general class GDTH10B Maths teaching methods at primary level, choosing the chapter:”Some normal measures of Maths explanation” with the general class LT11A and the genral class LT11B Before the experiment, exchanging opinion with the lecturer who takes part in the experiment about the experiment idea, the experiment requirements, the experiment contents and testing (before and after the experiment), the way to carry out the experiment, necessary activities for teaching so that the lecturer coordinates the experiment objectively During time of the experiment organization of each period, the author and the lecturer take part in the experiment and draw lessons regularly, adjust problems that are not suitable under the lecturer’s opinion, difficulties when the lecturer teaches, activities that affect time of teaching much and time preparation of students 3.2.3 Testing the experiment 3.2.2.1 Contents of question types for test (Allowed time: 60 minutes) Question (2 marks): Why is the process of teaching Maths, it is necessary to research, find contents of teaching, targets of teaching, demands of awareness of learners, expectation of difficulties, obstacles, mistakes happening to learners and their reasons? Question 2: (3 marks): Give some examples of using knowledge, skills of the chapter (the topic) that are learned in Maths at primary level Question3: (5 marks): List some difficulties, obstacles, mistakes when the students study knowledge and Mathematical concepts at primary level relating to knowledge and concepts of the chapter (the topic), defining reasons of difficulties, obstacles, mistakes and from that giving the way to resolve and overcome them 3.2.3.2 Meaning of the test The author of the thesis gives one same test with opening characteristics, testing for all experiment and general classes for two experiment periods (without notification) in order to evaluate improvement of students at first of the experiment class compared with the general class and one class taking part in improving diagnostic capacity for teaching through the experiment period compared with experiment period with different subjects 3.2.3.3 Point Chart of the test Because of testing knowledge and awareness of students about some problems relating to diagnostic activities in teaching Maths that students not care therefore points are marked under considering minimum requirements 3.2.4 Evaluation of the experiment’s result 3.2.4.1 Some comments on the preliminary experimental results Common opinion of the lecturer taking part in the experiment about awareness, attitudes and development of perception on diagnostic capacity, diagnostic activities for teaching Maths of students in the process of executing the experiment showing that most students have changes about perception of diagnostic capacity, diagnostic activities in the process of teaching They realize effectiveness, benefits of learning basic Maths, positive awareness and attitudes for exploiting and researching relationships between knowledge, skills they are studying in Maths at primary level however there are some limits on skills when teaching For students of the experiment class, the lecturers guide, exploit and use knowledge, skills that they are learned more than diagnostic activities through the experiment lessons, these students make progressive than others Some lecturers think that executing measures of improving diagnostic capacity as proposes takes much time of the lectures for reparation for the lesson, spends much time teaching and requires students learn much by themselves but at first it is able to deploy in the process of teaching and it brings some benefits to learners Meanwhile, students are formed some skills of executing diagnosis in teaching 3.2.4.2 Quantitative evaluation of the experiment Analyzing points of students after three tests shows that most marks of students of TN class have positive changes; many students show their diagnostic capacity with stable development tendency However some have limitations (low level and unstable development tendency) Statistical indicators of classification of marks in the first time (before the experiment) of all class show that the results are quite equal but low (Average mark from 4,44 to 4,74) and there is no much different from marks of each class This show that in the process of teaching Maths, the students not pay attention to find relationship between studied knowledge, skills of Maths at primary level and students are not practised much about diagnostic activities in teaching Statistical indicators of classification of marks in the second time (after finishing the first experiment) show that there are some positive changes at first, the marks are higher compared to before the experiment (Marks of the experiment classes are higher than the general classes respectively 5,35 compared to 4,87; 5,78 compared to 5,24 and 5,26 compared to 4,98) and there are many differences from indicators of each mark between the experiment class and the general class.) Statistical indicators of classification of marks in the third time (after finishing the second experiment) show that there are highly positive changes (Marks of the experiment classes are higher than the general classes respectively 5,75 compared to 5,00; 6,00 compared to 5,41 and 5,51 compared to 5,12) and there are many differences from indicators of each mark between the experiment class and the general class.) The above results show that diagnostic capacity of the experiment classes is higher than the general classes There is a question, if is the result of the experiment classes higher than the general classes or it is accidental? To conclude effects of the experiment, We will implement to test the suppositions on statistics of Ho “Average mark of experiment classes is higher than general classes” necessary for H1: Average mark of experiment classes is higher than general classes”, use the method of T- Student at the rate of false probability including 0.05 rejecting H0 Result of treatment showed that “Rejecting the suppositions of Ho, accepting the suppositions of H1” This showed that effect of experiment at the first step means in realistic teaching Conclusion of chapter In chapter 3, Thesis is presented on the purpose of experimental tasks, experimental organization on the solutions The process of experiment together with the results withdrawn after the experiment showed that: “Purpose and task of experiment have been completed” The feasibility and effectiveness of methods shown in the thesis at the first step has been affirmed If there is an overall implement to the methods proposed in the Thesis which will contribute to improve to develop the capacity of diagnosis in teaching elementary Mathematics, Method of teaching mathematics in primary school for the students at the pedagogic college CONCLUSION AND RECOMMENDATION CONCLUSION With the researching content of Thesis has achieved some results as follows: (1) On the basis of operating conception in diagnosis and vocational capacity, Thesis put forward and made clear about the conceptions in the activity of diagnosis in teaching Mathematics (1.1.1) and capacity of diagnosis in teaching Mathematics of the students (1.1.2) (2) Thesis has analyzed the activity of diagnosis and defined on the basic features of diagnostic capacity in teaching Mathematics (1.1.2); Role of diagnosis and diagnostic capacity in teaching Mathematics for the students (1.3); Levels on the capacity of diagnosis in teaching Mathematics for the students (1.4); Some bases on taking form and elements to promote the development of diagnostic capacity in teaching Mathematics in Primary School (3) Thesis showed in general about some results of original survey on the fact situation in improving the diagnostic capacity in teaching Mathematics for the students in the branch of Primary Education throughout teaching elementary Mathematics, Method of teaching mathematics in Primary School, Training the pedagogic staff regularly and organizing the pedagogic visit, pedagogic practice (1.6) (4) Thesis put forward general tendencies on building the methods of improving the diagnostic capacity in teaching Mathematics in Primary School for the students (2.1); Presenting in general about the structural features of program contents, targets of teaching and some attentions in teaching Mathematics in Primary School (2.2); It is shown on some requirements of improving to satisfy with the diagnostic capacity in teaching Mathematics in Primary School (2.3) (5) Thesis showed measures of proposal to put forward the implement to improve the capacity of diagnosis in teaching Mathematics in Primary School for the students in the branch of Primary Education throughout teaching elementary Mathematics, Method of teaching mathematics in Primary School, Training the pedagogic staff regularly and organizing the pedagogic visit, pedagogic practice in Primary School (2.4) is: Improving the knowledge in the activity of diagnosis, capacity of diagnosis in teaching Mathematics and showing the process of carrying out the activities of diagnosis in teaching Mathematics; Organizing for the students practice and carry out the activities of diagnosis in teaching Mathematics in Primary School throughout the exploration and application with the knowledge, skills of elementary mathematics; Organizing for the students practice and carry out the activities of diagnosis in teaching Mathematics throughout the exploration and application with the knowledge, skills on the methods of teaching mathematics; Organizing for the students practice and carry out the activities of diagnosis in teaching how to solve the mathematics; Organizing for the students early to be trained in the implement to the activities of diagnosis in reality of teaching throughout Training the teaching staff regularly and pedagogic visit, pedagogic practice (6) Thesis showed some results of test on the feasibility and effectiveness at the first step to apply as a model on the methods of improving the capacity of diagnosis in teaching Mathematics in Primary School proposed in the implement to teach some knowledge, skills in basic mathematics, methods of teaching mathematics in primary school as proposed in the implement to teach some knowledge, skills in elementary mathematics, Method of teaching mathematics in Primary School for the students in the branch of Primary Education at the pedagogic college (3.2.4) (7) Content of this thesis is shown by the author of thesis in the cinema at the division of method of teaching mathematics in the mathematical faculty, Vinh University and showed in the mathematical group directly under the Pre-school - Primary Faculty in Dong Thap University (8) Some of researching results in concern with thesis have also been declared in articles in science at the scientific magazine and scientific titles and technology at elementary level RECOMMENDATION Improving to develop the Capacity of Diagnosis in teaching Mathematics in Primary School for the students is a process which requires carrying out regularly and permanently, it is possible to carry out in many different ways and methods In other words, Thesis has not also been researched to deal with the restricted manifestations in particular with regards to the knowledge of pupils in reality of teaching Mathematics in Primary School, because the students are not really entitled to teach in classes and less condition in learning about the reality of teaching Mathematics in Primary School Therefore, the problem of improving the diagnostic capacity in teaching Mathematics in Primary School necessary to go on studying further, so it will become more and more perfect on the methods of carrying out the improvement in the diagnostic capacity in teaching Mathematics not only for the students in pedagogic college, but also for the primary teachers who are teaching directly in the Primary School LIST OF PROCLAIMED WORKS THE PROCLAIMED ARTICLES, SCIENTIFIC REPORTS 1) Do Van Hung (2009): “Improving diagnostic capacity in teaching Maths for students of Primary Education Branch” Educational Review, the special number (11/2009) 2) Do Van Hung (2011): “Improving diagnostic capacity for students of Primary Education Branch in teaching knowledge of numbers at primary level” Educational Review, the special number (01/2011) 3) Do Van Hung (2012): “Diagnosing the mistakes of primary students when they apply analogies in mathematics.” Journal of Science, Hanoi Nationnal University of Education, No 57 4) Do Van Hung (2012): “Practice of some diagnostic skills for pedagogy students major in Maths in teaching knowledge of numbers.” Educational Review, No 296, The second period 5) Do Van Hung (2012): “Diagnosis of some mistakes of primary pupils for using incompletely inductive inference in teaching Maths.” Educational Review, No 300, The second period CARRIED OUT SCIENTIFIC RESEARCH SUBJECTS 1) Do Van Hung (2010), Identifying necessary knowledge and suggesting some measures of improving diagnostic capacity in teaching Maths at primary level for students of Primary Education Brach, Research subject of science and technology, Vinh University, Code No: NCS 2010-37 2) Do Van Hung (2012): Measures of improving diagnostic capacity in teaching knowledge of numbers at primary level for students of Primary Education branch, Research subject of science and technology, Dong Thap University, Code No: NCS 2012-01 ... methods of improving the capacity of diagnosis in teaching Mathematics for the students in Primary Education in order to contribute the improvement of teaching ability in order to satisfy with the requirement. .. estimating, capacity of diagnosis in teaching Mathematics, role in estimation, capacity of diagnosis in teaching, showing the capacity of diagnosis in teaching Mathematics Presenting on the basis of formation... element of promoting the development in the capacity of diagnosis in teaching Mathematics Generalizing on the fact situation in setting up, improving the capacity of diagnosis teaching Mathematics for