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MINISTRY OF EDUCATION AND TRAINING VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES NGUYEN THUY PHUONG TRAM HELPING STUDENTS WHO ARE LOSS IN STUDYING MATHEMATICS IN TENTH GRADE IN HIGH SCHOOL Specialization: Theory and Method of Teaching Mathematics Code: 14 01 11 EDUCATIONAL SCIENCES DOCTORAL DISSERTATION HANOI, 2019 WORKS ARE COMPLETED AT VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES Instructors: Assoc Prof & Ph.D Dao Thai Lai Ph.D Phan Thi Luyen Reviewer 1: ……………………………………… Reviewer 2: ……………………………………… Reviewer 3: ……………………………………… The thesis will be defended in front of the Institute academic council at Vietnam National Institute of Educational Sciences, 101 Tran Hung Dao St., Hanoi At …(hour) … (day) … (date) (month) 2019 The thesis can be found at: - National Library - Library of Vietnam National Institute of Educational Sciences WORKS HAVE BEEN PUBLISHED BY THE AUTHOR Le Minh Cuong, Nguyen Thuy Phuong Tram (2015), Teaching mathematics based on the abilities of students in high school, Educational Equipment Journal, No 118, (p 3,4,26) Nguyen Thuy Phuong Tram (2015), Exploiting and using information technology in teaching weak students in high school, The summary record of the workshop on professional development of Vietnam high school math teachers, University of Education Press (p.183-186) Nguyen Thuy Phuong Tram (2018), Applying multi-intellectual theory to teaching math for Grade 10 students with difficulties in learning Mathematics, Educational Journal, special issue in May 2018 (p.193-196) Nguyen Thuy Phuong Tram (2018), Research on foreign students having math difficulties and suggestions for teaching students having math difficulties in high schools in Vietnam, Vietnam Journal of Science, No 01/2018 (p.112-119) Nguyen Thuy Phuong Tram, Nguyen Thi Thanh Tuyen, Nguyen Hoang Son, Do Duc Thong, Pham Anh Giang (2015), Forming SelfStudy Skills for Students Bad at Math in High Schools in Vietnam, International Journal of Learning, Teaching and Educational Research Vol 14, No 2, pp 53-67, Dec,2015 PREFACE The reason for choosing the topic +) The importance of Math: Math is one of the basic subjects throughout the whole studying process of students At high school level, Math is responsible for forming and solidifying basic mathematics knowledge for students, and having a strong impact on supporting other subjects (especially natural sciences) Therefore, improving the quality of Maths, reducing the ratio of weak students at Math in high school is an essential task In real life, Math is necessary for everyone, no matter what profession people do, where they live or in what era Math is not only important in students’ learning process but also has great significance in creating a basic, solid foundation for students' higher education However, not everyone can study Math well for many different reasons: the characteristics of each student, lacking knowledge taught at lower levels, having not found the appropriate method of learning, or other objective factors +) Reality shows that the existence of weak Math students is objective: Through practical investigation, weak Math students always exist and account for a high rate in high schools That situation leads to the concern of many researchers, society, and teachers Although educational experts have tried to resolve and overcome this problem, the ratio of weak Math students is high compared to other subjects at school In fact, in Duc Trong district - Lam Dong province, the ratio of weak Math students is quite high (according to our survey is nearly 20%) In recent years, the Party and the State have paid attention and created many advantages for improving the quality of education in general and helping weak Students in particular In the Resolution of the 8th Conference, the Central Executive Committee, Term XI (Resolution No 29-NQ / TW): " Improving the quality of education in all aspects , applying knowledge into practice Develop the creative ability, self-study and encourage lifelong learning " Implementing that resolution, the Ministry of Education and Training has directed teaching specific students with appropriate methods, teaching practical knowledge, which creates favorable opportunities for many weak Math students +) There have been a number of recent research projects close to the research direction of the topic but there is no topic on "Helping weak Math students in teaching mathematics for grade 10 in high school" Although the research works on weak Math students in Vietnam as well as in the world have given general concepts about weak Math students, weak students’ characteristics, causes of weak Math students and achieved certain results, most of those research focus on elementary students Besides, there are also research on maths in secondary school and high school but a few and not deep, especially those in high schools In Vietnam, there has not been sufficient and systematic research on weak Math students in high school In 2017, Nguyen Thi Thanh Tuyen presented the research results on students struggling with Math in grade in primary school Although weak Math students in grade and grade 10 share some similarities, there are many differences due to the Math curriculum at each level and characteristics of students’ ages Therefore, the measures to help weak Math students in these two levels have different features To help weak Math students in elementary schools, intuitive activities are conducted, while weak Math students in grade 10 are helped through cognitive reasoning (reasoning,thinking ) of each students +) The necessity of studying and helping weak Math students in high school For grade 10 students, the majority of students will face difficulties in learning, which are quite different from secondary school such as learning methods, knowledge needed acquiring Grade 10 - the first year of high school, has a great influence on grasping the knowledge of later years If grade 10 students fall into the Maths problem, it will lead to many obstacles to acquire mathematics knowledge in the following school years because one of the characteristics of mathematics is systematics From the above reasons, we choose the research topic of the thesis: "Helping weak students in teaching grade 10 Mathematics in high school" Research purposes and tasks The purpose of the study is to propose measures to help weak Math students at high school level to improve the quality of Math teaching In order to achieve the purpose of the study, the research tasks are set: - Study theoretical basis related to research topic: the concept of Weak Students, characteristics of Weak Students, classification of weak Math students, some Psychological and educational theories can be applied in proposing measures to help weak Math students - Identify the concepts, characteristics, and manifestations of weak Math students in high school - Find out the current status of weak Math students in grade 10 at some high schools - Determine the causes for the problem of weak Maths students in grade 10 - Proposing a number of measures to help weak Math students in grade 10 - Organization of pedagogical experiment to test the feasibility and effectiveness of the proposed measures Subjects, objects, and scope of research 3.1 Research subjects Subjects of the study are measures to help Weak Students in teaching Mathematics in high school 3.2 Object to study The object of research is the teaching process of Math in grade 10 in high school 3.3 Research scope - Content in grade 10’s Math textbooks, Math workbooks - The thesis only focuses on researching teaching activities in high schools, not mentioning the factors affecting weak Math students such as families and society Scientific hypothesis If the causes for weak Math students in grade 10 in high school are determined and feasible, reasonable pedagogical measures which can limit and fix the causes are applied, , weak Math students will reach the average level Research methods 5.1 Method of theoretical research Studying documents such as books and magazines about Psychology, Education, teaching theory, teaching Mathematics methodology related to the topic to clarify the rationale of helping weak Math students and improve the effectiveness of teaching math in grade 10 Do research on curriculum, high school textbooks and instructional materials 5.2 Observation investigation method Conduct a survey using questionnaire for high school teachers, observe some math classes in grade 10 to learn about the current situation of weak Math students in grade 10 5.3 Case study method (case study) Select a number of typical weak Math students in Grade 10 to monitor the progress of learning process, from which to analyze and have appropriate pedagogical effects to improve Weak Students’ math performance 5.4 The experiment methodology Organizing pedagogical experiments, using mathematical statistical methods to interpret pedagogical experiment results to assess the effectiveness and feasibility of the proposed measures 5.5 Statistical methods Quantitatively analyzing actual survey data, quantifying experimental results as a basis to demonstrate the effectiveness of the topic Issues of protection - Characteristics and manifestations of weak Math students in grade 10 in high school - The main reasons leading to the situation of weak Math students in grade 10 in high school - Measures to help weak Math students in grade 10 in high school - The effectiveness and feasibility of the proposed measures New contributions of the thesis 7.1 Theoretically - Concretizing the characteristics, manifestations of weak Math students in high school, and the causes of weak Math students in grade 10 in high school - Contributing to the theory of teaching Math methodology on measures to help weak students through teaching Mathematics in grade 10 in high school 7.2 In practice - Reflecting the reality of teaching Math for students in grade 10 - The implementation of proposed measures contributes to help weak Math students in grade 10 reach the standards of knowledge and skills of grade 10 Math - The thesis is a useful reference for teachers who are currently teaching Math by guiding the application of some pedagogical measures to help weak Math students in some specific lectures The structure of the thesis In addition to the Introduction, Conclusion, and Reference, the thesis content consists of chapters: Chapter The theoretical and practical basis Chapter Some pedagogical measures to help weak Math students in grade 10 in high school Chapter Pedagogical experiments Chapter THE THEORETICAL AND PRACTICAL BASIS 1.1 Overview of research results on weak students in general and in mathematics in particular The research on weak students in learning in general has been of interest to many scientists From these studies, some issues should be noted: - Firstly, there have been many studies showing the characteristics and manifestations of weak students in general and weak Math students in particular, but there has not been any work discussing weak Math students in grade 10 in high school Therefore, it is necessary to clarify the concept and characteristics of weak Math students in grade 10 - Secondly, the studies have pointed out the reasons for he situation of weak Math students in grade 10 in high school, classifying the subjective and objective causes of weak Math students However, there are unsuitable causes for weak Math students in grade 10, it is necessary to correctly identify weak Math students in grade 10, from which there are investigations to find out the main reasons and appropriate help measures - Thirdly: There have been research on offering solutions to help weak Math students However, these studies are mainly oriented at the macro level, not specific to each weak Math students 1.2 Characteristics of grade 10 students and grade 10 Maths curriculum in high school 1.2.1 Characteristics of high school students in high school From the research on age psychology, we have found that grade 10 high school students have just passed the secondary school stage, have not yet got out of their teen years, are not yet adults, and initially turn to adolescents so there are many physiological changes Therefore, teachers need to create a student-friendly learning environment: close, sharing with students, having timely encouragement, doing fair with all, especially with weak students Weak students need help from teachers and friends to help them more confident in learning and overcome their mistakes in learning 1.2.2 Characteristics of grade 10 Maths curriculum in high school In addition to ensuring the systematic and logical nature, grade 10 math curriculum content also has new objects built on the existing knowledge If students are "lacking" knowledge about the content studied at lower levels, they cannot perform tasks in learning mathematics Many times failing to so will cause students depression On the other hand, grade 10 math curriculum content has some impractical and abstract parts compared to that of lower levels, which also causes weak Math students in grade 10 high school 1.3 The problem of weak Math students in Grade 10 High School 1.3.1 Characteristics of weak Math students in Grade 10 High School Studies of weak Math students’ characteristics always refer to thoughts, attitude and perception of each student, descriptions of learning Math activities Article 5, Chapter II of Circular No 58/2011 / TT-BGDDT dated December 12, 2011, of the Minister of Education and Training, clearly states: "1 Bases for evaluation and classification of learning capacity: a) The degree of completing the program of subjects and educational activities in the Secondary and High School education plans; b) Results of the tests Academic performance is classified into categories: Very Good (G), Good (K), Medium (Tb), weak (Y), poor (Poor) " Thus, following a legal basis, we can see weak Math students in grade 10 in high school are students with average math score below 5.0 points (Mathematics scores are the average points of at least three consecutive tests), and not actively participate in Math activities However, in order to be able to "identify" more clearly about weak Math students in grade 10, we describe weak Math students in grade 10 with the following main characteristics: - Attitude: lack of concentration, not showing interest in Math class; inferiority and lack of confidence in studying Mathematics; not willing to perform the tasks assigned or not participate in the tasks of learning mathematics - Thoughts: remembering by heart (memorizing, learning parrots) formulas, concepts rather than remembering the nature of the problem; failing to perform or very slowly perform thinking processes such as specialization, concretization, analysis and synthesis at a minimum level; ability… - Knowledge: lack basic knowledge; Do not understand the nature or not understanding the relationship between concepts, theorems - Skills: limit in expressing concepts and properties in Mathematics; lack linking knowledge skills to solve math problems; limit in expression skills, have difficulties in presenting math solutions The ratio of number of weak students in each class usually ranges from 15% to 20% of all students in the classroom As for weak Math students: - There are many math tests that are constantly below the average points (at least three tests) - Difficulties in solving simple problems, often making mistakes when solving math problems Normally, teachers rely on the external (obvious) manifestations of Weak students to learn the nature of that weakness (internal function) to take measures to fix, support and help weak Math students in time weak Math students in grade 10 in high school may be weak at certain topics, in a sub-subject (algebra or geometry) or in all the whole process of learning mathematics 1.3.2 Causes of weak Math students There have been researchers categorizing weak students in learning in many different directions, so classifying weak Math students can be based on the assessment of the causes of weak students These causes can be described by the following diagram: Reasons of weak Students in Maths Subjective Objective Content of textbook program Students not have confidece in Math Class, school Students have poor thinking skills Teachers Family and Society Students lost knowledge from lower levels Students not have suitable learning method - Survey tools: the system of Math problems in grade 10; test of assessing knowledge and math skills of students in grade 10 2) For teachers - Contents of a survey: manifestations of weak Math students in grade 10, the causes leading to weak Math students in high school, some measures to help weak Math students in grade 10 in high school - Survey tools: survey forms; Interview questions through direct conversations with teachers, contact and discuss through social networks 3) For parents of students - The content of the survey: surveying the self-study time of weak Math students in high school - Survey tool: Survey questionnaires, interview questions through direct conversations Survey method The methods used in the survey process include analyzing and processing theoretical documents method; research students’ results method; questionnaires (Anket; observations and conversations; writing method; students’ biographical analysis method; method of processing information and data Survey results Through analyzing the characteristics of weak Math students in Grade 10, we found that: - Attitude: they can pay attention but may not understand the points that teachers want to convey or lose concentration during school hours, not show interest in Math class; inferiority, lack of confidence in learning Math - Thought: remembering by heart (memorizing, learning parrots) formulas, concepts rather than remembering the nature of the problem; failing to perform or very slowly perform thinking processes such as specialization, concretization, analysis and synthesis at a minimum level; ability… - Knowledge: lack basic knowledge; Do not understand the nature or not understanding the relationship between concepts, theorems - Skills: limit in expressing concepts and properties in Mathematics; lack linking knowledge skills to solve math problems; limit in expression skills, have difficulties in presenting math solutions, slower ability to participate in math teams, poor group interaction, slow response - Learning method: not showing their own learning style, there is no suitable learning method for individuals - There have been low scores in math results for a long time (below average), can have low scores in all subjects of some Math aspect - There are weak Math students at some points but good at other topics or other subjects Survey results have shown that the causes of students having difficulties in learning mathematics are: - Causes from students: Students not feel interested or not confident in studying Math (or a Math topic); Students not have faith in learning mathematics; +) Students lack knowledge from lower levels; +) Students who not have appropriate learning methods, especially very poor in self-study ability; +) Students have limit in thinking so they cannot or slowly perform specialization, analysis, synthesis of knowledge at a minimum level; - Causes from teachers, family, and society: +) Teachers not have measures to encourage and create motivation for students; +) Teachers have not set up and implemented their own impact and support plans for each weak math student; +) the current status of high school admissions in some provinces The actual situation of helping weak Math students in grade 10 in high school The investigation on the activities of helping weak Math students in grade 10 shows that the school always encourages teachers to help weak students but the helping forms of schools and teachers are not flexible; Teachers have not implemented measures to help weak students rise from their own internal forces but mainly teachers conduct extra tutoring for weak Math students in grade 10 1.7 Conclusion of chapter From the results of theoretical and practical research presented in chapter 1, we have come to some of the following statements: +) In this thesis, we conceive that weak Math students in grade 10 are students who are not or slow or only perform parts of the task in learning Math; weak Math students has at least consecutive tests below average; not actively participating in Math activities; not concentrating in math class; having difficulties in applying knowledge to homework; No selection of suitable studying method for each students 10 +) Current situation of weak Math students shows that: there is a significant proportion of weak Math students in grade 10 (17.34%) weak Math students in grade 10 math may be weak in only a few topics or a certain subject but there also are weak students in the whole process of learning Math Weak students in Grade 10 Math in high school often has the following characteristics: passive in Math learning activities, low scores for a long time, weak ability to generalize, systematize knowledge, lack knowledge from lower levels, not confident in learning Math, +) The cause of the situation of students in Maths first comes from the learners themselves: there is no belief in Maths; lack knowledge from lower levels; there is no suitable learning method; limited thinking capability; objective causes: from family, teachers, society, +) Overcoming the problem of weak Math students can be based on some theories in teaching such as the theory of the operation structure of AN Leonchev, the theory of Piaget, the teaching model of learning activities of Jerome Bruner, Vygotsky's socialist theory, multi-intellectual theory, and some teaching methods related to helping students' problems: teaching differentiation, focusing on operational hierarchy, +) The results of the survey of teaching and learning in grade 10 mathematics in some high schools show that weak Math students account for a small proportion of the total number of students (over 17%), even though the percentage of students with lower grades of Math is very low (some schools have only 5.2% of students have average semester results below average) The fact shows that the school and teachers have recognized the existence of weak Math students and have taken many measures to help weak students such as organizing extra teaching after class, assigning good students to help weak students, but not paying much attention to measures to help these children in a mass class, there are also teachers who neglect weak students Therefore, the proposed measures have not achieved the desired effect The above theoretical and practical bases will help us propose some pedagogical measures to help weak math student in high school 11 Chapter SOME VULNERABILITY MEASURES TO HELP STUDENTS WITH HIGH SCHOOL GRADE 10 2.1 The orientation of proposing pedagogical measures to help weak Math students in Grade 10 in High School Orientation 1: although measures to overcome the causes of weakness in learning Math of grade 10 students high school have been proposed in chapter 1, we have to overcome the limitations, difficulties and mistakes that weak math student are facing Orientation 2: creating balance between teaching in the whole class and helping weak Math students in grade 10 Orientation 3: those measures need to promote students’ math ability in a positive direction Orientation 4: The system of measures must be feasible, can be implemented in the actual conditions of the teaching process Orientation 5: Measures are not only used in teaching weak Math students in grade 10 but also can be used during the process of teaching mathematics at all levels 2.2 Some pedagogical measures to help weak Math students in Grade 10 2.2.1 Method 1: Learn, analyze and identify the causes leading to the situation of weak Math students in order to take timely measures to help Purpose: Not only finding out in time, identifying the weakness of weak Math students but teachers also need to find out the causes of weak Math students in grade 10 in order to choose suitable measures to help weak students Content: The discovery of weak Math students in grade 10 in high school was conducted based on the results of quantitative and qualitative analysis The basis of the measure There are many changes in psychology of high school students compared to that of lower levels Besides, they have many difficulties when they first started new ways of learning, new teachers which sometimes lead to the situation of weak Math students in high school In addition, there may be a number of 12 Mathematical topics or certain subjects of Mathematics due to the personal characteristics of students How to perform Determine weak Math students in grade 10 in high school by quantitative, qualitative methods After determining weak Math students by qualitative and quantitative methods and before making plans to help students, people should find out if weak students have any desire and wishes for the ones involved in the task of teaching Math through observing students' learning and playing activities, communicating with teachers, parents, and those students Based on the main reasons leading to the situation of weak Math students presented in Section 1.6.5.2, teachers determine the main causes of each student so that they can group students according to the main causes and give timely help 2.2.2 Method 2: Encourage, create excitement, strengthen students' beliefs in learning Math Purpose: This measure aims to create motivation for learning, creating confidence for students to perform the task of learning mathematics Content: According to Nguyen Ba Kim: "Encouraging motivation is to make students aware of the meaning of activities and objects of activity Encourage motivation is to make pedagogical goals turn into students' goals, not just introduction, questioning formally ” Building trust in success in learning will play an important role in promoting the motivation of weak students and vice versa Therefore, teachers need to focus on building trust for students in Mathematics in high school The basis of measure: - Activity theory has shown that: "Psychology and consciousness are the products of activity and intermediary stage for people to influence the object; psychological phenomena are of active nature” - Psychologist Bernard Weiner (1972, 1983) proved that when an individual is trusted, he or she can achieve higher results Studies were done by Covington (1983) and Harter (1980) also showed the influence of belief in human development efforts Through the survey, we found that there were math students who not believe that they can overcome math to achieve minimum learning 13 tasks In fact, they can complete the task if they get help from teachers and friends and their own efforts How to perform High school 10th graders have many psychological and cognitive changes, so it is recommended that some ways of motivation at lower levels such as giving grades, praising, informing the results to students’ families are not convincing enough but more intrinsic and extrinsic motivations are needed Motivating students should go along with teaching process: start from reality or from internal mathematics, such as creating motivation from students’ surrounding (e.g 1.4), from other science subjects, ; evoking an intermediate motive is an incentive for intermediate steps or for activities to be carried out in intermediate steps to achieve the goal, some of which are often used to evoke an intermediate engine: target (students are directed on the goals set, on the expected effectiveness of activities to achieve the set objectives), strange rules of familiarization, similar consideration, generalization, consideration of variation and dependence; suggesting an end-toend motive to improve self-discipline in learning activities, contributing to motivating motivations for learning activities in general and sometimes to prepare a motive for beginners after In order to maximize stimulation and promote the activities of students, teachers need to coordinate different motivational ways, pay attention to the development trend of individual learners weak Math students usually has a low test scores in Math, if the teacher only relies on scores to create motivation for learners, it is not enough Some weak Math students due to their career orientation, so with these cases, teachers need to apply motivational ways by emphasizing the importance of the lesson content on some careers in society 2.2.3 Method 3: Systematizing knowledge, "compensating" knowledge and skills that students are "lacking" Purpose: to help students get the minimum grasp of knowledge and skills required by the curriculum Content: According to Nguyen Ba Kim, universal mathematics curriculum is still logical and systematic: prior knowledge prepares for the following knowledge, the following knowledge relies on knowledge first, all closely connected links Therefore, whether or not Maths subjects achieve the expected results often requires a certain premise on the knowledge and skills available of students However, with Maths, many times, mathematicians not have enough of these 14 premises and teachers have to help them create a premise for the class to start Strengthening should be done based on specific content, taking place in the form of training, deepening, application, systematizing knowledge The basis of the measure According to L.X Vygotsky: The thinking process of students is consistent with the accumulated events, the product of the general reflection of the experience of social practice Therefore, weak Math students need to be revised, re-educating knowledge from low to high, from simple to complex, from the "gaps" of knowledge and skills to overcome tripping difficulties How to perform In the process of teaching in class, teachers are concerned about discovering and classifying knowledge and skills holes of students The typical holes that not have enough time to overcome the problem need to have a plan to continue to solve for each student in Mathematics 2.2.4 Method 4: Guiding students with positive learning methods, suitable for individual student characteristics Purpose: forming learning methods suitable for the characteristics of each student in order to maximize the activeness, initiative, and creativity of students, helping students in Maths to perform tasks minimum in math learning Content: The improvement of the learning method for each individual in Math is able to create an exciting, new and interesting environment for students, help them overcome their difficulties in learning Math The basis of the measure Gardner's theory has shown that each of us has all types of intelligence, however, there will be an out-weight intelligence in each person In other words, Howard Gardner's polymorphism helped scientists realize that intelligence is not merely available to each students, but also includes the results of learning and training Theory of Leonchiep has shown that: "Activities associates with motivation", the teaching process should come from activities, through activities In the process of teaching weak Math students, teachers need to divide a component into many smaller parts, the transfer of skills and knowledge takes time and needs repeating many times at slower speed than teaching other students Thus, in order to help weak Math students, teachers need to let students choose an appropriate way of learning the same content while detecting contradictions between forms and contents In particular, special attention is paid 15 so that students can overcome mistakes due to not understanding the nature of the contents, only interested in the forms How to perform Ensure the activeness in learning Learners are both objects and subjects Training students with self-study methods through discussion, practice, research, and study, applying personal and collective experience The personalities of students are formed through active and creative activities, conscious actions In order to that, teachers need to understand the needs of weak Math students, organize interesting and various activities to stimulate their interest Organizing teaching activities based on the interest of students, diversifying teaching activities Learn what and how much depends on the learner's motivation Organizing activities for students in Mathematics, teachers need to be active, exploit their experience to guide students to new knowledge Reality shows that most of the weak Math students are more interested in subjects related to the phenomena, specific activities that they are experiencing Diversify teaching activities to improve the activeness of students Exercises should be carried out in many different forms, creating a sense of comfort and excitement for weak Math students when learning 2.2.5 Method 5: Provide requirements and tasks that are suitable for students' abilities but improve them sequentially Purpose: Design learning systems in accordance with the capacity of each student to help them complete the tasks of Maths Content: weak Math students are likely to absorb knowledge slowly if they study the same program with other normal students If teachers not prepare the adjustment plan in accordance with their cognitive abilities, they will become more and more self-deprecating They become depressed and not want to learn any more Therefore, providing suitable requirements and tasks in accordance with the capacity of the weak Math students in high school must be based on the lesson objectives and teaching objectives Based on the general objectives of the lesson and based on the needs and cognitive abilities of students, teachers should set appropriate lesson objectives, break up exercises to suit the ability of weak Math students The basis of the measure 16 According to constructivism psychology, learning is primarily a process in which learners build their knowledge by relating new experiences to existing knowledge J Paige thinks that personal intelligence grows from low to high and follows a strict order Based on the theory of "zone of proximal Development", we realized that when walking along the steps that were just right for them, weak Math students would not be agitated, missed, or fall so that they would be more likely to climb all the stairs to gain the knowledge and skills required at their levels Even if the steps are low and the transferring steps are short, when students succeed, they will create a very important psychological factor: they will believe in themselves and strength, and then have enough energy and determination to overcome Math weakness How to perform Setting requirements, tasks that are appropriate for students' abilities but sequentially raising requirements based on difficulty according to Bloom's cognitive model, levels ranging from low to high and typical behaviors according to these levels expressed in the cognitive model Teachers need to give specific requirements according to the target levels of awareness to ensure the compatibility of the capacity of different students in the same lesson weak Math students can also participate in learning activities with other students but with cognitive objectives determined at the appropriate level of their awareness 2.3 The relationship between measures to help weak Math students in Grade 10 in high school Each measure plays an important and indispensable role in the success of the process of helping weak Math students in high school At the same time, these measures have a mutual dialectical relationship For weak Math students who are not motivated, not have confidence in learning mathematics, teachers can use the first measure, then apply the second measure, the third or even the forth measure But there are also cases of weak Math students in grade 10 in high school because they have not been familiar with the new learning environment, not yet catching up with the learning speed of the new school level, have not found the appropriate learning method for themselves, so applying the first and the fourth measure, then the third and the fourth method will be the appropriate choices for the process of helping weak Math students in grade 10 17 In the process of implementing teaching and learning activities, students can escape the title “weak Math students” but they might fall into it again at a certain period Therefore, teachers need to determine weak Math students timely to select appropriate measures to help them, the first measure we offer for such purposes When identifying students who are weak at Math, teachers need to determine the main reason that leads to that problem in order to have timely and correct options for help 2.4 Conclusion of chapter To help weak Math students in grade 10, we propose the following measures: - Learn, analyze and identify the reasons leading to weak Math students to have timely helping measures - Encourage, create excitement, reinforce students' confidence in Maths in order to help weak Math students because the main reason is that students not have confidence in learning mathematics - Systematizing knowledge, "compensating for" knowledge and skills that students are "lacking" to help weak Math students because the main reason is that students are lacking knowledge at lower levels - Guiding students with positive teaching methods, in accordance with the personal characteristics of students in order to help weak Math students because the main reason is not selected the appropriate method for each students - Provide the requirements and tasks in accordance with the capacity of students but sequentially raise requirements to help weak Math students because the main reason is that students have limited thinking ability Measures linked with the main causes leads to weak Math students problem (presented in chapter 1) A number of measures have been tested through pedagogical experiment, which will be presented in the next chapter 18 Chapter PEDAGOGICAL EXPERIMENTAL 3.1 Purpose of the pedagogical experiment The purpose of the pedagogical experiment is to test the scientific hypothesis of the topic 3.2 Time and place of pedagogical experiment Pedagogical experiment round 1: Conducted in the second semester, the school year 2015 - 2016 for some grade 10 students of Duc Trong High School and Hoang Hoa Tham High School in Lam Dong Province Pedagogical experiment round 2: Held in the 2016-2017 school year for grade 10 students of Duc Trong High School, Hoang Hoa Tham High School, Da Tong High School in Lam Dong Province 3.3 Experimental objects Experimental subjects are defined as helping weak Math students in teaching mathematics in grade 10 3.4 Pedagogical experiment method: investigation method; observation methods; Mathematical statistical methods; case study method; professional solution 3.5 The content of pedagogical experiment: Experimental implementation of some measures to help weak Math students in high school 3.6 Results of the pedagogical experiment 3.6.1 Experimental pedagogical results in round 3.6.1.1 Select pedagogical experimental samples The controlled group (ĐC) and experimental group (TN) are selected similar in level and ratio of weak Math students 3.6.1.2 Analysis of pedagogical experiment results in the first round The results of studying mathematics in experimental classes are higher than that of the controlled class and compared with the beginning, the ratio of weak Math students decreases significantly and is lower than the control group 3.6.2 Experimental pedagogical results in round 3.6.2.1 Select pedagogical experimental samples The controlled group (ĐC) and experimental group (TN) are selected similar in level and ratio of weak Math students 19 3.6.2.2 Analysis of pedagogical experiment results in round The results of studying mathematics in experimental classes are higher than that of the controlled class and compared with the beginning, the ratio of weak Math students decreases significantly and is lower than the control group 3.6.3 Analyze results in typical cases 3.6.3.1 Sample selection point of view The selection of typical cases of weak Math students is based on the following criteria: + There are differences in student characteristics; + There is a difference in the cause of weak Math students; 3.6.3.2 Sample selection results With the above criteria to select the case study sample, we have selected weak Math students due to different main reasons to observation, monitor, and process information to make judgments about the teaching process in the direction of helping weak Math students The analysis of four typical cases shows that the level of mathematical awareness of weak Math students increases obviously after the time of help 3.7 Investigate the proposed pedagogical measures through the lessons of teachers and students With the evaluation of teachers, it is shown that, basically, the measures to help weak Math students at high school level can meet the innovation of teaching methods Most teachers highly appreciate this lesson and will apply it to teaching mathematics When investigating the experimental lessons, most of the students responded excitedly and liked the lessons, were able to make plans for themselves, and felt more confident in learning 3.8 Investigation of proposed pedagogical measures through teacher surveys In order to assess the feasibility and effectiveness of the measures to help weak students in general and weak Math students in particular, we have set up a proposal for 67 teachers to teach mathematics in high schools in Lam Dong province on proposed measures in chapter 3.9 Conclusion of chapter Pedagogical experiment is allowed to be conducted in high schools in Lam Dong province with periods and rounds The results obtained: 20 Compared with the initial results before conducting experiments, students of experimental classes have significantly improved the quality of Maths, especially the weak Math students rate has decreased, weak Math students have many positive behaviors in learning process The level of general awareness of experimental classes is higher than that of control classes, preventing the situation of some students who are just above the weak level from falling into weak math level; All students are more responsible and more active in math learning process This is an important result, the basis for the first step to prove the feasibility of measures to help weak Math students in high school Measures and techniques to help weak Math students in grade 10 that we proposed to use in experiments have been positively received by students, and applied by teachers in specific ways: weak Math students are more interested in learning math, are not under pressure, promote personal strengths and improve math awareness; Teachers have initially become familiar with the new approach in helping students learn math Thus, through data and data processed by the statistical method, observation method, investigation method, expert method, case study method has partly shown that the pedagogical measures proposed in chapter are feasible and effective CONCLUSION AND RECOMMENDATIONS CONCLUSION In the world, there are research results presenting the concept of weak students and measures to overcome that situation The common point in the orientation of the studies starts from solving psychological problems, then teaching methods to help weak students perform the minimum learning tasks as required The results of the research show that weak Math students in grade 10 in high schools have not performed some simple math learning tasks in some topics,or some weak students cannot even complete the Mathematics task in a whole course of Maths weak Math students in Grade 10 in high school often have little participation in math activities, lack confidence in school hours and make many mistakes in the solutions There are many reasons for the situation of weak Math students in grade 10 in high school so we classify them according to subjective causes and objective reasons Subjective causes include many factors: Students have limited thinking ability, students have knowledge gaps from lower levels, 21 students not have confidence in learning mathematics, students not have appropriate learning methods for themselves to achieve the best learning results Understanding the causes of weak students in grade 10 in high school is the basis for proposed measures to help students In fact, schools and teachers were interested in using many different forms to help weak Math students but there was a lack of specialized measures to help weak Math students to develop their internal energy Therefore, the results of helping weak Math students are not satisfactory Based on the theoretical basis and the results of studying the weak students' situations in grade 10 at some high schools, we propose measures to help weak Math students in grade 10 as follows: actively care for and discover weak Math students, timely help measures; motivate, encourage and create excitement, reinforce beliefs for students in Maths; systematizing knowledge, "compensating" knowledge and skills that students are "lacking"; guide students on positive learning methods, in accordance with the personal characteristics of students; make requirements and tasks in accordance with the capacity of students but sequentially raise requirements Some measures to help weak Math students in Grade 10 in high school have been experimentally implemented at some high schools in Duc Trong district and Dam Rong district in Lam Dong province The results of the pedagogical experiment showed that weak Math students have certain progress: in cognitive psychology and in math solving skills The research results show that the scientific hypothesis is acceptable, the research task has been completed RECOMMENDATIONS For teachers: + Measures to help weak Math students in grade 10 need to be implemented flexibly, ensuring respect for characteristics and needs of each student, helping weak students gain confidence at school, overcome the "lack" of knowledge and skills, help weak students choose suitable learning methods to maximize the strengths of students themselves Regular and periodic monitoring and evaluation are also needed to the progress of weak students for timely adjustments (if necessary) + Promptly encouraging weak Math students to make progress and consciously improve their studying attitude 22 For managers + Closely supervise the help and tutoring activities of weak Math students in grade 10 in high school + Having a reasonable remuneration policy, encouraging teachers to have achievements in helping weak students + There is timely encouragements for students to improve and consciously improve their studying attitude 23 ... grade 10 students of Duc Trong High School and Hoang Hoa Tham High School in Lam Dong Province Pedagogical experiment round 2: Held in the 2016-2017 school year for grade 10 students of Duc Trong. .. classes in grade 10 to learn about the current situation of weak Math students in grade 10 5.3 Case study method (case study) Select a number of typical weak Math students in Grade 10 to monitor... students in grade 10 in high school - The main reasons leading to the situation of weak Math students in grade 10 in high school - Measures to help weak Math students in grade 10 in high school