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Purposes of the study: Introduce and clarify the concept the competency of exploring and obtaining knowledge through elemental competencies and compatible activities in teaching maths for high school students; Find out the reality and need of improving the competency of exploring and obtaining knowledge in teaching maths for high schools students majoring in physics, chemistry and biology; Build and test the feasibility of pedagogy method applied in teaching maths at high school classes majoring in physics, chemistry, and biology to foster this capacity for students.
i MINISTRY OF EDUCATION & TRAINING VINH UNIVERSITY NGUYEN TRAN LAM TEACHING MATHEMATICS FOR HIGH SCHOOL STUDENTS MAJORING IN PHYSICS, CHEMISTRY, BIOLOGY IN ORIENTATIONS TOWARDS IMPROVING THE COMPETENCY OF EXPLORING AND OBTAINING KNOWLEDGE Major: Theory and Method of Math Teaching Code: 9.14.01.11 SUMMARY OF THE THESIS NGHE AN – 2019 i The dissertation is finished at: Vinh University Names of supervisors: Dr Nguyen Van Thuan Prof Dr Dao Tam Reviewer 1: Assoc Prof Dr Tran Kieu Reviewer 2: Assoc Prof Dr Vũ Vu Duong Thuy Reviewer 3: Dr Thai Huy Vinh The research will be defened at Ministerial Thesis Evaluation Committee held at Vinh University Time: , date: month The Thesis can be found at: - Vietnam National Library - Vinh University Library year 2019 INTRODUCTION Justification of the study 1.1 Nowadays the educational systems of all countries in the world have been facing challenges and practical requirements: being required to actively innovate to catch up with current changes because of the rapid development of technology, and the growth in the quantity and quality of human knowledge The distance between theory and practice is on the increase, so the task of Education and Training (ET) is said to create active students Together with the orientation towards action, the orientation of developing ability has been able to fulfill this important task 1.2 The concep “ability”, especially the term “ability of teaching maths” have been found in many researches in Vietnam and in the world However, the topic Developing the competence of exploring and obtaining knowledge in teaching maths for students, especially at high school level, has not been deeply studied In fact, there are not any studies of teaching maths for high school students oriented towards improving the competency of exploring and obtaining knowledge 1.3 The students majoring in physics, chemsitry and biology are chosen to take part in this research since practical surveys have found that these students have a habit of studying and discovering new things, and they are often interested in what they studied by themselves Moreover, the students majoring in physics, chemistry and biology are usually eager to learn maths as it is considered as a good tool to support them to studies their majors more effectively 1.4 The concept Teaching maths through activities, which can shape and develop ability, have been researched by a large number of educators Innovating teaching method towards learner-centered has been implemented in schools Intuitively, the term "the competency of exploring and obtaining knowledge" more or less expresses the ambition as well as active participation of learners in approaching and mastering the knowledge Basing on theoretical and practical basis, the paper has set requirements and facilitated the research on ability of discovering and acquiring knowledge on the basis of giving conception, proposing pedagogy methods to foster this capacity in teaching maths at high school and the gifted high schools Purposes of the study 2.1 Introduce and clarify the concept "the competency of exploring and obtaining knowledge" through elemental competencies and compatible activities in teaching maths for high school students; 2.2 Find out the reality and need of improving the competency of exploring and obtaining knowledge in teaching maths for high schools students majoring in physics, chemistry and biology; 2.3 Build and test the feasibility of pedagogy method applied in teaching maths at high school classes majoring in physics, chemistry, and biology to foster this capacity for students Scientific hypothesis Basing on the research to identify the elemental capacity of the ability of creativity and the knowledge –grasping competennce, if methods can be given to create effective teaching activities for the high school students majoring in physics, chemistry and biology, they can improve the competence of discovering and the knowledge –grasping competence Besides, it can boost the effectiveness of teaching maths at the gifted high schools Research task: The thesis will answer the following questions Questions 1: What are the viewpoints of researchers in regard to the topic of this thesis? What are the reasons to choose the topic? Questions 2: What are activities or cognitive activity defined? What are definitions of discovery activities and knowledge acquisition; discovery competence and knowledge acquisition? How can compatible activities of the elemental ability, and its levels be displayed?; Questions 3: What are characteristics of the high shcool students majoring in physics, chemistry and biology? What are the method of teaching maths suitable for encouraging these students to improve the competency of exploring and obtaining knowledge?; Questions 4: What is the reality of improving discovery ability and the competency of exploring and obtaining knowledge in teaching maths for high school students majoring in physics, chemistry and biology? What are the reasons and solutions of this issue? Question 5: How is the discovery ability and knowledge acquisition of the students majoring in physics, chemistry and biology improved after being taught maths basing suggested methods in the thesis? What are the results of pedagogical experiment? Research method 5.1.Theoretical methods 5.2 Practical methods 5.3 Experimental methods The significance and meaning of the thesis 6.1 Theoretical viewpoints 6.1.1 The paper has introduced the connotation concept of the term discovery activity and knowledge acquisition; discovery ability and knowledge acquisition as well as elemental ability and its levels in teaching maths for the high school students in general and the gifted high school students in particularly 6.1.2 The paper has given directions and six pedagogical measures to improve the competency of exploring and obtaining knowledge for the students through teaching maths 6.2 Practical viewpoints 6.2.1 The paper has built learning topics that can be used in teaching maths to improve the competency of exploring and obtaining knowledge for the students majoring in physics, chemistry and biology at the gifted high schools 6.2.2 The paper has initially tested the feasibility of the pedagogical measure built through pedagogical experiments and expected to be successful to be implemented on a large scale 6.2.3 The paper can be used as a reference for math teachers, which aims to improve the effectiveness of teaching maths at high schools and gifted high schools The contents of the paper defended 7.1 Viewpoints on improving the competency of exploring and obtaining knowledge based on elemental competencies in teaching maths for gifted high school students (these elements are really necessary and can be transfered to students in teaching maths at high schools) 7.2 The system of proposed measures in teaching maths is appropriate and feasible in training compatible activities to improve the competency of exploring and obtaining knowledge for high school students in general and high school students majoring in physics, chemistry and biology in particularly 7.3 Some developed teaching topics connect with the use of pedagogical measures proposed by the thesis are specific ways to improve the competency of exploring and obtaining knowledge in teaching maths at the gifted high schools Design of the paper In addition to the Introduction and Conclusion, the paper consists of three chapters Chapter Literature review Chapter Some pedagogical measures to improve the competency of exploring and obtaining knowledge for high school students majoring in physics, chemistry and biology Chapter Pedagogical experiment CHAPTER 1: LITERATURE REVIEW 1.1 Overview 1.1.1 Competence 1.1.1.1 Previous studies in the world Perrenoud's definition of competence can be considered to be the most meaningful andaccurate among given definitions of this concept According to Perrenoud, a competence is the ability to act before an assumption, the situation that someone can master because they have both the requisite knowledge and the ability to consciously mobilize this knowledge to identify and solve real problems [62] 1.1.1.2 Previous studies in Vietnam There are some main characteristics in studies of competence Firstly, the ability express individual psychological, physiological characteristics that are different from that of a biological genetically inherited factor, developed or limited due to other conditions of the habitat Secondly, the ability or competence is not only an innate factor, but also develops in activities, by activities, exists and manifests itself in activities of individuals In other words, the term “competence” should be mentioned in a specific type of activity 1.1.2 Studies relating to the thesis topic With regard to effect of teaching through discovery activities, there were a large number of researches by researchers, such as Heather C Hill, Merrie L Blunk, Charalambos Y Charalambous, Jennifer M Lewis, Geoffrey C Phelps, Laurie Sleep & Deborah Loewenberg Ball, [206] Besides, Martin C Libicki, Stuart E Johnson [209], indicated important roles and trends in improving the knowledge- grasping competence while Daeka [169] studied the model that was based on experience and collaboration in work group to develop the creativity of students J Bruner [164] studied teaching basing on discovering and methods of discovery activities; Malin Brännback, Patricia Wiklund[211] studied principles of improving the knowledge – grasping competence; and Peter Sullivan [214] refered teaching maths by owning the knowledge In Vietnam, Nguyen Huu Hau [62] has researched activities to dominate knowledge in teaching Algebra and Calculus The authors Dao Tam and Le Hien Duong [112] mentioned knowledge -grasping competence in general and proposed some pedagogical measures to support students to develop this capacity in teaching elementary geometry at the University of Pedagogy However, there have not been any researches on improving the knowledge – grasping competence, which can be studied in full and in detail, especially in term of teaching for high school students majoring in physics, chemistry and biology basing on this orientation 1.1.3 Teaching perspective-oriented capacity development 1.1.3.1 In the world Teaching from the perspective of capacity development has been paid attention to and conducted in many nations in the world because it not only encourages students to concentrate on intellectual activities but also enhances them to develop problem - solving skills within situations of life and career; it can also link intellectual activities with practical activities Summarizing theories on competencybased teaching approaches in education, training and development, Paprock (1996) outlined five basic characteristics of this approach Firstly, competency-based approach on the learner's philosophy is the center Secondly, competency-based approach meets the requirements of professional activities Thirdly, competencybased approach is oriented to real life and real career activities Fourly, competencybased approach is very flexible and dynamic Finally, competency-based approach is formed in learners clearly 1.1.3.2 In Viet Nam In summary, there are several core factors of the teaching from the perspective of capacity development: Teachers organize activities to promote positive and proactive learning of students; create a supportive learning environment (linked to the real context); encourage students to reflect ideas and actions, encourage communication; enhancing the learning responsibilities of learners; creating favorable conditions for learning, sharing, exchanging, debating, connecting to learning; provide full opportunities for learners to explore, experience and create; and teaching is like a learner's learning process 1.2 Improving the competency of exploring and obtaining knowledge 1.2.1 Activity and cognitive activity 1.2.1.1 Activity An activity includes folowing characteristics Firstly, it always has objects and it is done by a subject Moreover, it always has its own purpose, and can operate according to indirect principles According to A N Leonchev [82, p 579], activity is a process of performing the mutual exchange between two poles: the subject - the object The author described the macro structure of the activity with components that have dialectical relationship with each other 1.2.1.2 Cognitive activity The term Cognitive activity is defined as the following basic characteristics Initially, it is the subject of discovering and recreating the world, thereby forming and developing the understanding of subject of the world and its methods of movement The subject does not directly affect objects but indirectly through labor tool The Cognitive activity often takes place in direct or indirect interactions between individuals It is said to have many levels, which depends on the involvement of both cognitive and rational cognitive functions It is a dynamic, positive and creative process of the subject; which starts from unknown to knowing, from superficial to internal attributes, that is, from sensory, intuitive, separate to the complete, stable, regular, and deeper substance of a whole class of objects, phenomena and finally return to reality Cognitive activities in general and mathematical cognitive activities in particular have three levels, which includes being aware of the problem, understanding and clarifying it 1.2.2 Activity of exploring and obtaining knowledge We propose the concept of connotation of the concept of discovering and acquiring knowledge in accordance with that satisfies students' requirements to positively study learning as the following viewpoints Discovering and acquiring knowledge is a series of activities that actively experience, discover, think, attempt, and use intellectual abilities (observation, comparison, analysis, synthesis and experience, verification ) along with personal qualities such as desire for learning, perseverance, flexibility, critical thinking as well as endurance towards issues that need to be addressed without specific knowledge, to capture and master the problem more fully, to be more independent, creative as well as to gradually expand it with related issues, adding to their existing knowledge Thus, it can be understood that discovering and acquiring knowledge is a sequence of activities done by the subject, which can transform the logic of the object into the thinking process due to the subject’s active, positive participation; thereby grasping, mastering, thoroughly understanding the subject and including the expansion of research and mastering of other related subjects Discovery not only indicates what exists inside each object or phenomenon of the problem, but also shows an extension of the mastery of the subject being studied beyond what is inside the thing, the phenomenon of that problem 1.2.3 The role and meaning of organizing activity of improving the knowledge – grasping competence for students in teaching maths According to B Maskey, J Collum: concept card (Nepal Training Institute), using verbal methods and encouraging student self-organization, combining methods to mobilize multiple senses at the same time to participate in the learning process is limited Studies show that students want to gain in-depth understanding and longterm memory, it is important to encourage them to participate in activities directly because, they will be able to use the acquired knowledge in a better way due to their own experience This can make the process of discovering and acquiring knowledge more fully and deeply Moreover, it is essential to give students joy and excitement because it is the motivation to promote their self-discipline and positive learning, especially the joy and excitement of a person who finds the truth on his own It is said that students should be put into real-world situations, and required to directly observe and make experiment, discuss and to solve problems in their own way Thereby, students will acquire new knowledge, learn new skills and methods as well as find out that knowledge and skills not necessarily have to follow the existing patterns to reveal their potential creation [12, p 3] 1.2.4 The concept of improving the competency of exploring and obtaining knowledge From psychology and education perspectives, from studies on activities, awareness, competence, which are being applied in teaching mathematics at high schools, and the concept that considers discovering and acquiring knowledge as an important competence to be develop, the competency of exploring and obtaining knowledge can be defined as personal psychological characteristics, through a combination of elemental competencies expressed in activities of individuals in order to actively explore, comprehend, master and address concerned issues flexibly and creatively 1.3 Expression and elemental competencies, as well as compatible activities of the competence of exploring and obtaining knowledge in teaching maths The ability of discovering and acquiring knowledge of students in learning maths can be evaluated according to the following criteria Firstly, they can Mobilize math knowledge related to discovering and mastering a specific math content Secondly, they can be able to conduct activities such as doing exercises, understanding mathematical concepts and proving theorems properly, and gaining results consistent with required purposes For example, in proving the theorem, students' ability to discover and gain knowledge is shown through their understanding of theoretical proof, independently conducting theoretical proof In addition, learners also know how to apply creatively in many other related exercises, or other topics of which a higher level is applied in life Students have clear attitude and emotions with problem solutions, such as finding mistakes and correcting mistakes, realizing the good and profound sides of each solution Moreover, students learn to be persistent in expanding assignments and problems The competence of exploring and obtaining knowledge of learners in studying mathematic can be described basing on the following six elemental competencies and 21 suitable activities 1.3.1 The first elemental competence: The ability to experience, explore situations, detect problems, detect contradictions appearing in situations and problems This component competence includes compatible activities, such as hands-on experience, consideration of ongoing issues It also includes experiencing, discovering signs of nature, general properties as well as mathematical relationships of things and phenomena Another important characteristic is to limit problems, identify the hypotheses and the conclusions of the theorem, and the relationships of those elements as well The last point is said to discover and detect contradictions that appear in the problem 1.3.2 The second elemental competence: The ability to observe, intuitively solve problems, formulate and implement problem solving in common logic ways for similar problems This component competence includes compatible activities, such as discover and detect visual symbols and their relationship that appears in the problem and know how to choose good images to support the problem domination The second criterion is to analyze and explore knowledge through research and observation of visual images or animation Besides, it is necessary to make good use of the mathematical software or visual images, which can create symbols and images relating to the problem as well as point out mistakes to solve them Finally, a suitable approach should be given to solve problems in an appropriate sequence 1.3.3 The third elemental competence: ability to predict and infer reasonably, associate and mobilize knowledge, perform thinking manipulations in the process of acquiring knowledge This component competence includes compatible activities, such as making reasonable predictions and inference, selecting reliable predictions Besides, it is required to associate, mobilize knowledge to the "nearest development zone" to facilitate in finding a way to solve the problem Finally, it is essential to implement systematization as well as infer effectively in the process of discovering and mastering the problem 1.3.4 The fourth elemental competence: Ability to use language in mathematical communication There are some compatible criteria The first requirement is to express mathematics content in different ways accurately to have better access to the problem to be solved The second requirement is to be able to "interpret" from the common language form of maths clauses to mathematical terms and symbols, and vice versa Thirdly, it is required to use language of set theory and mathematical logic along with mathematical symbols and terminology accurately and rationally to express solutions Moreover, it is necessary to use the right rules of proof, reciprocal clauses Last but not least, it is required to explain the nature of a formula or the final steps of an exercise Below is the example of this competence Example 1.1 (cited [139, p 109 - 110]) According to the design, the original height of the Eiffel Tower is 300m, but the antenna mast on the top of the tower increases its height reaching at 325m The lowest temperature in March 2015 in Paris was 8oC on March 1, 2015 and the highest temperature in July 2015 was 26 oC and measured on July 18, 2015 Calculate how many centimeters the tower has grown from March to July 2015, assuming the tower is 325 meters tall on March To this exercise, the students majoring in physics relate and mobilize to the following contents - Every solids have changes in length because of the change of temperature, which is described by the following formula l = l0 + l0 ( t − t0 ) , in which l0: The length of the object at time of temperature t0; l: The length of the object at time of temperature t; and : Long expansion coefficient - Students look up the board to find out the length of expansion due to the heat of iron: 11.10-6 From this the answer can be given However, students show their ability at different levels through solving the problem Solution 1: The height of the tower in July is l = 325 + 325.11.10−6 ( 26 − ) 325,064(m) The height difference between March and July is 325,064–325= 0,064 (m) = 6,4 (cm) Solution 2: For better students, they have mastered a better formula to calculate the difference: l = l0 ( t2 − t1 ) , thus, the difference in height of the tower between March and July is calculated: 325.11.10-6(26-8) 0,064(m) = 6,4(cm) 1.3.5 The fifth elemental competency: Competence in mathematical modeling practical problems This competence can be showed by the following activities Firstly, It can build mathematical models for practical issues Secondly, it can orient and solve model problems and master practical problems 1.3.6 The sixth elemental competency: critical and creative ability This ability can be displayed via some compatible activities Firstly, it can collect results of solving problems with right situations and right limits Secondly, it can make comments on problem-solving results, compare problem-solving methods to choose the best solution Besides, it requires students to adapt and critique in assessing the process of problem-solving, contemplate solutions, detecte and correct mistakes; and solve the problem from a new perspective and expanding 1.4 Levels of improving the competency of exploring and obtaining knowledge in teaching maths in high school The competency of exploring and obtaining knowledge is classified according to various levels *) The first level: Students fulfill the basic requirements of discovering and acquiring knowledge when situations and issues are clearly raised by teachers *) The second level: Students have a clear awareness of situations and problems that are raised by teachers, and they know how to complete improving the knowledge grasping actively and effectively Teachers act as acatalyst to accelerate students' discovery and acquisition of knowledge *) The third level: Students actively identify unclear issues through activities of discovering, predicting conditions and commenting on approaches to firmly, flexibly and critically Moreover, by this way, they also know how to expand and master the subject Below is example showing the levels of improving the competency of exploring and obtaining knowledge Example 1.2 There is a park showed in Figure 1.1.a It is planned to put a lamppost to illuminate the park Find an option to locate the lamppost This problem is conducted in the following steps: +) Step 1: Measuring and simulating the park as Figure 1.1b 11 a) Students have dfficulties in learning the content of subjects: Because learners bring incomplete insights into the subject, they often bring the previous knowledge into the relevant content b) Some research findings on teachers: straight teachers will greatly influence students' style, ability, and learning outcomes c) The obstacles from the current textbook program: Author Dao Trong Thi wrote: “The program and the amount of knowledge shown in the textbooks is too much compared to the understaning of students to Besides, the content puts more emphasis on theory and imparting knowledge without paying much attention to train students' skills and personality” [195] 1.7.5.2 Analysis of quantitative results Most of surveyed participants (93.8%) find that it is necessary to design and organize activities for students to discover and gain knowledge Only 6.2% of them did not see the need to organize this activity In contrast, 100% of teachers and administrators agree on the necessity of organizing discovery activities and gaining knowledge, and most of teachers and managers are interested in the manifest activities of discovering and acquiring knowledge, but the capacity and organization of those activities are not equal Students are encouraged to practice activities that are part of the ability to discover and dominate knowledge, but these activities are not conducted regularly It is said that students’ improving the competency of exploring and obtaining knowledge is only at fair level Besides, there are some activities that shows their ability only at average level, accounting for nearly 50% This shows that the capacity to discover and dominate knowledge should be paid attention and continue research Most of students want to be trained in compatible activities to improve the knowledge – grasping competence, but the training of those activities in learning is chaired and controlled by teachers has not been focused properly Teachers and students also think that about 25% -30% of students often face difficulties and passively when actively implementing compatible activities of discovering and acquiring knowledge in the classroom 1.7.6 Cause of the situation There are some main reasons Firstly, the teacher has not really considered improving the competency of exploring and obtaining knowledge in terms of competencies of component activities, and has not clearly identified the elemental competencies of this capacity, as well as typical manifestations of these competencies so that activities can be organized in accordance with the teaching content, which aims to formulate and train students' ability to discover and acquire knowledge Secondly, generally teachers have not identified measures and ways to implement measures to improve the competency of exploring and obtaining knowledge in association with the content of maths teaching Finally, teachers have difficulty identifying and exploring opportunities for students to be experienced, trained, and fostered improving the competency of exploring and obtaining knowledge in the teaching process 1.8 Conclusion of Chapter On the basis of research, analysis and practical experience, in Chapter 1, we draw some results as follows: Firstly, the thesis has codified the views of a number 12 of authors about receiving activities, make a point of of exploring and obtaining knowledge; as well as the status of exploiting activities of discovering and acquiring knowledge in teaching Maths in high schools today; Secondly, the thesis has given the viewpoint and the competency of exploring and obtaining knowledge in teaching mathematics for high school students; level of this ability in teaching mathematics among high school students; Thirdly, the thesis has presented the expression of the competency of exploring and obtaining knowledge through component competencies and component activities; Fourthly, the thesis has pointed out the urgency and reality of developing the of the competency of exploring and obtaining knowledge in teaching mathematics in particular, in educational innovation and practical needs in general At the same time, we gave a view on teaching mathematics to high school students specialized in developing the cmpetency of exploring and obtaining knowledge Chapter SOME PEDAGOGICAL MEASURES CONTRIBUTE TO FOSTERING THE COMPETENCY OF EXPLORING AND OBTAINING KNOWLEDGE FOR HIGH SCHOOL GIFTED IN MATHEMATIC, CHEMITRY AND BIOLOGY 2.1 Orientation of Construction 2.1.1 Ensuring the compatibility between content, goals with skills, knowledge standards of Mathematics curriculum 2.1.2 Thoroughly grasping the operational viewpoints in forming and developing competency of exploring and developing knowledge 2.1.3 Building a positive collaborative environment in studying, in which students are the center, always encouraged to experience - exchange - discuss explore - explore and gain knowledge 2.1.4 Focusing on helping students create relationships between Maths content, focusing on the relationship between Mathematics and the subjects of Physics, Chemistry, and Biology; contributing for dominating, applying with practice, discovering and developing new ideas in process of the teaching 2.2 Pedagogical measures 2.2.1 Measure 1: Creating opportunities for students to practise compatible activities with competency of exploring and developing knowledge components through installation of situation of discovery in teaching, finding and solving problem in teaching a) Scientific basis of measures Methods are forms and modes of operation of teachers and students in teaching environments preparing, aiming to achieve the purpose of teaching and developing individual competencies ([157]) *) Educators believe that teaching discovery has the following strengths ([83]): Firstly, As a method aimed at learners' activities, the activity is encouraged to consider that learning is their own work rather than teachers’ one, the level of learners' demands is also increased Second, A method to support the development of individual cognitive capacity and talent of learners 13 Thirdly, A method that allows learners to have time to acquire, update information and assess their true ability in the learning and research process + According to Jerome Bruner, teaching discovery consists of the following five principles: Problem solving; managering of student; Connection; analysising information analysis explanations; Failure and feedback *) With teaching method of discovery and solving of problem, it will develop students' creativity, competency of solving of, helping students acquire knowledge, skills, cognitive methods and self-development Meeting the requirements of modern practice, with experiential learning This measure will contribute to foster the overall of competency of exploring and developing knowledge b) Method of implementation of the measure + Solution 1: Organizing compatible activities in the direction of applying discovery teaching methods, fostering learners' interests and interests Through to Roger Bybee and his colleagues, we consensus with discovery teaching process consists of steps, called the 5E process: Engage; Explore; Explain; Elaborate; Evaluation + Solution 2: Organizing -compatible activities according to method of discovering and solving problem in order to increase the activeness, actively discovery c) Attention of using measures *) Applying teaching method of discovery requires the following conditions: almost of students must have enough knowledge and skills necessary to carry out activities organized by teachers; Teacher's participation in each activity should be necessary, not too little, not too much, causing students to understand exactly what they have to in each discovery activity To ensure this, teachers must understand their students' abilities and know their "nearest developmental area" *) Applying problem-solving and problem-solving learning, the following should be noted: + Giving students to discover and solve problems for a part of the learning content, teachers can help with different or lesser levels + The proportion of problems discovered and solved by the learners and the program depends on the characteristics of the subject, the object of the student and the specific situation + Teaching discovery and solving of problem can be applied in different stages of the teaching process: forming new knowledge, consolidating knowledge and skills, applying knowledge This method should be aimed at all students, not just for good students 2.2.2 Measure 2: Enhancing activities using visual means, teaching tools, activities relating to discover the nature of the problem so that students can improve their ability to observe, be proactive and interested in acquiring knowledge a) Scientific basis of measures The visual representations create vivid images, easy to impact on the human senses, thereby attracting attention, creating motivation for learners J.A Komensky (1592 - 1670) was the first educator setting up the principle of teaching systematically and scientifically Among the principles stated by the author, 14 visualization is ranked the firstly, J.A Komensky said: "There is no intellect in things that had not previously felt" The author said that in order to have solid knowledge, you must use visual methods Not only does visual media participates in the process of forming concepts, it but also support for teaching theorem to teach Math problems Visual media is a bridge and an intermediate step in the abstraction stage This measure will contribute to fostering elemental competencies 1, 2, and b) Method of implementation of the measure Teachers can perform follow these forms: + Organizing observation and experiment activities on models, drawings, , to help students draw attributes, typical signs of concepts, things and phenomena on the basis of that formed the symbol and came to dominate; + Training the ability to predict knowledge through specialization, generalization and similarization through the organization of open teaching phases; + Rationaly using of support software to enhance discovery, support for predicting and acquiring knowledge for learners Example 2.1 Having to hang a mirror with a height of 1m on a wall that how much the bottom edge of the flat so that a person with a height of 1.8 m can look in a mirror, knowing that person is 0.8m from the mirror? How will the result change when we change the distance between the person and the mirror? c) Attention of using measures From the obtained results, we find that in teaching mathematics at high schools, it is necessary to use visual means and activities to discover the nature of teaching, but to get the desired effect, we must be paid to the following principles: + Principle 1: Visual aids need to be built and applied in a spirit that must meet the purpose of teaching mathematics in high school + Principle 2: Visual aids in teaching must respect and inherit curricula and textbooks + Principle 3: The construction and using of visual aids must be based on the orientation of innovating teaching method, notably creating a positive and self-motivated working environment + Principle 4: Means of teaching must focus on students' self-discovery, independently explore problems, actively dominate and solve problems 2.2.3 Measure 3: Organizing teaching activities in the direction of integration and differentiation, focusing on mathematical modeling problems of practical issues and STEM-oriented learning topics a) Scientific basis of measures *) According to Do Ngoc Thong “In general education, integration and differentiation are two requirements that cannot be ignored and need to be done in a uniform and unified manner in all aspects: i) Desgigning program; ii) Compiling textbooks; iii) Organizing teaching and iv) Testing, evaluating ” Integration is one of the educational perspectives that have become a trend of teaching in high schools and in developing of curriculum in many countries around the world “STEM education is an interdisciplinary approach in the process of study, in the conceptual academic principles and it is integrated with real-world lessons, 15 where students apply the knowledge in the department study, technology, engineering and Mathematics into specific contexts, helping to connect schools, communities, workplaces and global organizations… to develop STEM capabilities and competitiveness in a new economy” + There are important characteristics of STEM education: i) Interdisciplinary approach; ii) Integrating with real-world lessons and Connecting from schools, communities to global organizations *) In terms of differentiation in teaching, teaching must ensure a differentiation for each student, for a whole group of participants The division of children into a group to ensure the mutual support between members of the group as well as assigning appropriate work for them, that is the guarantee of differentiated teaching, from the perspective of perceptions of Vygotsky about "nearest development zone", differentiated teaching to ensure the following requirements: The plan of teaching bases on the interests, readiness and outstanding intelligence of the learners; students are often guided and supported by making choices basing on their interests, thereby facilitating independent and cooperative development of skills; The assessment process is ongoing, helping teachers have the appropriate orientation and adjustment Students are assessed in a variety of ways and forms; The classification process bases on academic achievement and students *) Regarding the modeling problems, basing on Nguyen Danh Nam and other athors, we think that modeling is a situation, a problem with a model or a real context that can be used with mathematical knowledge to solve In other words, this is the situation, the problem containing elements in the real world, but they were simplified, specialized, concretized, adding appropriate conditions, assumptions, and limited factors of elements which are not necessary, allowing learners to access and solve by math as tools according to their intentions, however they still reflect a part of the situation in the world Formulating situations, the problem should be associated with a real, familiar, closed context with students This measure also helps students directly connect Math with practice through learning It is an opportunity for students to practise knowledges of theories, applying knowledge to solve practical problems This measure will contribute to fostering elemental competency 2, competen and b) Method of implementation of the measure *) The first solution: Organizing interactive activities with high experience like project-based teaching *) The second solution: Strengthening integrated and differentiated teaching, teaching according to STEM orientations to ensure specificity of the subject and ability of the learners, which can be conducted in the following directions: Organizing teaching mathematics and the meaning of Mathematics to study Physics, Chemistry and Biology well; Using tools that are subjects, contents of Physics, Chemistry and Biology subjects to teach Maths well; Seeing Mathematics, Physics, Chemistry, Biology is a tool for sovle problem well, this is the orientation of teaching STEM For example, with the solution of organizing teaching according to STEM orientations, considering Mathematics as a part of STEM, lessons can be designed as 16 follows: Setting up the objectives of; Identifying potential integration of organizations; Identifying cored and suggestive questions; Designing potential activities in subjects, mapping activities and setting allocation of time; The final step is to evaluate the integrated lesson and share the solution Figure 2.1 Students of high school for gifted of Vinh university in studying STEM class, March, 2019, The candidate participated in classroom research with projects "Measuring and monitoring quality of water" and "Sensors and data" *) The third solution: Organizing the construction of activities selecting and using situations, modeling issues *) The fourth solution: Organizing the activities creating opportunities for students to collect and exploit modeling problems containing inter-subject content Example 2.2 (Reproduction of amoeba metamorphosis): An amoeba can divides into amoebas after a second And every second, every child also divides into amps Counts to see how many amoebes after 30 seconds? After 30 seconds, the number of amps is: S = + + 22 + +230 - is the sum of an geometrich sequense with 31 terms, u1 = 1, q = 2, so: S = 231 − = 2.147.483.647 (amps) −1 For students gifted in Chemistry, we can include the following example Example 2.3 guessing the spatial structure of the methane CH4 Students with certain intuition predict that: there are C-H bonds created and to create the stability of the molecule, the structure needs to ensure symmetry, the distance between H and H is equal, the bonding angles H - C - H¬ are equal, therefore, CH4 must be composed of regular tetrahedra, where C is the center of the molecule Figure 2.2 Model of methane’s In fact that, experiments have shown that molecule the prediction is correct, but to get the results, chemists have gone through more complex theories, such as the VB theory of valence and the re-orbitalization AO (Figure 2.2) c) Attention of using measures *) In order to effectively ensure differentiation and integration in study, in our opinion, teachers need: to be flexible, dynamic, creative and constantly strive to improve their professional qualifications and competence; the requirements of renovating methods; understanding students clearly, the style of learners, Since, teachers designed the content suitable for each student and demonstrated the differentiation; It is necessary to have an overview of the subjects and each subject in order to adjust and integrate the content in design of lessons accordingly, contributing 17 to the format and develop of the capacity for students; focusing on both time and conditions of classroom *) In addition, in order to apply widely and effectively implement of differentiated teaching perspective, educators need to understand the nature of the problem, and at the same time, they must change their awareness in content development, the program as well as in teaching and testing, assessing the reality of the teaching process In order to organize a successful division of teaching, teachers need to create a democratic relationship between teachers and students, between students and students to help students be more ativitive and confident In particular, in differential teaching, students need to follow the process: Investigating and surveying students before teaching; Making of plans, preparing lessons from students' needs analysis; During the lesson, teachers must combine a variety of teaching methods, selecting the appropriate in teaching arrangements for the lesson objectives; Checking and assessing the progress of students during the process of studying *) Situations and modeling problems must be arranged from easyly to difficultly, from simply to complexly Students who themselves solve a problem have great psychological meaning On the contrary, the failure from the first problem easily makes of losing their morale, easily creates a negative mood for the organization of the next activity Therefore, while designing a system of model of situations and problems, teachers need to pay attention to the levels of modeling, Nguyen Danh Nam has divided into different levels and built the Compatible situations to foster modeling capabilities for students in teaching +) If mathematical situations are constructed, it is necessary to ensure: The situation is brought up closedly, linking with the real context Each situation may contain one or several related questions, but it need to ensure of various solutions; Increasing opened questions, promoting flexibility and creativity; closed situations, attracting students +) To collect mathematical modeling problems, it satisfies that the following requirements must be ensured: Learners must necessary have mathematical knowledge; Learners should know practical knowledge at their age appropriated level and experience, natural language skills, ability to switch to mathematical language or vice versa in general; Learners must recognize the hidden mathematical knowledge in real-life situations in general and in specific subjects Understanding how to link Math knowledge with knowledge in practice and other subjects, with personal experiences in real life +) In practical activities, it is necessary to ensure: the good teaching of prescribed practice lessons, looking for more practical opportunities from Maths topics In practice, it is able to organize practice in the classroom and outside the classroom To attract students of participate and meaningful exercises, the exercises should be associated with specific situations, specific phenomena in the real life 2.2.4 Measure 4: Organizing students acitivities of practical thinking and some other intellectual aim to practice their ability of discovery of the natural problems arcodding logically, as well as to expand problems a) Scientific basis of measures 18 According to Dang Vu Hoat, intellectual activity competence is expressed in the capacity to manipulate intellectual manipulations, especially thinking manipulation confronting of a problem, the most important thing is to predict how to approach the problem correctly and provide a simulation, the way of solving the problem This is important because it cultivates a sense of self-confidence as well as a sense of wellbeing, certainty in thinking and solving problem Generalization has an organic relationship with other thinking manipulations and is closely related to specialization and similazation G Polya asserts: "Specialization, specialization, and similarization often cooperate with each other in solving mathematical problems" and "generalizations, specializations and the like are combined together naturally in trying to solve the problem.” Not only are comparisons, analogies, generalizations, abstractions, etc a means to conduct cognitive activities and solve problems they but also provide methodological knowledge for students This measure focuses on fostering elemental competency 1, elemental competency and elemental competency b) Method of implementation of the measure We support to the opinion of the author Nguyen Thi My Hang, training of thinking manipulations through compatible activities can be conducted such as: + Practicing for students to analyze the contents, externalities of mathematical concepts, as well as the ability to apply those concepts to solving mathematical problems + Training for students to clarify the meaning of each element given in the hypothesis, thereby seeing the applicability of the theorem + Training for students to express definitions, theorems, and solving problems in different ways + Instructing students to find common signs, the nature of elements and relationships in a problem or a class of problems + Create opportunities for students to practice similarization skills in the process of solving math problems + Encouraging students to propose new problems that is based on exploiting the given problem + Developing some situations that contain solutions to problems with mistakes, guiding students to analyze to identify common mistakes, whereby finding appropriate teaching methods to overcome c) Attention of using measures The activities aimed at training the thinking and other intellectual activities presented above are mainly conducted through provocative questions of teachers' instructions and groping, exploring, creative experience of students Through activities, not only students solve of problems, they but also learn the ways of thinking, way of discovering solutions Therefore, the role of the teacher in the direction and control is very important, the question system and the anticipation of the discoveries and experiences of the students must be really good, the teachers need to direct the situations occuring in student activities, contributing to supporting students well in conducting intellectual activities and fostering thinking manipulations 19 2.2.5 Measure 5: Enhancing activities that create opportunities for students to argue, learn personally, activities to detect and correct mistakes, to gain knowledge and practice critical thinking a) Scientific basis of measures The school of psychology with typical representatives such as L X Vygotsky, A N Leonchiev, A.V Petrovski, the age of high school is a very important stage in development of thinking, especially theoretical thinking (due to the development of the brain and due to changes in the natural activity) study) Intellectual development includes changing of both quantitative and qualitative More activetily, they are more active and increase the ability to think independently and creatively with the subjects This depends on the attractiveness of the subject according to their perceptions High school students' thinking is more critical, rigorous, consistent, and more grounded than in their teens Although there is a period of strong and profound development in thinking, but because of that, they can not avoid wrong thinking This measure will make an important contribution in training students the elemental competencies of competency of exploring and obtaining knowledge in particular, and to competency of exploring and obtaining knowledge in general This measure focuses on fostering elemental competency 3, 4, and b) Method of implementation of the measure First way: training for students to ask and answer questions themselves; Second way: creating opportunities for students to find and analyze grounded arguments when solving problems; Third way: activities situations in designing collaborative learning for students to debate for finding out solutions, presenting and evaluating the solutions; Fourth way: exploiting and using reasonably exercises that have the advantage of refraining in critical activities in the teaching process; fifth way: Organizing teaching multiple choice exercises Exercises of this type enable students to reason in different ways to find the fastest way to choose the correct option, eliminating the interference plans However, the disadvantage of solving objective tests is difficult to assess the thinking process leading to the test results, so it is difficult to test thinking capacity (especially creative thinking) and detect and correct mistakes for students Therefore, objects of designing test assignments need to ask students to analyze the alternatives as a good opportunity for students to present their reasoning At the same time, the teacher also knows why students choose the answer c) Attention of using measures In order to effectively implement this measure, attention should be paid to the following: Firstly, teachers design situations that can lead to mistakes for students in challenging with them; Secondly, paying attention to the requirements: education, timeliness, accuracy in the process of detecting and correcting mistakes for students; Thirdly, it is necessary to create conditions for students to express mistakes through training the self-examination and self-assessment skills 2.2.6 Measure 6: Organizing forstudents activities of analyzing, identifying relationships, activities of transformation of language from different perspectives, focusing on interaction in communication activities, in order to enrich the 20 expression and increase of solving problem, contributing to practice critical thinking and creativity a) Scientific basis of measures: *) About language conversion activities, according to L.X Vygotsky [159], language is the process by which individuals use a certain language to communicate and to think The ability to identify and represent the same mathematical problem in different representations, and the flexibility to move from one representation to another, is crucial in learning math The author said that the meaning of the word is both a language and a thought, so it is a unit of linguistic thinking Mathematical language is a scientific language that requires shortness, accuracy and comprehension, students are often not good at expressing mathematical language in many aspects, such as not being able to grasp other forms of problems, can not convert to equivalence problems *) Activities aimed at cultivating critical and creative thinking, teaching in the direction of fostering competence requires teachers to orient and help students promote positive, proactive and creative skills, to verify information correctly and choose problem-solving methods getting high efficiency According to Toan Nguyen: “To be creative must have critical thinking, to have critical mind must have an independent spirit Indeed, creativity makes a new product better than the old one, critical thinking helps to evaluate the product, which comes from its independent thinking”; "Creative thinking develops from independent thinking, critical thinking" [141, p.59] Critical and creative thinking intertwined, penetrating each other, operating in a way of criticism - creativity - criticism - creativity - criticism in which the next level of creativity is higher Nguyen Ba Kim analyzed: "Flexibility, independence and criticism are necessary conditions of creative thinking" The creativity of Thinking is evident in the ability to create new things: discovering new problems, finding new directions, creating new results Creativity and criticism always go hand in hand, complementing each other This measure contributes to fostering elemental competencies 1, 3, 4, 5, and b) Method of implementation of the measure *) In order to practice language conversion activities, we use the following solutions: Encouraging and asking students to analyze exercises according to different aspects from which to express problems in various forms; Encouraging students to use the representations to illustrate the requirements of exercises; Organizing the conversion of languages within an discipline of Mathematics, as well as from different subjects, transforming from a subject, a subject to content related to the subject, the other subject and vice versa again Example 2.4 In teaching physics for students of the 10th division specialized system, it is possible to Figure 2.3 teach students the following exercise: Two homogeneous iron balls of the same weight are fastened on a homogeneous iron bar as shown in Figure (iron bars are negligible mass) Hanging vertically on a wire at the midpoint of AB, the iron is balanced horizontally as Figure A I B E A I C B 21 Contining to hang the same three marbles on A, B, C as Figuer 2.3 I is the point of satisfaction of equality, where, E is the midpoint of BC In order for the iron rod to stand still horizontally, it is at the point I Please explain the results above Can you generalize the results of the above problem? *) For the practice of critical and creative thinking, the following methods may be conducted: +) Conducting according to Ngo Bao Chau's point of view: “ Approach in a way not from definition, proof, and to exercises that we have to learn the opposite, from solving problems firstly, then we learn concepts that help us understand those issues Even that concept, we don't necessarily have to learn right away, we need to localize it into conceptual areas We have these black boxes, we manipulate and think about using those black boxes to solve our questions When we are proficient what those concepts reflect our thoughts, then we will find out the definitions, theorems, proofs of form and that are necessary, that is foundation for our knowledge to be more solid ” +) Organizing in the way of author Nguyen Canh Toan on the process of expanding a concept, a theorem, a problem to foster critical thinking: including steps +) Organizing activities, helping students see the problem from different perspectives, fostering critical thinking and creativity of learners c) Attention of using measures *) In defining terminology, transferring to equivalence problem, we need to anticipate difficulties, initial conditions of the original problem in order to rewrite to equivalent conditions of the following problem and students should be noted to avoid misunderstandings; Teaching students to exploit the above typical applications will enable students to explore and discover new knowledge related to the subject in other situations; increase the ability to associate, see the problem from many ways Thereby, improving the ability to change the language of the problem *) At the same time, this measure also contributes to educating dialectical thinking, creative perspective, educating the scientific worldview for students to look at things and phenomena in relation, different phenomena and in a state of constant change Therefore, it is important to pay attention to the following: Teachers, educators need to know how to look at the "particular" from different ways, because each way gives us a direction to find out the individual in the common, the common in the private; And, needing to guide students to persevere in the implementation, then success in learning Math will achieve high results 2.3 Conclusion of Chapter The main content of this chapter deals with pedagogical orientations and measures to foster the competency of exploring and obtaining knowledge for students in teaching Maths in high school Orientations are a necessary condition for developing the knowledge - grasping competence In the process of implementing the measures, we focus on teachers paying the experiential activities of students, activities of exploring, actively mastering knowledge At the same time, in some measures, we also focus on 22 situations, ways to create motivation, forms of leading students in the direction of experience, and positive activities to promote their ability The measures also focus on creating vivid, interesting images, associated with reality, enhancing student experience The coordinated combination of these measures will promote the development the competency of exploring and obtaining knowledge for high school students in general and high school gifted in Physic, Chemistry and Biology in other hand Chapter PEDAGOGICAL EXPERIMENT 3.1 Purpose of pedagogical experiment: Pedagogical experiments are conducted in order to test the feasibility and effectiveness of the pedagogical measures that have been proposed to foster competency of exploring and obtaining knowledge in teaching mathematic for students of Grade 10 and 11 3.2 The content of pedagogical experiment At the time of conducting the first round of experiments, Vinh University High School is using the 10th grade book of basic books edited by Tran Van Hao At the time of conducting the second round of experiments, Vinh University High School is using the 10th grade book of basic books edited by Tran Van Hao Two experiments were conducted in 2018 and 2019, namely: the first one took place from September to December 2018, and the second one took place from January to April 2019 The first: Experiments are conducted for students of grade 10, 26 periods of content Geometry 10 Session: Experiments are conducted in 36 periods of contents of Algebra and analysis 11 3.3 organizing experiment Organizing the experiment was conducte in two phases: * Phase I: Experimental class is class 10A4; teacher of experimental class: Dang Thi Viet Ha; The control class is grade 10 A5; The teacher of the control class is: Phan Xuan Vong Phase II: Experimental class is class 11A3; teacher of experimental class: Nguyen Cong Chuan; The control class is grade 11 A4; The teacher of the control class is: Phan Viet Bac 3.4 Qualitative assessment according to empirical process Teachers lecturing in expermental classes have the opinion that : It is not obstacles and feasible to apply the views and measures in the thesis obstacles, not feasible to apply the views and measures in the thesis Opinions, especial suggestions on how to organize that the role of teacher control is ensured, the central role, the student's selfexperience; and making of questions and the appropriative direction, moderate and diversified activities for students; not only does such the organization stimulates students' activeness, independence in exploration and discovery, it but also motivates them to acquire methodological knowledge in problem solving Many other observations have led to the result that students in the experimental class have developed and fostered 23 the elemental competencies of the competency of exploring and obtaining knowledge, the level of perfection is getting better at the end of the experiment, while in the control class, this compehtency of the students did not improve and it is more clearly to see that the increasing of the distance between the experiment and the control in order to the later of the experiment 3.5 Assessing by the tests 3.5.1 Content of the tests During each experiment, the students had been finished two tests: the between and the end of the experiment The first experiment, we conducted in Geometry, while in the second, we conducted in Algebra and Analysis 3.5.2 Qualitative assessment the tests 3.5.2.1 Assessing of the content of test Analysing above, it can be seen that the four tests above have clearly shown their intention: to survey the knowledge - grasping competence of students gifted in Physics, Chemistry and Biology In empirical classes, because of training of this competency through pedagogical measures, the quality of the tests is better 3.5.3 Assessing quantitativily through the tests’ result The test results of students of experimental classes and students of general classes are shown through the following statistics Diagrams: Diagram 3.1 The ratio of the results of the tests I and II of the first and second round of experiment Diagram 3.1 is show that: The average mark; The percentage of students who achieved good and excellent mark in the experimental class is higher than the control class The question is: Is the method of experimental class better than the method of control class, or is it just random? We propose the statistical hypothesis H0: "There is no difference between the two methods" and using Method U (See [73, p 58]) to refute H0” With significance level = 0.05, the critical value in all four tests are shown evidently: Because u U , then Hypothesis H0 is rejected So the method of teaching in the experimental class is better than the method of teaching in the control class 3.6 General conclusion of Chapter The experimental process with the results drawn after the experiment shows that: the purpose has been completed, the feasibility and effectiveness of the views have been confirmed Implementing pedagogical measures in teaching Maths to students specializing in Physics, Chemistry, and Biology, which the thesis proposes will contribute, is very well to foster the competency of exploring and obtaining knowledge for students of these specialized subjects and high school in general At the same time, the results of the thesis have contributed significantly in theory and practice to improve the effectiveness of teaching mathematics in high schools, specialized high schools, and especially the specialized system of Physics, Chemistry and biology 24 CONCLUSION There are some main findings of the paper It has systematized scientists’s views on activities, cognitive activities; giving defintion of the term improving the knowledge – grasping competence, which contribute on the identification of typical components of improving the knowledge – grasping competence It has introduced high school students the concept of improving the knowledge – grasping competence in teaching maths through six elemental competencies that has been described by compatible activities The paper also has studied the reality of improving the knowledge – grasping competence in teaching maths in gifted high schools in general high school studens majoring in physics, chemistry and biology in particularly It is essential to develop this competence by applying pedagogical measures and teaching topics It has introduced directions and developed six pedagogical measures to improve the knowledge – grasping competence in teaching maths for high school students majoring in physics, chemistry, and biology The paper has designed some topics that can be suitable for the main aim of the research It has organized pedagogical experiments to illustrate the feasibility and effectiveness of the proposed pedagogical measures LIST OF SCIENTIFIC RESEARCH OF AUTHOR RELATED TO THE THESIS Nguyen Tran Lam (2015), “Some measure contributing to training the problem identifying and solving skills in teaching Chaper III: The space coordinate method (12th grade Geometry), Jounal of Education Science – Ministry of Education and training, Volume 355, p 52 – 55 Nguyen Van Thuan - Nguyen Tran Lam (2016), “Difficulties affected students’ abilities of exploration and knowledge achievement in teaching soil Geometry in current textbook grade 11 and its solution”, Vietnam national journal of education science, Volume 134, p 62 – 65 Nguyen Van Thuan - Nguyen Tran Lam (2018), “Improving the knowledge grasping competence for high school students in teaching Polyhedron volume”, Vietnam national journal of education science, Volume 07, July, p 50 – 55 Nguyen Tran Lam (2018), “Teaching the Theorem of the Continuous Function sourced in Algebraic and Analysis textbook of current Grade 11 aims to train intelligent Maths students in high school”, Vinh university Jounal of science, Vol, p 53 – 63 TÀI LIỆU THAM KHẢO A TI ẾNG VIỆT 10 11 12 13 dạng câu hỏ i NXB G iáo dục 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 [1]Vũ Thị Phương Anh (201 0), NL làm việc (competency ) gì?, http://ncgdvn.b logsp ot.com/2011 /10/anh-g ia-nlr-3-nang-luc-lam-viec-la-gi.html [2]M Alêcxêep, V Onhisuc, M Crug liăc, V Zabôtin, X Vecxcle (1976), Phát triển tư d uy HS, Nxb G iáo dục, Hà Nội [3]Thomas Amstrong (2007), Bảy loại hình thông minh, N xb Lao động , Hà Nội [4]Thomas Armstrong (2011), Đa trí tuệ tro ng lớp học, Ng ười dịch: Lê Quang Long, H iệu đính : Lê Thị K im Dung, Nxb G iáo dục Việt Nam, Hà Nội [5]Anderson, L W & Krathwohl, D R (2001) P hân lo ại tư cho việc dạy, học đán h giá New York: Longman [6]Annie Bessot, Nguy ễn Thị Nga (2011), Mơ h ình hó a Tốn học tượng biến thiên d ạy học nhờ h ình h ọc động d ự án n ghiên cứu Mira, Tạp ch í Khoa học ĐH SP TPHCM, s ố 28, tr 55 - 63 [7]Ăng ghen Ph (1994), “Biện ch ứng tự nhiên”, C Mác Ph Ăng ghen n tập, tập 0, Nxb Chín h trị Quốc g ia, Hà Nội [8]Bernd Meier - Nguy ễn Văn Cường (20 14) Lí luậ n dạy học đ ại - Cơ s đổi m ục tiêu, nộ i dung phương p háp dạy học NX B Đại học Sư phạm [9]Lê Võ Bình (200 7), Dạy học hình học lớp cuố i cấp THCS theo địn h hướng b ước đầ u tiếp cận phương p háp khám ph á, Luận án tiến sĩ g iáo dục học, Đại học Vinh [10] Vũ Thị Bình (201 6), bồi d ưỡng năn g lực b iểu diễn toán học nă ng lực giao tiếp to án học cho học s inh dạy học mơn tốn lớp 6, lớp , Luận án Tiến s ĩ giáo d ục học, Viện khoa học g iáo dục Việt Nam [11]Bộ Giáo dục Đào tạo (20 18), Ch ương tr ình g iáo dục ph ổ thô ng tổn g thể (ban hành kèm theo th ông tư số 32/20 18/TT -BGDĐ T ngày 26 tháng 12 năm 2018 Bộ trưởng Bộ Giáo dục Đào tạo [12]Bộ Giáo dục Đào tạo, (20 05), Tài liệu bồi d ưỡng giá o viên th ực chương trình , Sách gi áo khoa thí điểm lớp 1, Nxb G iáo dục, Hà Nội Nguy ễn Hải Châu, Nguy ễn Hữu Châu, Nguy ễn Văn Cường, Trần Bá Hoành, Nguy ễn Bá Kim, Lâm Quang Thiệp (2007), Đổi nội du ng ph ương pháp đ tạ o giáo viên TH CS theo ch ươn g tr ình CĐSP mới, Dự án đào tạo giáo v iên THCS, Hà Nội [15]Nguy ễn Hữu Châu (1996), “Vấn đề dạy giải phương trình Tốn học trườn g phổ thơng”, Tạp chí nghiên cứu giáo dục, (12), tr 10-11 [16]Nguy ễn Hữu Châu (Chủ biên), Đỗ Th ị Bích Loan, Vũ Trọn g Rỹ (2007), Giáo dục Việt Nam nh ững n ăm đầu kỉ XXI, Nxb G iáo dục, Hà Nội [17]Trần Đình Châu (199 6), Xây dựn g hệ thốn g tập s ố học nhằm bồi d ưỡn g số yếu tố năn g lực Toá n học cho HS g iỏi đ ầu cấp THCS, Luận án Phó tiến sĩ khoa h ọc Sư phạm - Tâm lý, Viện Khoa học giáo dục Việt Nam, Hà Nội Trần Đình Châu, Đặng Thị Th u Thủy (2011), Th iết kế đồ tư d uy dạy – học mơn Tố n, Nxb Giáo dục Việt Nam, Hà Nội Chiến lược phát triển giáo d ục 2011 – 2020 (Ban hành kèm theo Quyết đ ịnh số 711/QĐ- TTg ngày 13 tháng năm 20 12 Thủ tướn g Ch ính ph ủ) Văn Như Cươn g, Phan Văn Viện (2000), Hình học 10 ( Sách chỉnh lí hợp năm 2000), Nxb Giáo dục, Hà Nội Văn Như Cươn g, Phan Văn Viện (2000), Hình học 11 ( Sách chỉnh lí hợp năm 2000), Nxb Giáo dục, Hà Nội Văn Như Cươn g, Phan Văn Viện (2000), Hình học 12 ( Sách chỉnh lí hợ p năm 2000), Nxb Giáo dục, Hà Nội Văn Như Cươn g, Trần Văn Hạo, Ngô Thúc Lanh (2 006), Tài liệu hướng d ẫn giả ng dạy Toán 10 , Nxb Giáo dục, Hà Nội Văn Như Cươn g, Trần Văn Hạo, Ngô Thúc Lanh (2 006), Tài liệu hướng d ẫn giả ng dạy Toán 11 , Nxb Giáo dục, Hà Nội Văn Như Cương, Trần Văn Hạo, Ngô T húc Lanh (2006), Tài liệu h ướng dẫn g iảng dạy Toán 12, Nxb G iáo dục, Hà Nội De Chen X I (1998), H ình học m ới tam giác, Nx b Giáo dục, Hà Nội Phạm Xuân Chung (2001), Kha i thác tiềm SG K – H ình học Tr ung học ph ổ thô ng h ành qu a s ố dạng tập điển h ình n hằm phá t tr iền lực tư sá ng tạo cho HS, Luận văn thạc sĩ, Đại học V inh Phạm Xuân Chung (2012), Chuẩ n bị cho sinh viên n ghành sư p hạm Toán trường đ ại học tiến hành HĐ đánh g iá kết học tập mơ n Tốn HS trung học phổ thơng, L uận án Tiến sỹ Giáo dục học, Đại học Vinh, Vin h [29]Hoàng Chúng (1 969), Rèn luyện khả n ăng sán g tạo Toá n học phổ th ông, Nxb Giáo dục, Hà Nội [30]Côvaliov A G (1971), Tâm lí học cá nhâ n, Tập 2, Nx b Giáo dục, Hà Nội [31]Cruchetx ki V A (19 73), Tâm lí lực Tốn học HS, Nxb Giáo d ục, Hà Nội [32]Cruchetx ki V A (19 80), Nh ững c sở Tâm lí học s ph ạm, Tập 1, Nxb Giáo dục, Hà Nội [33]Cruchetx ki V A (19 81), Nh ững c sở Tâm lí học s ph ạm, Tập 2, Nxb Giáo dục, Hà Nội [34]Ngô Hữu Dũn g (1996), Sách giáo khoa việc hình th ành nhâ n cách học sin h, Nghiên c ứu giáo d ục, tháng 10-19 96, Hà nội [35]Vũ Dũng (chủ biên) (2000), T điển Tâm lý h ọc, NXB T điển Bách khoa, Hà Nội Hồ Ngọc Đại (2000), Tâm lí dạy học đại học, Nxb Đại h ọc Quốc gia Hà Nội, Hà Nộ i Đanilôp M A., Xcatkin M N (1980), Lí luận d ạy học tr ườn g phổ thông, N xb Giáo dục, Hà Nộ i [38]Đỗ Tiến Đạt (chủ nhiệm đề tài cấp bộ) (2011), Phương thức bồ i dưỡng h ọc sinh khiếu nhà trường p hổ thô ng Việt Nam, Đề tài khoa học n ghiên cứu cấp , mã số B200 8-37-59, Viện khoa học giáo dục Lê Thị Mỹ Hà (đồng chủ biên, 201 2) PISA 25 39 [39]Đavưđov V V (20 00), Các ng khái q uát dạy học, Nxb Đại h ọc Quốc gia Hà Nội, Hà Nộ i 40 [40]Trương Quang Đệ (dịch giải, 20 00), René Déscartes tư khoa h ọc, Nxb Giáo dục, Hà Nộ i 41 [41]Nguy ễn Hữu Điển (2003), Sáng tạo Tố n học phổ thơng, Nxb Giáo d ục, Hà Nội 42 Nguy ễn Quang Điển, Huỳ nh Bá Lân, Phạm Đình Nghiệm (2003), C Mác, Ph Ăngghen, V I Lênin vấ n đề Tr iết học, Nxb Đại học Quốc gia Thành phố Hồ Chí Min h 43 [43]Bùi M inh Đ ức (2013), “Năng lực” vấn đề phân loại “năng lực” nghiên cứu h iện , Tạp chí Giáo dục, (306), tr 28 – 31 44 [44]Phạm Gia Đức, Nguy ễn Mạnh Cảng, Bùi H uy Ngọc, Vũ Dươn g Thụy (1998), Phương pháp dạy h ọc mơn Tốn, Tập 1, N xb Giáo d ục, Hà Nội 45 [45]Phạm Gia Đức, Phạm Văn Hoàn (1976), Rèn luyện kĩ công tác độc lập HS qua m ôn Toán, Nx b Giáo dục, Hà Nội 46 [46]Franz Emanuel Weinert (1998) (Ch ủ biên), Việt A nh – Nguy ễn Hoài Bão (d ịch), Nxb Giáo dục, Hà Nộ i 47 [47]Giáo trình Triết h ọc Mác - Lênin (200 3), Nxb Chính trị Quốc g ia 48 [48]Phạm Minh Hạc (1992), Một số vấn đề tâm lí học, Nxb Giáo d ục, Hà Nội 49 [49]Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Ch ủ biên), Doãn Minh Cường – Đ ỗ Mạnh Hù ng (2006), Đạ i số 0, Nxb G iáo dục Việt Nam, Hà Nội 50 Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Chủ biên), Doãn Minh Cường – Đỗ Mạnh H ùng (2006), Đ ại số 10 (Sách giáo v iên), Nxb Giáo dục Việt Nam, Hà Nội 51 [51]Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ biên), Ng uy ễn Văn Đoành – Trần Đức Huy ên (2006), Hình học 10, N xb Giáo d ục Việt Nam, Hà Nội 52 Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ b iên), Nguy ễn Văn Đoành – Trần Đức Huy ên (2006), Hình học 10 ( Sách giáo viên), Nx b Giáo dục Việt Nam, Hà Nội 53 [53]Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Ch ủ biên), Đào Ngọc Nam – Lê Văn Tiến – Vũ V iết Yên (2006), Đạ i số G iải tích 11, Nx b Giáo dục Việt Nam, Hà Nội 54 Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Chủ biên), Đào Ngọc Nam – Lê Văn Tiến – Vũ V iết Yên (2006), Đạ i số G iải tích 11 ( Sách giáo viên), Nxb G iáo dục Việt Nam, Hà Nội 55 Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ b iên), Khu Quốc Anh – Nguy ễn Hà Thanh – Phan Văn Viện (2016), Hìn h học 11, Nx b Giáo dục Việt Nam, Hà Nội 56 Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ b iên), Khu Quốc Anh – Nguy ễn Hà Thanh – Phan Văn Viện (2016), Hìn h học 11 ( Sách giáo viên), Nxb G iáo dục Việt Nam, Hà Nội 57 Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Chủ biên), Lê Th ị Thiên H ương – Nguy ễn Tiến Tài – Cấn Văn Tuất (2006), G iải tích 12, Nx b Giáo dục Việt Nam, Hà Nội 58 Trần Văn Hạo (Tổng chủ biên), Vũ Tuấn (Chủ biên), Lê Th ị Thiên H ương – Nguy ễn Tiến Tài – Cấn Văn Tuất (2006), G iải tích 12 ( Sách giáo viên), Nxb G iáo dục Việt Nam, Hà Nội 59 [59]Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ biên), Kh u Quốc Anh – Trần Đức Huy ên (2006), Hình học 2, Nxb Giáo dục Việt Nam, Hà Nội 60 Trần Văn Hạo (Tổng chủ biên), Nguy ễn Mộng Hy (Chủ b iên), Khu Quốc Anh – Trần Đức Huy ên (2006), Hình h ọc 12 (Sách giáo v iên), Nxb Giáo d ục Việt Nam, Hà Nội 61 [61]Nguy ễn Thị Mỹ Hằng (2014), Rèn luyện kỹ th ực thao tác tư cho học s inh tr ung học p hổ thô ng tr ong dạy học Đạ i số G iải tích, Luận án Tiến sĩ Khoa học g iáo dục, Đại học Vinh, Vin h 62 [62]Nguy ễn Hữu Hậu (2012), Kha i thác tập luyện cho HS HĐ n hằm phá t tr iển khả ch iếm lĩnh tri thức d ạy học Đại s ố - Giải tích bậc tru ng học phổ n thôn g, Luận án Tiến sỹ Giáo dục học, Đại học Vinh, V inh 63 [63]Trần Bá Hoành (2007), Đổi m ới p hương phá p dạy học, chương trình sách giáo khoa, Nxb Đại học Sư Phạm, Hà Nội 64 Trần Bá Hoành (2007), Vấn đề giáo viên nh ững nghiên cứu lí luận thực tiễn, Nxb Đại h ọc Sư Phạm, Hà Nội 65 [65]Phạm Văn Hoàn, Nguyễn Gia Cốc, Trần Thúc Trình (1981), G iáo dục h ọc mơn Tốn, Nxb Giáo dục, Hà Nội 66 Phạm Văn Hoàn (1985), “Một số vấn đề lịch sử phá t triển học thuy ết phươn g trình”, Tạp chí To án học Tuổi trẻ, (6), tr 5-8 67 [67]Đặng Vũ Hoạt, Hà Thị Đ ức (1994), Lí lu ận dạy học đạ i học, Trường Đại h ọc Sư phạm Hà Nội I 68 [68]Lê Văn Hồng, Lê Ngọc Lan, Nguy ễn Văn Thàng (1999), Tâm lý học l ứa tu ổi tâm lý học s phạm, N xb Đại học Quốc g ia, Hà Nội 69 [69]John Dewey , Phạm Anh Tuấn dịch (2017), Dân Chủ Và Giáo Dục, NX B Tri Th ức, Hà Nội 70 [70]Trần Kiều nhóm nghiên cứu (20 12), Về mục tiêu mơn Tố n tro ng chương trình phổ th ơng Việt Nam, Báo cáo Hộ i thảo Việt Nam – Đan Mạch, Hà Nội 71 Trần Kiều (1998), “Toán học nhà trường y cầu phát triển văn hóa tốn h ọc”, Tạp chí nghiên cứu Giáo dục, (10), tr - 72 Nguy ễn Bá Kim, Đinh Nho Chương, Nguy ễn Mạnh Cảng, Vũ D ương Thụy , Nguy ễn Văn Thường (19 94), Phương pháp dạy h ọc mơn Tốn - phầ n 2: Dạy học nh ững nộ i dung bản, N xb Giáo dục, Hà Nộ i 73 Nguy ễn Bá Kim, Vũ Dương Thụy , Phạm Văn Kiều (1997), Phát tr iển lí luận dạy h ọc mơn Tốn, Nxb Giáo dục, Hà Nội 74 Nguy ễn Bá Kim, Vương D ương Min h, Nguy ễn Sỹ Đức (1997), “Tính g iải quy ết vấn đề tồn q trình dạy học”, Thông tin Khoa học Giáo d ục, (66), tr 13 75 Nguy ễn Bá Kim (2004), Phương pháp dạy học mơn Tốn, Nxb Đại học Sư phạm, Hà Nội 76 [76]Nguy ễn Bá Kim (1998), Học tập tro ng hoạ t động h oạt độ ng, Nxb G iáo dục, Hà Nội 77 Nguy ễn Bá Kim, Vương D ương Min h, Tôn T hân (1999), Khuyến khích s ố HĐ tr í tuệ HS q ua mơn Tốn trường THCS , Nxb Giáo d ục, Hà Nội 78 Nguy ễn Bá Kim, Vũ Dương Thuỵ , Phạm Văn Kiều (1987), Phát tr iển lí luận dạy h ọc mơn Tốn, tập 1, Nxb Giáo dục, Hà Nội 79 Đào Thái Lai, (2003), “Ứng dụng côn g nghệ th ông tin giú p HS tự khám phá giải quy ết vấn đề học Tốn trường p hổ thơ ng”, Tạ p chí Giá o dục, (57), tr 2 80 [80]Nguy ễn Hữu Lam (2007), Mơ hình lực giáo dục đào tạo phát triển nguồ n nhân lực, http://www.saga.vn 81 [81]Lecne I Ia (1977), Dạy học nêu vấn đề, Nxb Giáo dục, Hà Nội 82 [82] Leonchiep A N (1989), HĐ, ý th ức, nhâ n cách Nxb Giáo d ục, Hà Nội 83 [83]Nguy ễn Phú Lộc (2006), “Sự “thích n ghi” trí tuệ q uá trình n hận thức theo quan điểm J.Piage”, Tạp chí G iáo dục, (18 3), tr 11-13 84 [84]Nguy ễn Phú Lộc (2010) “Dạy học khái niệm khám khá”, Tạp chí Khoa học, Tr ường Đại họ Cần thơ, tr 16 – 21 85 Luật G iáo dục (19 98), Nxb Giáo dục, Hà Nội 86 [86]Trần Luận (1996), Vận dụng tư tưởng s ph ạm G Pô lya xây dựng n ội du ng ph ương pháp s hệ thống tập theo chủ đề nhằm phá t huy năn g lực sáng tạo HS chuyên Toán cấp II, Luận án Phó tiến sĩ Khoa học Sư phạm - Tâm lí, Viện Khoa học Giáo dục, Hà Nội 87 Marzano, R J (2000) Thiết kế phân loạ i tư cho mục tiêu g iáo dục Th ousand Oa ks, CA: Ấ n phẩm Corwin 88 Trần Thành Minh ( Chủ b iên), Phan Lưu Biên, Vũ Vĩnh Thái, Phan Thanh Thiên (2000), G iải Toán hình học 12 (dùng cho HS lớp ch uy ên), Nxb Giáo dục 89 [89]Nguy ễn Danh Nam (2015), Quy trình mơ hìn h hóa d ạy học To án trường p hổ th ơng, Tạp chí KH ĐHQ GHN, Tập 31, s ố 3, tr 1-1 0, Hà Nội 90 [90]Phạm Sỹ Nam (2013), Nâng cao hiệu q uả dạy học mộ t số khái niệm giả i tích cho học sin h tru ng học phổ thơng chun Tốn s vận dụ ng lý th uyết kiến tạo, Luận án T iến sĩ G iáo dục học, Đại học Vinh, Vin h 91 Phạm Thanh Nghị, Nguy ễn Huy Tú (1993), “Sáng tạo chất ph ương p háp chuẩn đoán”, Th ông tin khoa h ọc Giáo dục, số 39, Hà Nộ i 92 Bùi Văn Ngh ị (1996), Vậ n dụng tư thuậ t giả i vào việc xác định hình để giả i tốn Hình học không gian tr ườ ng tr ung học ph ổ thơ ng, Luận án Phó tiến sĩ Kh oa học Sư phạm - Tâm lí, Trườn g đại học Sư p hạm - Đại học Quốc gia Hà Nội 93 [93]Phan Trọng Ngọ (2005), Dạy học ph ươn g pháp dạy học tro ng nhà tr ường, N xb Đại học Sư phạm, Hà Nội 94 [94]Hà Thế Ngữ, Đặng Vũ Hoạt (19 87), Giáo dục học, Tập 1, Nxb Giáo dục, Hà Nội 95 Ơkơ n V (1982), Tâm lí học lứa tuổi tâm lí h ọc sư p hạm, Nxb G iáo dục, Hà Nội 96 Phạm Phụ (1997), Ứng dụng Toán s cấp g iải toán thực tế, Nxb Giáo dục, Hà Nộ i 97 [97]Petrovski A V (1982), Tâm lí học lứa tuổi tâm lí học sư phạm, tập , Nxb Giáo dục, Hà Nội 98 Petrovski A V (1982), Tâm lí học lứa tuổi tâm lí học sư phạm, tập 2, Nxb G iáo dục, Hà Nội 99 [99] Petty Geoffrey (2000), Dạy học ngày nay, Dự án Việt – Bỉ 100 [100]Hoàng Phê (chủ biên) (1997), Từ đ iển Tiếng Việt, NXB Đà Nẵng 101 [101]Nguy ễn Thị Lan Phương (20 02), Cả i tiến phương p háp dạy toán với yêu cầu tích cực hóa H Đ học tập theo h ướng giúp H S phát giải vân đề (qua phần g iảng d ạy “Qua n hệ vuông góc khơ ng gia n”, lớp 11 tr ường tr ung học ph ổ thôn g), Luận án Tiến s ĩ Giáo dục học V iện Khoa học Giáo dục, Hà Nội 102 [102] Piaget J (1996), Tuyển tập tâm lí h ọc, Nxb Giáo d ục, Hà Nội 103 [103] Poly a G (1997), Giải toán n hư nào?, Nx b Giáo dục, Hà Nộ i 104 [104] Poly a G (1997), Sáng tạo toán học, Nx b Giáo dục, Hà Nội 105 [105] Poly a G (1995), Tốn học nh ững suy luận có lí, Nxb Giáo dục, Hà Nội 106 Đồn Quỳ nh (Tổng chủ biên), Nguy ễn Huy Đoan (Chủ biên), Trần Phương Dung, Nguy ễn Xuân Liêm, Đặng Hùng Thắng (2006), Đ ại số 10 nân g cao, Nxb G iáo dục, Hà Nội 107 Đoàn Quỳ nh (tổng chủ biên), Nguy ễn Huy Đoan (chủ biên), Trần Phương Du ng, Nguy ễn Xuân Liêm, Đặng Hùng Thắng (20 06), Đại số 10 n âng cao (Sách g iáo viên), Nxb G iáo dục, Hà Nội 108 [108]Đoàn Quỳ nh (Tổng Chủ biên), Nguy ễn Huy Đoan (Chủ biên), Trần Phươn g Dung, N guy ễn Xuân Liêm , Đặng Hùng Thắng (2006), Đạ i số G iải tích 11 n âng cao, Nxb Giáo dục, Hà Nội 109 [109]Đoàn Quỳ nh (Tổng Chủ biên), Nguy ễn Huy Đoan (Chủ biên), Trần Phươn g Dung, N guy ễn Xuân Liêm , Đặng Hùng Thắng (2006), Đạ i số G iải tích 11 n âng cao (Sách g iáo viên), Nxb G iáo dục, Hà Nội 110 [110]Đoàn Quỳ nh (Tổng chủ biên), Nguy ễn Huy Đoan (Chủ biên), Trần Phương Dung, Nguy ễn Xuân Liêm, Đặng Hùng Thắng (2006), G iải tích 12 n âng cao, Nx b Giáo dục, Hà Nội 111 Đoàn Quỳ nh (Tổng chủ biên), Nguy ễn Huy Đoan (Chủ biên), Trần Phương Dung, Nguy ễn Xuân Liêm, Đặng Hùng Thắng (2006), G iải tích 12 n âng cao ( Sách giáo viên), Nxb G iáo dục, Hà Nội 112 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Vũ Khuê, Bùi Văn Ngh ị (2006), H ình học nâ ng cao 10, N xb Giáo d ục, Hà Nội 113 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Vũ Khuê, Bùi Văn Ngh ị (2006), H ình học nâ ng cao 10 ( Sách giáo viên), Nx b Giáo dục, Hà Nội 114 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Khắc Ban, Tạ Mân (2007), Hình Học nâ ng cao 11, Nxb Giáo d ục, Hà Nội 115 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Khắc Ban, Tạ Mân (2007), Hình Học nâ ng cao 11 ( Sách giáo viên), Nx b Giáo dục, Hà Nội 116 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Khắc Ban, Lê Huy Hùng, Tạ Mân (2008), Hình Học nâ ng cao 12, Nxb Giáo d ục, Hà Nội 117 Đoàn Quỳ nh (Tổng chủ biên), Văn Như Cương ( Chủ b iên), Phạm Khắc Ban, Lê Huy Hùng, Tạ Mân (2008), Hình Học nâ ng cao 12 ( Sách giáo viên), Nx b Giáo dục, Hà Nội 118 [118]Raja Roy Singh (1994), Nền giá o dục cho kỉ XXI Nh ững triển vọng Châu Á - Th Bình Dương, Nx b Giáo dục, Hà Nộ i 119 [119]Sacđacôp M N (1970), Tư HS, Tập 1, Nx b Giáo dục, Hà Nội 120 Rogiers X (199 6), Kho a s phạm tích hợp hay làm để ph át triển lực nhà t rường, Nxb Giáo dục, Hà Nội 121 Đào Tam, Trương Thị Du ng (2014), “ Bồi d ưỡn g lực quan sát cho h ọc sinh dạy học toán tr ườn g trung h ọc phổ th ơng”, Tạp chí Khoa khọc Giáo dục, số 100 – tháng 1/2014, tr 18 – 122 [122]Đào Tam (Chủ biên) – Lê Hiển Dương (200 8), Tiếp cận phương phá p dạy học không truyền thố ng tro ng dạy học Toán tr ường đạ i học tr ườn g phổ thông, N xb Đại học Sư p hạm 123 [123]Đào Tam (2004), Dạy học hình học trường trung học phổ thông, N xb Đại học Sư p hạm 124 [124]Đào Tam (Chủ biên), Trần dạy học môn To án tr ường THP T, Nxb Đại học Sư phạm, Hà Nội 125 [125]Nguy ễn Thị Thanh Tâm (2016), Bồi d ưỡng thủ phá p HĐ nhận th ức theo tư tưởng sư p hạm G Po lya cho HS d ạy học mơn Tốn tr ườn g tru ng học s ở, Luận án T iến sỹ Giáo dục học, Đại học Vin h, Vinh 126 Vũ Văn Tảo, Trần Văn Hà (1996), Dạy - học giải q uyết vấn đề: Một h ướng cần đổi m ới công tác giá o dục, đào tạo, h uấn luyện, Trường Cán quản lí giáo dục đào tạo, Hà Nộ i 127 Vũ Văn Tảo (1997), “Một hướng đổi mục tiêu đào tạo: Rèn luy ện lực g iải quy ết vấn đề”, Bước đầ u đổi m ới phương ph áp dạy học trun g học s theo h ướng tích cực hóa HĐ h ọc tập, Viện K hoa häc gi¸o dục, Hà Nội 128 [128]Vũ Xuân Thái (1999), Gốc ng hĩa từ Việt thơng dụ ng, NX B Văn hóa Thơng tin, tr.576 129 [129]Từ Đức Thảo (20 11), Bồi d ưỡng năn g lực phát h iện giả i vấn đề cho HS trung học phổ thông d ạy học hình học, Luận án Tiến sỹ Giáo dục, Đại h ọc Vinh, Vinh 130 [130]Tôn Thân (1995), “Bài tập “mở”, Một dạng tập gó p phần bồ i dưỡng tư sáng tạo cho H S”, Tạp chí n ghiên cứu G iáo d ục, số 6, Hà Nộ i 131 [131]Tôn Thân (1995), “Cấu trúc hệ thống dạng tập Toán học nhằm bồi d ưỡng số y ếu tố tư sáng tạo cho HS giỏi trườn g phổ thơng sở”, Tạp chí n ghiên cứu Giáo d ục, số 4, Hà Nộ i 132 [132]Tôn Thân (1996), Bồ i d ưỡng lực tư sán g tạo cho HS hệ thống câu hỏi tập toá n học, Viện Kh oa học Giáo dục, Hà Nội 133 Tôn Thân (1996), “Đổi ph ương pháp dạy học Toán trường trun g học s theo h ướn g phát triển tư sáng tạo cho HS”, Thôn g tin Kho a học Giáo dục, Số 70, Hà Nội 134 [134]Tôn Thân (1996), Xây d ựng hệ thống câu hỏi bà i tậ p nhằm b ồi d ưỡng s ố yếu tố tư sá ng tạo cho HS giỏi tr ường trun g học s Việt Nam, Luận án Phó tiến s ĩ Khoa học Sư phạm – Tâm lí, Viện K hoa học giáo dục, Hà Nộ i 135 [135]Đỗ Ngọc Thống, “Xây dựng ch ương trình g iáo dục phổ thông theo hướng tiếp cận NL”, http ://tiasang.com.vn 136 [136]Nguy ễn Văn Thuận (chủ biên), Nguy ễn Hữu Hậu (2010), Phát s ửa chữa sai lầm cho HS dạy học đại số - giả i tích trường phổ thông , Nxb Đại h ọc Sư phạm, Hà Nội 137 [137]Nguy ễn Văn Thuận (2004), Góp phần phát triển nă ng lực tư lôg ic sử d ụng xác ngơn ng ữ to án học cho HS đ ầu cấp THPT tron g dạy học Đại số, Luận án T iến sĩ Giáo dục học, Trường Đại học V inh, Vinh 138 [138]Nguy ễn Quang Thuấn (2016), “Đánh giá theo đ ịnh h ướng lực”, Tạp chí nghiên c ứu Giáo dục, Tập 32, Số 2, tr 68-82 139 [139]Trần Trọng Thủy , Nguy ễn Quang Uẩn (1998), Tâm lí học đạ i cương, Nxb Trẻ, Thành phố Hồ Chí Minh 140 Lê Văn Tiến (2004), Từ cải cách giáo dục Pháp bàn v iệc cải cách Toán học phổ thông đào tạo giáo viên Việt Nam, Kỉ yếu hội thảo kho a học “Đ ổi m ới Nội du ng Ph ương pháp d ạy học cá tr ường Đại học Sư phạm ” (Ba Vì t háng năm 2003), Hà Nội 141 [141]Nguy ễn Cảnh Toàn (1997), Ph ương pháp luận vật biện chứng với việc học, dạy, n ghiên cứu toán học, tập 1, Nx b Đại học Quốc gia, Hà Nộ i 142 [142]Nguy ễn Cảnh Toàn (1997), Ph ương pháp luận vật biện chứng với việc học, dạy, n ghiên cứu Toá n học, tập 2, N xb Đại học Quốc g ia, Hà Nội 143 [143]Nguy ễn Cảnh Toàn (2001), Tuyển tập tác p hẩm tự giá o dục tự học t ự ngh iên cứu, Tập 1, Trườn g Đại học Sư p hạm Hà Nội, Trung tâm văn hóa - Ngơn ng ữ Đơng Tây , Hà Nội 144 [144]Phạm Hữu Tịng (2004), Dạy học Vậ t lý trường p hổ th ông theo định h ướng phá t tr iển HĐ học tích c ực, tự chủ , sáng tạo tư khoa học, Nxb Giáo dục, Hà Nội 145 [145]Nguy ễn Thị Hương Trang (2002), Rèn luyện nă ng lực giải toán theo h ướng phát h iện giả i vấn đề cách sáng tạo cho HS giỏi tr ường trung học phổ thông (qu a dạy học giải ph ươn g tr ình bậc i - ph ương trình lượng giác), Luận án Tiến sĩ Giáo d ục học, Viện Khoa học g iáo dục, Hà N ội 146 [146]Trần Thúc Trình (1998), Cơ s lí luận dạy học nâng cao, Viện Khoa học G iáo dục, Hà Nội 147 [147]Trần Thúc Trình (2003), Đề cương mơn học: Rèn luyện tư tron g học Toán, Viện K hoa học Giáo dục, Hà Nội 148 [148]Tsuneharu Okabe (200 7), Tr ắc nghiệm t duy, Nxb Lao động, Hà Nộ i 149 [149]Nguy ễn Anh Tuấn (2004), Bồi d ưỡng lực p hát h iện giải vấn đề cho HS THCS tron g dạy học khái niệm To án học (thể h iện qua mộ t số khái niệm Đại số Tru ng học s ở), Luận án Tiến sĩ Giáo d ục học, Viện Khoa học G iáo dục, Hà Nội 150 [150]Thái Duy Tuy ên (1998), Những vấn đề g iáo dục h iện đại, N xb Giáo dục, Hà Nộ i 151 [151]Thái Duy Tuy ên (2001), “Vấn đề tái sáng tạo dạy học”, Thôn g tin Kho a học giáo dục (83), Hà Nội 152 [152]Nguy ễn Văn Tường (2010), Tâm lí học nh ận th ức, Trung tâm ngh iên cứu tâm lí trẻ em (Trung tâm N – T Nguy ễn Khắc Viện) 153 [153]Nguy ễn Quang Uẩn, Nguy ễn Văn Lũy , Đinh Văn Vang (2006), Giáo trình Tâm lý h ọc đại cươn g, NXB ĐH SP, tr.21 154 [154]UNESCO (2 008), Chân du ng nh ững nh cải cách giá o dục tiêu b iểu giới, Nxb Văn hóa Thơng tin, Hà Nộ i 155 [155]K D Usinx ki (1995), Tâm lý h ọc giáo dục Nxb Hà Nộ i, Hà Nội 156 Trần Văn Vuông (1998), Cơ s lí luận giải tốn phổ th ơng, Viện K hoa học Giáo dục, Hà Nội 157 [157]Trần Vui (Chủ b iên), Lê Quang Hùng (20 07), Kh ám phá H ình học 11 với The Geometrer’s Sketchpad, Nx b Giáo dục, Hà Nội 158 [158] Từ điển tiếng Việt (200 5), Nxb Đà Nẵng Trung tâm Từ điển học, Hà Nội – Đà Nẵng 159 [159]Vy gotsky L X (1997), Tuyển tập tâm lí học, Nxb Đại học Quốc gia Hà Nội 160 Zaruđnaia A A (chủ biên), (1970), Tâm lí học, Nxb Đại h ọc, Min xcơ (Bản dịch tiếng V iệt, Thư viện Đại học Sư phạm Hà Nội) B TIẾNG NƯỚC NG OÀI 161 Almeida D (2004), Justify ing and proving in the mathematics classroom, Philo sophy of mathematics educatio n Ne wsletter 162 Australian Educatio n Co uncil and Ministers of Vocational Education, Employ ment and Training (1992), “The key competencies report” 163 [163] Bloom, B.S et al (1956), Taxon omie des objectifs pédagogiques, tome I, Domaine cognitif, Traduit de l' anglais, 1969 Québec (Canada): Les Presses de l'Université du Québec 164 [164]Bruner J, Discovery and Unco/donna Fergu son/ETH istory /BRUNER.HTM 165 [165]Biss onnette, S et Richard, M.(2001), Comment construire des compétences en classe Des outils pour la réforme Montréal: Chenelière/McGraw-Hill 166 Bransford J D (1984) The Ideal Pr oblem So lving, Freeman, New York 167 [167]Chevallard Y (1989), “Le passage de l’arithmétique l’algèbre dans l’enseignement des mathématiques au Co llège”, 2èm e partie, perspectives curriculaires: la notion de modélisation , Petit x 9, 43-72 168 [168]Chevallard Y (1992), Concepts fon damentaux de la didactique : perspectives apportées par une approche anthropolog ique, Recherches en Didactique des Mathématiques, v ol.12 /1, 73-11 2, La Pensée Sauvage / Grenoble 169 [169] Daeka, “Experimentation of Cooperative Learning Mo del Numbered Head Together (NHT) and Thin k Pair Share (TPS) in terms of Student Creativity Grade VII SMP Negeri in Pacitan Regency ” Ph D thesis, FKIP UNS, 2014 170 Ernest P (edited) (1994), Con structing ma thematica l knowledge: Epistemology and ma thematica l education , The Falmer Press, London 171 Ernest P (edited) (1994), Mathematics, Education an d Philosophy: An In ternational Perspective, The Falmer Press, London 172 [172]Erwin, T Dary (2000) Definitions an d Assessmen tMethods for Critical Thinking, Pr oblem Solving and W riting U.S Government Printin g Office 173 Finney R.L., Th omas (1994), Ca lculus (second edition), A ddins on - Wesley publish ing company , New York 174 Jaworski B (1 994), Investiga ting m athematics teaching: A structivism Enq uiry, The Falmer Press, London and Washing ton D C 175 [175]Jennifer Stepane k (1999), The Inclus ive Classroom: Meeting the Needs of Gifted Studen ts: D ifferentiating Mathematics and Science Instruction 176 John Dewey (2008), Democracy and Education, 177 Katz V J (1 998), A history o f mathema tics: an intro duction, Addin son - Wesley , Amsterdam 178 [178]Kerensa White, Felicity Fletcher, Campbell, Kate Rid ley (2003), What wo rks for gifted and talented pu pils: a review of recent research, LGA educational research programm e 179 Lial M L., Miller C D (19 89), Ca lculus wi th app lications, Scott, Foresman and company , Glenview, USA 180 [180]Michael Agner, David B Guralnik (20 01), Webster’s New world college d ictionary , IDG Boo ks Worldwise, Inc, USA 181 National council of teachers of mathematics (2000), Princip les and stand ards for scho ol mathematics, U SA 182 Passow E (1996), Theory and pr oblems o f unders atand ing caculu s concepts, McGraw – Hill, New Yor k 183 Robert Fischer (1992), Teaching Child ren to Think, Simon & Schu ster Education 184 [184]Romainville, M.(1996 0, L'irresistib le ascension du terme "compétence" en éducation, Enjeux, 37/38 185 Suy dam M N (1980), “Untang ling Clues from research on pro blem solving” 186 Tall D.(ed) (1991), Advanced mathematics th inking, K luwer Academic Publishers, Dordecht/Bos ton/L ondon 187 [187]Tomlinson, C A (19 99) The differentiated classroom : Resp ondin g to the needs all learners Alexandra, VA ASCD 188 [188]Toh, T L - Ques, K S - Leong , Y H - J D iny al - Tay , E G (2011) Assessing Problem So lvin g in the Mathematics Curriculum: A New Approach, Assessment in the Mathematics Classrom Yearbook 011 As sociaf of Mathematics Educators, pp 33-36 189 [189]OECD, Key Competencies - A developing concept in general compulsory education, http ://www eury dice.org 190 UNESSCO (197 3), “Internatio nal A ssociation for the Eva luation of Education Achievement”, Paris 191 [191]William Maltas (201 5), From S TEM to STEAM: Integrating Ar ts Educa tion into the STEM disciplines o f Science, Technology, Engineeri ng and M ath, In partial fulfillment of the Masters of Science degree in Arts Administration Drexel University , Philadelphia, U SA 192 [192]Wu, M L (200 3) The applicatio n of Item Response Theory to measure problem solving proficiencies T he University of Melbo urne, Melbourne C Tài liệu internet 193 [193]https ://v tc.vn/g s-dao-trong-thi- kien-thuc-sg k- khong- sat-thuc-te-d112800 html 194 [194]https ://g iaoductho idai.vn/giao-duc/day -hoc-phan-hoa-trong-chuong-trinh-giao-duc-pho-tho ng-moi-3892719 html 195 [195]http://dantri.com.vn /giao-duc- khuy en-hoc/boi-duong-h oc-sinh-gio i-o-mot-so-nuoc-phat-trien-119070 9634.h tm 196 [196]http://www.xn t-in-1ua7276b5 ha.com/kh% C3%A1m%20ph% C3%A1 197 [197]https ://tuoitre.vn /nhun g-ky -nang-sinh-v ien-viet-nam-can-biet-199821.htm 198 [198]https ://www tienpho ng.vn/giao-duc/gs-do-d uc-thai-khong-con-dat-cho-toan-lat-leo-phuc-vu-th i-cu-1230978.tpo 199 [199]http://khoahocp hattrien.vn /khoa-hoc/giao-duc-stem-khong-de-bien-hoc-sinh-thanh-nha-khoa-hoc/20170 419034 255815 p1c160.h tm 200 [200]https ://tailieupro.com/huo ng-dan-giai-mot-so-bai-toan-nang-cao-ve-ung-dung-cua-tich-phan-vu-hong-quy / 201 [201]http://danhng oncuocsong vn/danh-ng on/biet-ma-hoc-kh ong-bang-thich-ma-hoc-thich-ma-hoc-khong-bang-vui-say html 202 [202]http://hoctructuy en.ued.udn.v n/mod/page/v iew.php ?id=559 203 [203]https ://tusach.thuv ien khoahoc.com/wiki/Kinh _nghi%E 1%BB%87m_qu%E1% BB%91c_ t%E1%BA% BF_v%E1%BB%81_ ph%C6% B0% C6%A1ng_ ph%C3%A 1p_d%E1% BA%A1y _h%E1%BB%8Dc_theo_% C4%91%E1% BB%8 Bnh _h%C6% B0%E1% BB%9 Bng_ ph%C3%A 1t_tr i%E1%BB%83n _n%C4%83n g_l%E1% BB% B1c 204 [204]https ://tusach.thuv ien khoahoc.com/wiki/Kinh _nghi%E 1%BB%87m _qu%E1% BB%91c_ t%E1%BA% BF _v%E1%BB%81_ ph%C6% B0% C6%A1ng_ ph%C3%A 1p_d%E1% BA%A1y _h%E1%BB%8Dc_theo_% C4%91%E1% BB%8 Bnh _h%C6% B0%E1% BB%9 Bng_ ph%C3%A 1t_tr i%E1%BB%83n _n%C4%83n g_l%E1% BB% B1c#Kin h_ngh i.E1 BB.87m_c.E1 BB.A 7a_.C4 90an_M.E 1.BA.A1ch 205 [205]https ://tusach.thuv ien khoahoc.com/wi ki/Kinh _nghi%E 1%BB%87m_c%E1%BB%A 7a_Vi%E1% BB%87 t_Nam _v%E1%BB%81_ph% C6% B0%C6%A 1ng_ph% C3%A1p_ d%E1%BA%A 1y _h%E1%BB%8Dc_ theo_%C4% 91%E1%BB%8 Bnh_h% C6%B0%E1%BB%9 Bng_ph% C3%A1 t_tri%E1% BB%83n_n% C4%83n g_l%E1% BB% B1c_ng% C6%B0%E1%BB%9Di_ h%E1%BB%8Dc 206 [206]https ://www tandfonline.com/doi/full/10.1 080/0 737000 080217 7235 207 [207]https ://b oo ks.g oogle.com.vn/bo o ks ?id=RLINAQAAIAAJ&q=Discovery +capacity +in+mathematics+teaching,+phd+thesis&dq=Discovery +capacity+in+mathematics+teaching,+phd+thesis&hl=vi&sa=X&ved=0ahUKEwixrd6szMDiA hVP_GEKHRW_ BUoQ6AEIJ zAA 208 [208]https ://aip scitation.org/d oi/p df/10.10 63/1.4 995164 209 [209]http://www.do dccrp.org/files/L ibic ki_D ominant.pdf 210 [210]https ://aip scitation.org/d oi/1 0.1063 /1.499 5155 211 [211]https ://o nlinelibrary wiley com/doi/pdf/10 1002/kpm.123 212 [212]https ://www.academia.edu/5947158 /Discovery _learning_in_mathem atics_by _using_dy namic_geometry _software_GeoGebra_action_research 213 [213]https ://www.researchgate.net/publication/305174 476_Discovery _Learning_in_the_Classroom 214 [214]https ://research.acer.edu.au/cgi/viewcontent.cgi?art icle=1022& context=aer 215 [215]https ://www.jstor.org /stable/246419 58?seq=1#page_scan_tab_contents 216 [216]https ://www.m icrosoft.com/en-us/education/educatio n-workshop/brain-impact-simulator.aspx Trung (2010), Inquiry Tổ chức Learning , HĐ Nguồn thức nhận Website: http :/www ... school students; 2.2 Find out the reality and need of improving the competency of exploring and obtaining knowledge in teaching maths for high schools students majoring in physics, chemistry and biology; ... and students in teaching maths to high school students majoring in physics, chemistry, and biology; Learning about the implementation and viewpoints of maths teaching in particular and teaching. .. exploring and obtaining knowledge in teaching mathematics for high school students; level of this ability in teaching mathematics among high school students; Thirdly, the thesis has presented the expression