Training integrated teaching skills for teachers of mathematics in high schools

in our country in particular, is a learning field consisting of subjects and knowledge circuits such as: Arithmetic, University Numbers, Geometry, Trigonometry, Analysis, Statistics, Probability, Combination, Aggregation, ... Therefore, when choosing and arranging topics, or knowledge circuits in a reasonable way to teach ( from lower grade to upper class, from lower level to upper level, from elementary to high school), it can be considered as integrating curriculum, in the direction of integration within the subject. (2) Interdisciplinary integration: In high schools many math knowledge is used to solve different subject contents: Physics, Chemistry, Biology, Geography, ... and application in practice, labor, production. Accordingly, mathematics is a subject with many opportunities for interdisciplinary integration. On the level, it can be integrated in one post or integrated by topic. integrated in a lesson, integrated knowledge is often integrated at a certain point in the lesson (to state 8 situations, or reinforce, practice, ...); integrating according to topics often mobilizes interdisciplinary knowledge, creating topics. Accordingly, learners need to mobilize knowledge and skills of Mathematics and other subjects, including life experiences to handle situations arising from the orientation topic. The problem of building integrated topic has been studied quite in detail in the thesis of Nguyen The Son, so we do not mention it in this thesis. We see that in high school Math today is mainly integrated towards internal subjects, students only solve problems through theory, so they encounter many obstacles in learning. However, using knowledge of mathematics to solve practical problems related to other subjects is being widely, diversely and effectively applied, thus, students are very passionate about learning and experience. experience, explore. 1.2. Overview of the research related to the topic 1.2.1. Some studies on integrated teaching 1.2.1.1. Some studies on integrated teaching abroad a) Integration is one of the trends that many countries in the world are interested in researching and applying to schools. b) Applying the concept of integration into teaching is a common trend in countries in the region and around the world. 1.2.1.2. Some studies on integrated teaching in the country In Vietnam, integrated teaching has actually existed for a long time in many levels of our country with names such as "practical relation, education, ..." and integrated teaching in primary schools, more prominent than junior high or high school. During the past time, there have been many studies on integrated teaching, according to many different approaches, the concepts of integration have been stated such as: Approach from the perspective of the program, the subject is shown through: program integration; integration of subject content; method integration, integration of knowledge, skills, ... here integration is understood as the organic, systematic combination of knowledge in a subject into a unified content. Nguyen The Son has researched to design integrated teaching topics, the author has carefully researched the process of building integrated topics, clearly defined the tasks of teachers and students' learning tasks through Specific integrated topics of Mathematics. In addition to the works and projects of scientists and research institutes, on August 7, 2014, the Ministry of Education and Training issued the official dispatch No. 4188 on the organization of the Contest Applying Interdisciplinary Knowledge to Solve decide practical situations for students and a teaching contest on integrated topics for high school teachers. In addition, a number of scientific seminars on integrated teaching were held in this period such as: Scientific seminar “Integrated teaching in high schools to meet the requirements of 9 curriculum and textbook innovation after year. 2015 ”organized by the Ministry of Education and Training in Ho Chi Minh City 12/2014; Scientific seminar "Integrated teaching - Differentiated teaching at high schools to meet the requirements of curriculum and textbook innovation after 2015" by the pedagogical research institute - Ho Chi Minh City Pedagogical University held in December 2014. Conferences with the participation of scientists and teachers across the country, seminars to discuss solutions to apply integrated teaching in high school programs meet the requirements of changing new curriculum and textbooks after 2015. In these seminars, scientists and high school teachers in participating provinces discussed about integrated teaching, how to implement integrated teaching to address the requirements. Program and textbook innovation after 2015 set out. Thus, we can see that the construction of integrated teaching programs has been and is being studied and deployed extensively by the Ministry of Education and Training and scientists from primary to university. high-quality education and integration with the world. Through the above section, the PhD student agrees with the results of teaching and teaching skills in Mathematics and with Nguyen The Son on building topics, processes, lessons ... But the skills are needed to design. and integrated teaching organization has not been researched and we will continue to research and clarify in the next sections. The PhD student will continue to do research to clarify the basic skills of Mathematics integrated teaching in high schools that need to be fostered for Math teachers, to contribute to promoting their competencies and qualities to improve teaching effectiveness. study Math, especially towards the successful implementation of the 2018 general education program in Vietnam. 1.2.2. Some studies on teaching teaching skills training To help us have a theoretical support for proposing integrated teaching skills, we learn about teaching skills in some countries, according to the data obtained. It can be seen that in Vietnam, researches on teaching skills have strongly developed over the past few decades. The studies related to skill training for teachers or students are shown through the works of the authors such as: Nguyen Nhu An has systematically approached to the theory of deeply researching the system of educational skills in the classroom following the approach to education (classroom preparation skills; classroom teaching skills; skills the ability to guide other forms of teaching organization; skills for testing and evaluating teaching results); Phan Thanh Long presented relatively systematically the theoretical issues related to training teaching skills at pedagogical schools. Pham Van Cuong has built a set of Standards of Math teaching skills for students of primary education at college level to help evaluate the practice of students' math teaching skills in the learning process; Nguyen Thang gave the concept of career skills in math pedagogy; propose career skills that need to be trained for math pedagogy students; Nguyen Thi Nhan has overviewed teaching skills through domestic and foreign projects and proposed 3 skills: lesson 10 design skills, student research skills and learning, writing skills. Nguyen Minh Giang has clarified the theoretical basis of developing math teaching skills for pedagogical students according to the professional standards of teachers; identify component skills in math teaching capacity according to professional standards that teachers need to develop for students; building a set of criteria and tools for assessing the development of math teaching skills of pedagogical students according to teachers' professional standards through functional teaching; Proposing measures to develop math teaching skills for pedagogical students according to teacher professional standards through functional teaching. Le Minh Cuong has researched on skills of applying information technology in teaching Mathematics. Identify 5 skills (using Math software to calculate, describe problems, interact with problem models on computers, apply information technology to support the application of reasoning in teaching. math, to evaluate the learning results of students); Author Allen & Rayan (1969) of Stand Ford University (USA) classified 14 skills. Author B.K. Passi (1976) et al. Defined 13 skills. The National Education Research and Training Council of the United States in its core teaching skills publication (1982) has listed 19 teaching skills. EU countries orient to 10 teaching skills. 1.3. Proposing groups of teaching skills integrated in Mathematics in high schools Through research and synthesis, we propose the necessary skills to implement the teaching of integrated mathematics topic in high schools through the following table: Symbols Skills TH1 Determine integration opportunity, integration theme, define integration goal, integration type TH2 Design integrated topics (clarify learning activities, clarify the required products after each activity, subject knowledge, interdisciplinary knowledge, ...) TH3 Organize integrated lessons (Choose methods, means and forms of teaching organization that are suitable for each part of integrated lessons (project teaching, organization of experience, ..)) TH4 Designing to assess learning outcomes after integrated lessons (setting (rubric), evaluating, for each job, activity, with each part in the case study) TH5 Integrated lesson research (Draw lessons from experiences in designing and organizing integrated lessons; Expected plans for coordination between teachers of subjects, in integrated and interdisciplinary teaching) TH6 Prepare conditions for integrated lessons (facilities, facilities, teaching technology for integrated teaching) 11 1.4. Conclusion of chapter To have a fulcrum for the presentation of the thesis and propose skills as well as pedagogical measures, in Chapter 1 we have focused on clarifying the issues: - Skills, career skills, teaching skills, math teaching skills, professional standards for high school teachers. - Integrated, integrated teaching, characteristic of integrated teaching and integrated form of Math. - Domestic and international experience in training integrated teaching skills. On that basis (considered as a theoretical basis), the author has proposed the integrated teaching skills needed in high school math teachers (Table 1.6), which is considered a new dedication to theory. The proposed Mathematics Integrated Teaching Skills can be seen as "theoretical model" of math teachers who know integrated teaching. It can be seen that this is the proposed model based on domestic and foreign experiences as well as the author's experience (subjective after research). Whether they are consistent with Vietnamese educational practices or not, will be analyzed and tested through the survey in Chapter 2 (considered as a practical basis). After the survey and editing, the feasibility of the proposed model will be further tested through Chapter 3 and Chapter 4 of the thesis. Chapter 2 LEARN THE REALITY OF INTEGRATED TEACHING SKILLS MATHEMATICS IN HIGH SCHOOL In Chapter 1, we have researched and based on the theoretical basis proposing integrated teaching skills, which is considered the "a priori model" of math teachers who know integrated teaching. In Chapter 2, we clarify the practical basis of proposing integrated teaching skills for math teachers in high schools. 2.1. Survey purpose Having a practical basis for proposing necessary skills so that teachers can design and organize integrated teaching in Mathematics in high schools. Accordingly, we learn, collect information and analyze survey data on the reality of teaching integrated math in high schools; consult teachers (see as experts) on the necessary integrated teaching skills for high school math teachers. The main jobs are as follows: - Ask some math teachers (see as experts) about the teaching skills of integrated Mathematics proposed in Chapter 1 and adjust the skills model to suit the national educational practice; Learn about how to practice integrated teaching skills. 12 - Find out the difficulties and advantages of designing and organizing Mathematics integrated teaching at high schools and the causes of the difficulties and advantages; lessons about designing, organizing teaching in integrated mathematics in high schools. 2.2. Objects and survey tools - Subjects: Including math teachers of 18 high schools in the Central Highlands region. - Tools: Questionnaire survey, (with 175 questionnaires (Appendix 6)); in-depth interviews with 3 inexperienced teachers who still have little experience and much experience; Form of seminars, professional cluster activities. 2.3. Survey content for math teachers The content of the survey was inserted into the questionnaire (details are shown in Appendix 3), in order to ask for the opinion of math teachers about: - Mathematical integration teaching skills proposed in Chapter 1. - Difficulties and advantages in designing and organizing Mathematics integration teaching at high schools and their causes. - Experiences of teaching integrated math in high schools. 2.4. Survey method Methods of investigation, survey: Using questionnaires of teachers, combining with seminars, in-depth interviews a number of subjects. Expert method, in-depth interview: Exchanging with some education managers with expertise in Mathematics and Mathematics teachers at high schools. 2.5. Survey results and analysis 2.5.1. According to the questionnaire - The results show the majority of teachers with working years from 6 to 18 years (70%). This is a source of teachers who are enthusiastic, knowledgeable in information technology and easily receptive to modern teaching methods. Therefore, the deployment of training integrated teaching skills will be very favorable. - When asked about the necessity of using Mathematics integrated teaching skills in high schools, we received the survey results in the following table: Symbols Skills Levels (1) (2) (3) (4) TH1 Determine integration opportunity, integration theme, define integration goal, integration type 5% 9% 40% 46% TH2 Design integrated topics (clarify learning activities, clarify the required products after each activity, subject knowledge, interdisciplinary knowledge, ...) 2% 7% 69% 22% 13 TH3 Organize integrated lessons (Choose methods, means and forms of teaching organization that are suitable for each part of integrated lessons (project teaching, organization of experience, ..)) 0% 6% 75% 21% TH4 Designing to assess learning outcomes after integrated lessons (setting (rubric), evaluating, for each job, activity, with each part in the case study) 4% 7% 72% 17% TH5 Integrated lesson research (Draw lessons from experiences in designing and organizing integrated lessons; Expected plans for coordination between teachers of subjects, in integrated and interdisciplinary teaching) 3% 65% 15% 17% TH6 Prepare conditions for integrated lessons (facilities, facilities, teaching technology for integrated teaching) 28% 25% 30% 17% The results show that the majority of teachers questioned support the skills, from TH1 to TH4, with a necessary and very necessary level; only the TH5 skill is considered to be less necessary by the majority of the people; The number of TH6 skills that are unnecessary and less essential accounts for a higher proportion than necessary and very necessary. - Among the above skills, is there any skills that need to be added or removed to suit teaching integrated math: 21% of the votes say that a few small skills are needed such as "expected pedagogical situation" or "the skills to use scientific language of relevant subjects". However, we find that these are covered by the above skills. Thus, it can be seen that most of the teachers questioned agree highly with the skills TH1, TH2, TH3 and TH4; only skills TH5 and TH6 have little support. However, there are no objections or additions to other skills, so it can be said that there is no need to adjust the skills proposed in Table 1.6, Chapter 1. - When asked: What practice measures are needed in order to formulate Mathematical integration teaching skills in high schools? Teacher has choices with the following results: (1). Raising awareness of the creation of integrated teaching skills in Mathematics for teachers at high schools through professional activities (lesson study, professional group activities, schools, the Department of Education and Training, ...) (75%). (2). Focus on teaching model in the process of forming, training teaching skills integrated in Math for high school teachers (93%). 14 (3). Orientation for self-study, self-training of integrated teaching skills for high school teachers (79%). (4). Organize for high school teachers to experience teaching skills integrated in math (65%) (5). Designing a number of sets of questions to assess students' high school math learning results after integrated teaching (72%). (6). Other measures (20%), such as: Using information technology, social networks to exchange content and knowledge of integrated teaching and integrated teaching in Mathematics; Train teachers to build integrated topics through other subjects' contents at the same time; Hone Mathematics Integrated Teaching Skills through Integrated Opportunity Discovery; Train skills to connect programs of related subjects through current textbook research. Through this, it shows that the organization of integrated teaching in Math at high schools is facing certain difficulties, teachers need to have sample teaching periods to learn and follow. - When asked about the difficulties and advantages in practicing Mathematics integrated teaching skills in high school today, we received answers focusing on the following issues: + Advantages: Large materials resources, adequate facilities, modern teaching facilities meet teaching requirements; Students take the initiative in their assigned work and work effectively in groups; + Difficulty: It takes a lot of time to prepare lessons; The association between the teachers of the relevant subject has not ensured the agreement and sharing; Implementation of integrated teaching topics is not regular and continuous; Some weak students cannot fulfill the requirements set out by the teachers. - Some measures to overcome difficulties and problems encountered in practicing Mathematics integrated teaching skills in high schools are currently mentioned by teachers: Building topics of integrated teaching for the blocks. class from the beginning of the school year; Efficiently combine with other subject teachers; Arrange equally about the level and sense of learning of the students in the groups. - On the other hand, when asked which content has many opportunities for integrated and interdisciplinary teaching with Mathematics in high schools, the majority said: (1) - Integrate internally in Mathematics (65%), (2) - Integrate with Physics (52%), (3) -Integrate with Chemistry (42%), (4) - Integration with Biology (48%. (5) - Integration with other subjects (15%) such as: Civil Education, Geography, Security and Defense, ... - Moreover, when asked about the current math integration teaching skills of teachers themselves? We get the following results: (1) Imitation (20%); (2) It has been done but not 15 exactly and clearly (43%); (3) Do exactly (16%); (4) Proficient implementation (12%); (5) Perform a metamorphosis (9%) 2.5.2. According to in-depth interview 2.5.2.1. Interview with school administrators 2.5.2.2. Interviewing the teacher 2.6. Conclusion chapter 2 In this chapter, we have conducted a situation survey, in order to ask teachers' opinions about proposed skills, to learn about the advantages and disadvantages of teachers when teaching integrated in Mathematics in high schools. The results showed that, basically the teachers agreed with the proposed skills, no need to adjust. Therefore, we consider the following 6 skills as "theoretical model" (a priori model that does not need adjustment after the survey) of Mathematics integrated teaching skills that teachers need to achieve. Moreover, through the survey, we also obtained valuable opinions from the majority of teachers: in order to be able to teach integrated math well, it is necessary to organize fostering so that teachers understand deeply about integrated teaching theory, drafting sample topics on integrated teaching; teaching samples in professional activities of schools, clusters, ..., strengthening facilities and materials in schools today. The proposed skills and theoretical basis in Chapter 1, the practical basis in Chapter 2, are considered as the bases (scientific fulcrum) for us to propose pedagogical measures in Chapter 3. Chapter 3 METHODS TO TRAIN OUR TEACHING SKILLS INTEGRATED FOR TEACHERS IN HIGH SCHOOL 3.1. Orientation proposed measures In order to propose appropriate and feasible measures to practice integrated teaching skills for math teachers at high schools, in our opinion, it is necessary to base on the following orientations: 3.1.1. Meet the goals of teaching Mathematics in high schools According to the ideology of the general education curriculum in Mathematics, one of the innovations this time is to enhance integrated teaching. Therefore, the measures must be directed to help teachers to integrate Math teaching. 3.1.2. Ensure consistency between theory and practice In order to train good math integration teaching skills for high school teachers, they must help them master the theory of integration, teaching integration and practice of preparing integrated topics, through professional sessions, facilities, or professional cluster activities, as well as after regular training and retraining sessions conducted by the Ministry of Education and Training or the local Department of Education and Training. 16 Besides, the self-study and self-study activities of integrated teaching skills of high school teachers are extremely important and practical in order to further improve the teachers' integrated teaching skills in Mathematics. 3.1.3. The measures taken must be feasible and effective in terms of the subject's curriculum, as well as the school facilities Currently, the facilities of schools in each locality are different. Therefore, teachers need to rely on their actual units to ensure feasibility and effectiveness in teaching integrated topics. Moreover, teachers need to clearly define the goal of implementing the integrated topic to ensure the feasibility and efficiency of the teaching process. From there, promoting the capacity of students, contributing to improving the quality of education. 3.2. Pedagogical measures aim to train teachers of Mathematics at high schools in integrated teaching skills Through research, we believe that in order to be able to teach integrated math well, teachers need to have integrated teaching skills as in the skill board. In order to help high school Math teachers to design and organize integrated teaching, we propose 4 pedagogical measures to practice proposed skills. 3.2.1. Measure 1: Help teachers understand integrated teaching, especially integrated teaching skills, through self-study and self-training. 3.2.1.1. The purpose of the measure Help teachers understand deeply about integrated teaching theory, especially integrated teaching skills, so that they can confidently design and organize integrated teaching in high schools. 3.2.1.2. How to perform Teachers understand integrated teaching, especially integrated teaching skills, mainly through professional group activities, self-study. Therefore, besides helping teachers deeply understand knowledge, they also contribute to training self-study ability, applying knowledge in teaching practice. Since then, increasingly perfecting teaching skills and improving the quality of education. In the scope of this thesis, we orient self-study to foster math integrated teaching skills as follows: - Self-study about integration, teaching integration in documents; - Self-study the theme design process integrated in the documents; - Self-study skills of integrated teaching Mathematics; - Self-study about the organization of integrated teaching in Mathematics, through documents; - Self-study professional activities on