DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .DẠY HỌC XÁC SUẤTTHỐNG KÊ Ở TRƯỜNG TRUNG HỌC NƯỚC CHDCND LÀO THEO HƯỚNG KẾT NỐI VỚI THỰC TIỄN .
NISTRY OF EDUCATION AND TRAINING HANOI NATIONAL UNIVERSITY OF EDUCATION THONGCHANH VONGLATHSAMY TEACHING PROBABILITY - STATISTICS AT LAO PDR SECONDARY SCHOOL BASED ON CONNECTION WITH THE REAL LIFE Major: Theory and Methods of Teaching Mathematics Code: 9140111 SUMMARY OF DOCTORAL THESIS OF EDUCATION SCIENCE Hanoi, 2022 THE WORK WAS COMPLETED AT: HANOI NATIONAL UNIVERSITY OF EDUCATION Supervisor: Prof PhD BUI VAN NGHI PhD NGUYEN VAN DUNG Reviewer 1: Assoc Prof PhD Tran Kieu The Vietnam Institute of Educational Sciences Reviewer 2: Assoc Prof PhD Nguyen Trien Son Tay Bac University Reviewer 3: Assoc Prof PhD Ngo Hoang Long Hanoi National University of Education The dissertation will be defended in front of the School-level Thesis Assessment Council Hanoi National University of Education at … … hour … date … month … year 2022 The thesis can be found at: Vietnam National Library, Hanoi or Library of Hanoi National University of Education LIST OF WORKS PUBLISHED BY THE AUTHOR RELATED TO TOPIC OF THE DISSERTATION Thongchanh Vonglathsamy and Nguyen Van Dai (2021), The current situation of teaching the Statistical probability section in high schools of the Lao People's Democratic Republic in the direction of increasing application in practice, Journal of Education, special issue, period April, 2021, Volume 59, pp 332-336 Thongchanh Vonglathsamy (2021), Teaching the Statistical probability in schools of the Lao People's Democratic Republic in the direction connect with real life, Journal of Education, special issue, October 2021, pp 225 - 228 Thongchanh Vonglathsamy (2021), Methords of teaching the Statistical probability in schools of the Lao People's Democratic Republic in the direction connect with real life, Journal of Education, Volume 514, period November 2021, pp 60 - 64 PREFACE Reason for choosing the topic 1.1 The need for educational innovation in Laos; 1.2 The relationship between statistical probability and life; 1.3 The need and necessity of teaching statistical probabilities in the direction Purpose research Proposing a number of methord to teach probability statistics in Lao secondary schools in the direction of connecting with life, contributing to improving the quality of teaching probability statistics in Lao secondary schools Tasks research + The task of this research is to answer the following scientific questions: • What is the theoretical basis of teaching probability statistics in Lao secondary schools in the direction of connecting with life? • What is the current practice of teaching probability statistics in Lao secondary schools in the direction of connecting with life? • What are the methods of teaching probability statistics in Lao secondary schools in the direction of connecting with life? • Are the methods of teaching probability statistics in Lao secondary schools in the direction of connecting with life feasible and effective? Scope of the study Content Scope is the probability and statistics in Lao schools Research Objects and Mete Research topic within the content of Statistical Probability in Lao Secondary School Research object: The process of teaching Statistical Probability in Lao secondary schools (from grade to grade 12 in Laos) in the direction of connecting with life Research object: Methods of teaching Statistical Probability at Lao secondary schools in the direction of connecting with life The hypothesis On the basis of the objectives and tasks of teaching Statistical Probability in Lao secondary schools, if practical problems are enhanced to evoke motivation, practice in the process of teaching Statistical Probability, enhance students Experiencing practical activities according to the measures proposed in the thesis, students are not only more interested and have higher results in learning Statistics Probability, but also enhance their ability to apply knowledge, skills on Probability statistics into practice for students Research Method Theory research; Observation - Investigation; Pedagogy Experiment (PE) The protection issues raised • Teaching Statistical Probability in Lao secondary schools in the direction of connecting with life is necessary, with theoretical and practical basis • Measures proposed in the thesis contribute to improving the teaching effectiveness of Statistics Probability in Lao secondary schools New contributions of the thesis 9.1 Theoretical: Clarifying the theoretical and practical basis of teaching Probability statistics in Lao secondary schools in the direction of connection with life 9.2 Practical: Proposing some methods of teaching Statistical Probability in Lao secondary schools in the direction of connecting with life 10 Structure of thesis Outside Opening, Conclusion, the thesis include chapters: Chapter 1: Theoretical and practical Base Chapter Some methods of teaching statistics in secondary schools in the direction of connection with practice Chapter Pedagogy Experiment Chapter THEORETICAL AND PRACTICAL BASE 1.1 Overview of the research works related to teaching Statistical Probability in the direction of connecting with life 1.1.1 Researches on the problem of teaching Math in connection with the real life 1.1.1.1 In the world Teaching Math in connection with reality is an issue that has been of interest to many educational researchers around the world In the Netherlands, since the 70s of the twentieth century, the program "Realistic Mathematics Education" (RME) has been developed They believe that in mathematics education, students need experiential activities to "reinvent" mathematical knowledge for themselves or to mathematize practical problems in class Then the RME program was spread to a number of countries around the world, including the UK and the US (Romberg, 2001) Under this program, teachers can develop lesson content in the direction of increasing the application of Mathematics in real life.Theo Zemelman, Daniels, Hyde (1998): One of the doctoral theses in this direction is the thesis of Nguyen Thanh Thuy (2005) at the University of Amsterdam, Netherlands The author has researched and proposed some measures to help math pedagogical students in Vietnam apply the RME theoretical framework to the Vietnamese context Also in the Netherlands, Reidar Mosvold's doctoral thesis (2005) "Mathematics in everyday life - a study of beliefs and actions" proposed measures to connect mathematics with everyday reality day In the US, since 1990, the University of Arizona (USA) has implemented a STEM education program, which stands for the words Science, Technology, Engineering and Mathematics ), after school hours (After - School), so that students can discuss and solve practical problems related to the school and the locality The goal of math teachers is “to help students develop their math competence, to help students feel that math is useful and meaningful, to help them believe that they can understand and apply mathematics in their own lives.” Practice." Battista M T (2001) said that “Today, the goal of teaching Mathematics is always changing Teachers today need to help students develop skills they will use every day to solve math and non- math problem solving These include the ability to interpret ideas, the ability to use resources to find needed information, to work with others on a problem, and to generalize across different situations, as well as the possibilities provided by electronic computers and computer programs.” Yarhands Dissou Arthur (2018), in the work "Connecting Mathematics to Real-Life Problems" recommends that: Teachers are encouraged to connect mathematics to real-life and environmental problems as well as other fields Stoehr K (2015) did a study that provided a snapshot of a teacher's understanding and practice of the relationship between math and the real world Marja Van den Heuvel-Panhuizen and Paul Drijvers gave “core teaching principles of real mathematics education” including the practical principle: Solving “real life” problems as the goal of mathematics education; Mathematics education should begin with problem-solving situations that are meaningful to students, providing opportunities for them to associate meaning and mathematical structures with real life Mesture Kayhan Altay, Betỹl Yalvaỗ, Emel Yeltekin (2017) researched "skills to connect Mathematics with real life of students" and showed the meaning of mathematical concepts and their use in real life Realism should be emphasized and discussion should not focus solely on calculations, shapes and numbers According to Bomar, Michael (2009): Making math useful to students in the real world should be the primary focus of all math teachers However, there is no one and no easy way to this In particular, it is necessary to mention the Program for International Student Assessment (PISA) and the High School Mathematical Contest in Modeling (HiMCM) in the United States in recent years are also in the direction of connecting with reality In summary, there have been many works in the world that promote the role and meaning of math teaching in connection with practice This is completely logical and scientific; Because, like many other sciences, mathematics is rooted in reality and serves human practice 1.1.1.2 In Vietnam Researches on teaching Mathematics in high schools are associated with practice, first of all shown in doctoral theses on Mathematical Education Some of the dissertations of the following authors can be mentioned: Nguyen Ngoc Anh (2000), Bui Huy Ngoc (2003), Phan Anh (2012), Vu Huu Tuyen (2016), Nguyen Thi Tan An (2014) There are also a number of doctoral theses on teaching mathematics at the college and university level with the aim of strengthening the connection with professional practice of the authors: Nguyen Minh Giang (2016), Le Ba Phuong (2016), Phan Van Ly (2016), Ha Xuan Thanh (2017), Pham Nguyen Hong Ngu (2020)… Researches on teaching Mathematics in high schools in association with practice are also reflected in the pedagogical curricula, pedagogical methods of teaching mathematics at bachelor's or graduate level used in the University of Education There have been many articles published in specialized journals or in conference proceedings on Mathematical Education associated with practice In 2018, the International Scientific Conference on Mathematical Education (ICME) held at Hanoi National University of Education in Vietnam had 71 papers submitted to the Conference, including reports by researchers scientists and groups of foreign scientists In which, Tran Trung, Nguyen Manh Cuong, Pham Thi Phuc (2015), proposed four measures to teach Mathematics in high schools in the direction of strengthening the connection with practice; Nguyen Danh Nam (2017) has an article "Some problems in mathematics education associated with practice" Nguyen Tien Trung et al (2019) reviewed the existing literature to establish a framework for assessing the development of Practical Mathematics Education (RME) in terms of policy and practice and outline some possible directions for future RME research Thus, in Vietnam, research on teaching mathematics in association with practice is also a direction that many researchers in mathematics education are interested in Especially in recent years, there have been many research results and achievements in RME, STEM education and meeting the PISA global student assessment program 1.1.2 Some studies on teaching Statistics - Probability in the direction of increasing practical application 1.1.2.1 In the world In the world, there have been a number of studies on teaching Statistics - Probability in schools, including studies on teaching Statistics - Probability in the direction of connection with real life The following works can be mentioned: Joan Garfield (1995) studied how students learn statistics, Kucukbeyaz, Batto and Rosa (2006) studied a project on “Development of methods of teaching Statistics in primary and secondary schools” in the states of Argentina During the 13th International Conference on Mathematical Education (ICME) - Proceedings of the International Conference on Mathematical Education 2016 in Germany, Researches on teaching Statistics Probability in the direction of connecting with real life in the world focus on analyzing the role and great significance of Statistics - Probability knowledge in life and moving from teacher-centered teaching focus on student-centered teaching 1.1.2.2 In Vietnam a) Researches on teaching and learning methods of Statistics - Probability in schools Many research works on Statistics - Probability have been published at national and international conferences The National Conference on Savings: Research, Application and Teaching was held in Nha Trang (1983), Ha Tay (2002), Ha Tay (2005) The International Conference on Lottery and Applications was held in 1999 and 2008 in Hanoi Some doctoral theses by the authors: Tran Kieu (1988), Do Manh Hung (1993), Tran Duc Chien (2007), Pham Van Trao (2008), Nguyen Thi Tan An (2013), Vu Hong Linh (2020) b) Studies on teaching Statistics - Probability related to the application of Statistics Probability into practice A number of research works on teaching mathematical problems related to the application of mathematical problems in practice, first of all, the doctoral theses on teaching mathematical problems in vocational training schools The theses of Ta Huu Hieu (2010), Nguyen Thi Thanh Ha (2014), Nguyen Thanh Tung (2016), Vo Thi Huyen (2017), Mai Van Thi (2018) respectively research on the teaching of Statistics Probability in universities study in the direction of connecting with the professions: Physical Education - Sports, Economics - Technology, Medicine - Pharmacy, Police, Maritime The researches on teaching of Statistics - Probability in Vietnam in the direction of connection with practice focus on career development goals for students of universities, vocational colleges and practical applications 1.1.2.3 Some works of Lao authors on teaching Probability statistics in Laos Currently, there are only two Master theses of Lao students who have studied in Vietnam on teaching Probability - Statistics in universities in Laos, no research thesis related to teaching Probability - Statistics in high school From the above studies, it is shown that: Studying the teaching of math problems in secondary schools in the Lao PDR in the direction of connecting with reality so that students have more confidence, interest and active learning, know how to solve problems Solving practical problems, knowing how to apply knowledge of structural control in daily life is an open direction and this thesis can be directed towards 1.2 Teaching probability - statistics in the direction of connection with real life 1.2.1 Some basic concepts + Reality, practice, practical problems + Ability, Mathematical Competency, Ability to apply mathematics in practice + Connect is to make the parts that are separate to join, to stick together Based on the above viewpoints and research results, within the scope of this thesis, we conceive of a practical problem for school students in Laos as a problem in which the hypothesis or conclusion contains elements related to the practice to be solved, it is necessary to clarify the contents related to the practice The contents or elements related to that practice must be suitable to the children's knowledge, skills and cognitive abilities 1.2.2 Some conceptions of teaching Mathematics related to real life 1.2.2.1 Learning in real life context According to Van den Heuvel-Panhuizen (2005): In many textbooks around the world, we can see a series of exercises such as Performing calculations (3ẵ: ẳ ) The author calls it the "bare" exercise because there are only numbers, no meaning other than numbers The repetition of such tasks is only to train students to memorize and 10 accounts for 20% of the total number of math periods In the USA, Statistical Probability is two of the few Math topics taught at all levels of high school with very specific goals for statistical thinking and knowledge 1.3.2 In Vietnam Vietnam's 2018 Math program has introduced Statistical Probability content from grade 2, the teaching objective of Statistical Probability is determined specifically for each grade level 1.3.3 In Laos Since 1994, with the 11-year education system, the content of Statistical Probability has been included in the high school curriculum from grade 6; by 2016, with the 12year general education system, the content of Statistical Probability in grade 11 has 18 more periods (increasing the total to 34 periods) with the content of Probability distribution of random variables; Grade 12 adds 14 hours 1.4 The reality of teaching probability - statistics in the direction of connecting with reality in high schools in Lao PDR 1.4.1 Statistics of teaching time Probability – Statistics in the Math program, the ratio of examples and practical problems in Math textbooks in Lao schools Statistical results show that: The number of practical examples in the examples contained in Math textbooks in Lao schools is only about 3% on average; The number of exercises associated with practice in the exercises contained in the math textbooks in Lao schools accounts for about 8% on average From the survey results, it can be said that the number of teaching periods corresponds to the amount of knowledge that students are equipped with too much, too heavy, not suitable for the distribution of the program and the cognitive level of Lao high school students; In terms of practical examples and practical exercises, there are few and most are pseudo-practices, it is not suitable for teaching and applying in practice Since then, it is necessary to adjust the curriculum content of the Statistical Probability section and recompile the Lao textbooks to be more reasonable 1.4.2 Survey on the reality of teaching and learning Probability – Statistics in Lao 11 high schools in the direction of connection with reality 1.4.2.1 Survey objectives The Survey aim at assess the current situation of teaching probability and statistical in Lao secondary school in the direction of connection with reality for possessing a practical basis for proposing measures of teaching Statistical Probability in the direction of connection with practice 1.4.2.2 Survey object and time Subjects of the first survey included 100 math teachers teaching grade 11 and 12 and 200 students of grade 11 and 12 at 20 upper secondary schools in some districts in Vientiane Province and Vientiane capital, Laos from April to 30, 2019 Phase includes 100 math teachers teaching grade and and 200 students of grade and at 14 lower secondary schools, from May 04 to June 30, 2020 1.4.2.5 Survey results The survey results show that the majority (68%) of Math teachers think that Lao high school students not fully understand the knowledge of Statistical Probability in textbooks Students can only solve basic math problems 19% of teachers think that students can solve advanced math problems In particular, very few teachers assessed that students thoroughly understood the knowledge of Statistical Probability and used the knowledge of Statistical Probability to solve problems posed in real life The cause of the above situation is that teachers are loyal to what is written in textbooks, which leads to teachers' teaching methods that only focus on knowledge of mathematical science, paying little attention to math problems Practice Since 2016, in the Math program of grade 11 and grade 12, with additional time for the content of Statistical Probability, the situation has improved 12 CONCLUSION CHAPTER - The works on teaching Probability statistics in the world focus mainly on the role and meaning of the content of Statistical Probability for life and the sciences, much less this method of teaching this knowledge circuit - This thesis mainly mentions with practical problems in some aspects such as: close practice of life, practice within the subject of probability and statistics or interdisciplinary with other subjects and suitability with the awareness of Lao secondary school students; teaching probability and statistics in the direction of connecting with real life to aim to create a connection between knowledges, theory and skills about probability and statistics with real life The outside of the research direction on applying probability and statistics to solve practical problems, in Laos, attention should be paid to strengthening the connection of probability and statistics with real life through examples, math problems, games of learning, practical experience activities for students in the process of teaching probability and statistics These activities have not received adequate attention from both teachers and students in Laos 13 Chapter MEASURES TO TEACHING STATISTICAL PROBABILITY IN LAO SCHOOL TOWARDS CONNECTING WITH REAL LIFE 2.1 Orientation to build measures Orientation Minimize examples and problems that have no real practicality Orientation 2: Measures must follow the goals and contents of the Program on Statistical Probability in Lao secondary schools Orientation 3: Pedagogical measures must contribute to career guidance for students Orientation 4: Measures should contribute to improving students' ability to connect knowledge and skills about Statistics with practice 2.2 Some pedagogical measures to teach probability - statistics in the direction of connection with real life 2.2.1 Measures Using real-life contexts as examples, problems in teaching Statistics - Probability in secondary school 2.2.1.1 Purpose of the measure This measure aims to evoke motivation and interest in learning for students in the process of teaching Statistics Probability because the knowledge is closely connected with real problems in students' lives 2.2.1.2 Scientific basis of the measure As stated in section 1.2.2: If putting learning tasks for students in a real-life context will make the problems more useful, teaching math will be more effective (Van den Heuvel-Panhuizen), 2005) In teaching, the context set in the learning task must have clear evidence, the origin of the context must be explained through convincing sources (for example, through pictures); Authentic contextual tasks should contain meaningful questions (Vos, 2011,2015 and Wijers, Jonker Kemme, 2004) Inspiring learning interest is an activity that creates and causes students' interest in learning, creates pleasures and needs, and makes students try to achieve their interest to meet learning and training goals 2.2.1.3 How to take the measure 14 Method 1.1 Use real-life statistical data Example 2.1 Using data tables in teaching introductory statistical data table concepts (grade 9) from real classroom contexts Method 1.2 Get motivation from real stories in practice or folk stories, stories in the history of mathematics Example 2.2 Suggesting the opening motivation for some basic concepts of Probability from folk stories to create interest in learning for students At the beginning of the lesson on Probability, the teacher can tell students the story of Trang Quynh of Vietnam, then the teacher can ask interesting questions and approach the concept of Probability as follows: Question 1: Can Quynh borrow money from Lord Lieu? Why? This question is intended to reinforce the concept of trial, event, and possibility, in order to create a premise for the concept of Probability Question 2: What kind of event is Quynh's "borrowing money", the event "Lord Willow let the coins spin, not stopping"? 2.2.2 Measure Organize for students to experience activities in the process of teaching Statistics - Probability in high school 2.2.2.1 Purpose of the measure This measure helps students to actively and actively participate in lesson construction in the teaching process of Statistical Probability because the knowledge is built based on the students' inherent experiences and knowledge 2.2.2.2 Scientific basis of the measure Based on the theory of Experiential Learning by David Kolb (1984) 2.2.2.3 How to take the measure Method 2.1 Organizing students to experience for tabulating fact statistics data directly related to students, families, schools, and society; then calculating the characteristic numbers: mean, median, mode and making pie chart or column graph Example 2.1 Let students use Yenka software to practice virtual coin toss experiments, forming a statistical definition of probability Example 2.2 Group experiential activities in teaching the content "Conditional Probability, Total Probability - Bayesian Formula" (Laos 11th grade math) to help students explore and discover the Probability formula The activities are designed as follows: 15 Activity Each group of students solves a problem and fills in the results in the corresponding table, for example: A bag contains ATM cards of Lao Development bank (LDB) and ATM cards of Laos Agricultural Promotion Bank (APB) Randomly take cards in turn (taken non-refundable) Calculate the Probability of: a) Event A: First time getting LDB's ATM card b) Event B/A: The 2nd time got LDB's ATM card when the 1st time got LDB's ATM card c) The event of both times getting LDB's ATM card Activity Sum the results to discover the formula for calculating Conditional Probability Group P(A) P(B/A) P(AB) Discover the recipe 10 98 100 9 95 100 20 30 90 98 95 100 100 P(A) P(B/A) = P(AB) 2.2.3 Measures Clarifying the meaning and role of concepts, rules and theorems in Statistics – Probability lessons through connection with practice 2.2.3.1 Purpose of the measure This measure makes students understand the practical meaning of the typical signs in the Statistics table and the meaning of Probability; At the same time, it helps students initially see the practical value of the quantitative research process, the role of Probability in sampling 2.2.3.2 Scientific basis of the measure + According to Richard Kirkham (1984): Knowledge comes to us by faith; Knowledge needs to meet three criteria: it must be proven, correct, and reliable Therefore, 16 teachers need to make students see and believe the meaning and practical value of knowledge + According to Tran Thi Kim Thu (2012): The mean (or average) in statistics is the level of representation according to a certain criterion of a population consisting of many units of the same type The median represents the prevalence of the phenomenon, but by itself it does not equalize or offset the difference between the variables 2.2.3.3 How to take the measure Method 3.1 Clarifying the meaning and role of typical numbers in real-world data through practical examples close to students Example 3.1 Clarifying the need, meaning and usage of mean and median (Chapter "Statistics - Probability" in Math Textbook Laos * Why use average? * When to use (not use) mean, median? 2.2.4 Measures Organize learning games, and at the same time improve students' understanding of television games and games of chance 2.2.4.1 Purpose of the measure This measure creates an open, fun learning environment in the classroom; improve students' understanding of games of chance so that they can stand up to the temptations of prizes in games 2.2.4.2 Scientific basis of the measure Based on The Theory of Learning Games 2.2.4.3 How to take the measure Method 4.1 Game organization leads to concept For example, organize a game in Experimental Probability Method 4.2 Organize learning games to test reasoning results Method 4.3 Organize for students to discuss games of chance, games on television, Way 4.4 Raise students' awareness of games of chance Eg Discussing playing scratch numbers in Laos Figure 4.1 Play lottery winnings in Laos 17 Figure 4.2 Tickets of 10,000 kips not yet scratched and scratched tickets won After scratching the number of cards (in the left corner) as shown in Figure 4.2 above and numbers on the right half of the scratch ticket, if out of the numbers (each number consists of two digits) which number matches the number of cards, there is a prize, worth Prizes are clearly indicated below each number Know that the odds of winning the 10,000 kip ticket are as follows: In which x1, x2, x4 appear time, x3 only appear times, x5 loses money (no prize) Calculate the winning expectation Instruct E(X) = 10 000.0,000001 + 5.0,004 + 3.0,01 + 5.0,008 + (–1).0,9 = 0,01 + 0,02 + 0,03 + 0,04 – 0,9 = – 0,8 (kips) In general, we can also see that the player always loses, then out of a million tickets, there is the highest winning ticket; out of a thousand new tickets there is a second highest winning ticket; out of a hundred new tickets, there is one ticket with a one-tothree prize or two with a one-year prize; The rest of the house benefits 2.2.5 Measures Strengthening problems applying knowledge of Statistics Probability to solve practical problems in many different fields 2.2.5.1 Purpose of the measure This measure helps students see the great application of Statistical Probability in many different fields of life: agriculture, transportation, pharmacy, medicine, finance, 18 commerce Thereby helping students to have a career orientation in the future 2.2.5.2 Scientific basis of the measure + "Learning with practice, theory with practice" is one of the few teaching principles recognized by all countries + The National Council of Math Teachers (NCTM) believes that connecting Mathematics with real-life problems (Connecting Mathematics To Real Life Problems) is a necessary requirement for teachers 2.2.5.3 How to take the measure Example 5.1 Apply Statistical Probability to Agriculture Glutinous rice variety Thadokkham 1-13 in Laos in previous years was 32.5 (quintals/ha) This year, they rely on the research project of Dr Chai Bounphanuxay and his colleagues and hope to be more productive than last year Experimenting with 15 fields, Dr Chia and his colleagues obtained the following results: 33,7 35,4 32,7 36,3 37,3 32,4 30,0 32,4 31,7 34,5 42,0 33,9 38,1 35,0 33,8 (tạ/ha) At the 1% significance level, is it acceptable to accept that hope, knowing that rice yield is a normally distributed random variable with a variance of 10 (quintals/ha) Example 5.1 Apply Statistical Probability to Transportation Years ago, on the road from Vienchian to Louangphabang, a car ran out of 50 liters of gasoline It is suspected that now the road is degraded, so gasoline consumption is increased Investigating data of 30 trains running on this road, we have the following data: At the 1% significance level, conclude on the above suspicion, knowing that fuel consumption is a normally distributed random variable Example 5.3 Apply Statistical Probability to the food industry… CONCLUSION CHAPTER On the basis of theory and real life presented in chapter The guiding ideas on teaching probability and statistics in the direction of connection with real life have been identified The construction for measure of teaching methods of probability and statistics in Lao secondary schools in the direction of connecting with real life based 19 on the following orientations: Firstly, limit minimums for examples and math problems without practice Second, the measures must closely follow the goals and contents of the probability and statistics curriculum in Lao high schools Third, pedagogical measures contribute to students' career guidance Fourth, the measures contribute to heighten ability to connect knowledge and skills to apply probability and statistics to real life for students Some measures of teaching probability and statistics in Lao secondary schools in the direction of connecting with real life are proposed as follows: One is to take real life contexts as an example, math problems in the process of teaching probability and statistics in secondary school Second is to organize experiential activities for students in the process of teaching probability and statistics in secondary school The third is to clarify the meaning and role of concepts, rules and theorems in probability and statistics lessons through connection with real life Four is to organize learning games, and at the same time heighten understanding of students about television games, games of chance Fifth is to strengthen math problems applying knowledge of probability and statistics to solve practical problems in many different fields 20 Chapter PEDAGOGICAL EXPERIENCE 3.1 Purposes, requirements, and tasks of pedagogical experimentation 3.1.1 Purpose of pedagogical experiment Pedagogical experiment (PE) was carried out to test the correctness of the scientific hypothesis stated in the thesis; initially evaluate the feasibility and effectiveness of the measures proposed in Chapter of the thesis 3.1.2 Pedagogical experimental requirements - Choose an appropriate timeline - Select PE and control classes that are similar in quantity and level - Ensure objectivity, honesty and accuracy - Suitable for students, close to the content of the Lao secondary school math program 3.1.3 Pedagogical experimental tasks - The author of the thesis and the PE teacher discussed about PE lesson plans based on the pedagogical measures proposed in chapter - PE teachers conduct teaching in PE classes with the participation of the thesis author and a group of PE school's Math teachers - Collecting opinions from teachers and students participating in PE by ballot, and at the same time organizing for students of PE class and control class to take an exam after PE class - The author of the thesis collects and processes PE results to evaluate the feasibility and effectiveness of the proposed measures 3.1.4 Time, object, process and method of evaluating pedagogical experimental results PE was performed in two phases Phase 1: From October 4, 2021 to October 17, 2021, with PE classes and control classes at Meuangmet secondary School, Met District, Vientiane Province, Laos Phase 2: From November 1, 2021 to November 14, 2021, with PE classes and control classes at the Laos - Vietnam Friendship Secondary 21 School, Vientiane Capital, Laos The two math teachers in PE class and the second control class were also similar in age and years of teaching The scorecards of the math test at the beginning of the school year, September 2021 of these two groups of classes also gave similar results 3.2 Pedagogical experimental content Lesson Lesson “Average, median number” (2h ) Lesson Lesson “Conditional Probability, Total Probability - Bayesian ormula”(2h) 1.3 Evaluation of pedagogical experimental results 3.3.1 Qualitative assessment Qualitative assessment is based on the results of observing the activities of teachers and students in PE lessons, through student interviews after pedagogical experiments, through students' learning behaviors and attitudes, and through student survey results after PE classes 3.3.2 Quantitative assessment After each session of PE, the PE classes and the control class took an essay test Chart 3.1 Compare the test results of 9th grade PE and 9th grade control Result evaluation: - Some children have weak points because they don't know how to rearrange the data series in ascending order, so the median is not correct - The control class has lower average, good and good scores than PE class because the 22 students in the control class were not explained by the teacher why and when to take the average and the median as the representative numbers for the table data Hypothesis testing Hypothesis H0: The mean score of PE class is higher than the control class without statistical significance at the 0.05 level of significance Opposite theory: H 1: The mean score of PE class is higher than that of the control class with statistical significance at the 0.05 level of significance From the table of test results we have: xTN = 6,88; x ĐC = 5,18; 2 STN = 2,30; S ĐC = 3,11 Applying formula T = 5,31 > t0,05 = 1,671 So, refute H0, accept H1 So, the mean score of PE class is higher than the control class with statistical significance at the 0.05 level of significance b) Phase 2, classes 11/1, 11/2, 11/3, 11/4 take the test with a duration of 30 minutes: There are similar items in round Conclusion of chapter PE was conducted in two phases: Phase with the lesson "Average, median" in two 9th graders at a junior high school in a district close to the capital Vientiane; Phase with the lesson "Conditional probability, Total probability, Bayesian formula" with two 11th graders at a secondary school in Vientiane capital Comparing the test results of the two groups of PE and control classes, shows that students in the PE group have better test results Cause from the teaching method of teachers and PE lesson plan compiled according to the measures proposed in the thesis The connection of knowledge of low-income students with practice helps students of pedagogical experiments better understand the practical origin and meaning of concepts and formulas; They have the experience of finding out and discovering knowledge, so their ability to take tests and apply knowledge to take tests is better Although PE has just been deployed on a limited scale, the PE results partly show the feasibility and effectiveness of the measures proposed in the thesis 23 CONCLUSIONS AND RECOMMENDATIONS CONCLUSIONS It is very necessary to teach the elements of Statistical Probability in general education schools, because Statistical Probability plays an important role in many fields such as Physics, Biology, Economics, Politics This science promises to become one of the most important objects of human knowledge However, practice shows that the teaching of Statistical Probability in Lao PDR has not made students clearly see the necessity and importance of Statistical Probability, has not linked the knowledge of Statistical Probability with practice diversity and abundance Teaching Statistical Probability in Lao secondary schools in the direction of connecting with practice is necessary, having theoretical and practical bases This thesis has clarified the theoretical and real life basis of teaching Probability and statistics in Lao secondary schools in the direction of connecting with real life; At the same time, bringing out the concept of teaching Probability and statistics in the direction of connecting with real life is a type of teaching in which teachers not equip students on knowledge and skills on Probability and statistics Pure statistics in mathematical form that always connects the knowledge, probability and statistics skills with situations, examples and practice math problems, from posing problems, introduction to new knowledge, to the problem-solving process and to apply Probability and statistics into real life (Suiting with the awareness of Lao secondary school students) PE is conducted in two phases, each phase has a lesson plan implemented in lessons, at two high schools, a junior high school in Vientiane province, and a high school in Vientiane capital, Lao PDR The test results of the two groups of PE and control classes showed that the students of the PE group had better test results, compiled by the PE lesson plan according to the measures proposed in the thesis with knowledge connection of Statistical probability with practice The PE results partly show the feasibility and effectiveness of the measures proposed in the thesis, the 24 scientific hypothesis is acceptable RECOMMENDATIONS Currently, the presentation in textbooks and teaching methods of secondary school math teachers in Laos are still more inclined to equip students with knowledge and computing skills, and pay little attention to connecting knowledge with real life it is very necessary to innovate the way of writing textbooks and teaching methods in the direction of the thesis topic .. . experiences and knowledge 2.2 . 2.2 Scientific basis of the measure Based on the theory of Experiential Learning by David Kolb (1984) 2.2 . 2.3 How to take the measure Method 2.1 Organizing students .. . to the temptations of prizes in games 2.2 . 4.2 Scientific basis of the measure Based on The Theory of Learning Games 2.2 . 4.3 How to take the measure Method 4.1 Game organization leads to concept .. . P(A) P(B/A) = P(AB) 2.2 .3 Measures Clarifying the meaning and role of concepts, rules and theorems in Statistics – Probability lessons through connection with practice 2.2 . 3.1 Purpose of the measure