Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.Tóm Tắt tiếng Anh: Dạy học mô hình hóa trong môn Xác suất và Thống kê cho sinh viên ngành Kinh tế và Quản trị kinh doanh.
THAI NGUYEN UNIVERSITY UNIVERSITY OF EDUCATION DONG THI HONG NGOC TEACHING MODELLING IN PROBABILITY AND STATISTICS FOR STUDENTS OF ECONOMICS AND BUSINESS ADMINISTRATION Major: Theory and Methodology of Mathematics Teaching Code: 9140111 DISSERTATION SUMMARY THAI NGUYEN - 2022 The dissertation is completed at: University of Education - Thai Nguyen University Supervisors: Prof Dr Nguyen Huu Chau Assoc Prof Dr Nguyen Danh Nam Reviewer 1: ……………………………………… Reviewer 2: ……………………………………… Reviewer 3: ……………………………………… The dissertation will be defendedin the university committee: University of Education - Thai Nguyen University Time: ……………… Date: ………………………… The dissertation can be found at: National Library of Vietnam Learning Resource Center - Thai Nguyen University Library of Thai Nguyen University of Education THE AUTHOR’S PUBLICATIONS RELATED TO THE DISSERTATION TOPIC Nguyen Danh Nam, Dong Thi Hong Ngoc (2018), “Surveying student's competency in economics and business administration training programs”, Vietnam Journal of Education, ISSN 25881477, volume 2, pp 74 - 80 Dong Thi Hong Ngoc, Nguyen Danh Nam (2019), “The Role of Lectures and Factors Affecting Individual Working Competency of Students at Thai Nguyen University, Viet Nam through Mathematical Modelling Process”, Proceedings of the 11th Asian Conference on Education, ISSN: 2186-5892, pp 267 - 282 Dong Thi Hong Ngoc, Nguyen Danh Nam (2021), "Proposing the process of teaching mathematical modelling in Probability and Statistics at university level", Journal of Education, ISSN: 23540753, No 497 , Volume 1, pp 8-14 INTRODUCTION REASONS FOR CHOOSING THE RESEARCH TOPIC 1.1 Resolution 14/2005/NQ-CP on the fundamental and comprehensive renovation of higher education in the 2006-2020 period emphasized:“Renovation of higher education must ensure practicality, efficiency and synchronization; must carry out innovation from objectives, processes, contents to teaching and learning methods, methods of assessing learning results; develop research-oriented and applied career-oriented higher education programs, of which about 70-80% of the total number of students will have enrolled in applied career programs by 2020” Resolution No 29-NQ/TW dated November 4, 2013 sets out the task of scheming the network of higher education institutions and vocational education institutions according to the structure of occupations and training levels suitable to national human resource development planning, in order to meet the human resource needs of the domestic labor market and participate in the international labor market Article of the Education Law No 43/2019/QH14 clearly states: “Educational methods must be scientific, promote positivity, self-discipline, initiative and creative thinking of learners; fostering learners' selfstudy, practice and cooperation capabilities, passion for learning and the will to rise" 1.2 Article 39 of the Education Law sets forth the goal of higher education, which is to develop and improve skills to apply knowledge into learning situations, research, and real life; attach importance to the promotion of learners' self-study and selfresearch capacity and effectively mobilize the role of modern teaching means, techniques and technologies The role of the teacher shifts to guiding the learners, taking the learner as the center of the teaching process Teachers are not only imparting knowledge but also guiding and supporting students to self-direct in learning, helping students adjust their orientation in terms of the quality and meaning of information sources 1.3 Probability and Statistics are prescribed by the Ministry of Education and Training as a compulsory subject and are taught from the first year, when students have just learned advanced math before and some basic knowledge of Probability and Statistics in high school This makes it difficult for lecturers to clarify the role of Probability and Statistics in the economic majors of each faculty Moreover, teaching mathematical modelling has been introduced in many international studies, and its role has been proven to be significant in the teaching process at all levels; however, in Vietnam, especially at the university level in the field of economics - business administration, it has not been paid enough attention to and exploited much (in published studies), especially in the field of Probability and Statistics Stemming from the strategic goal of modern education, from the goal of higher education and from the characteristics of the subject, we chose to research the topic: "Teaching modelling in Probability and Statistics for students of Economics and Business Administration" LITERATURE REVIEW 2.1 Research works related to mathematical modelling and mathematical modelling competence 2.1.1 Modelling connects mathematics with practice Modelling in mathematics education formally first appeared at a conference by Freudenthal (1968) discussing aspects of applied mathematics in education [16] Mathematical modelling shows the application of mathematics in problem solving, and the process of mathematical modelling will connect mathematics with practice ([96], [1]) The process of modelling is a process of building realistic transformation models with mathematics ([95], [67], [36], [16]) The validity of the modelling depends on the following criteria: the problem to be solved is identified, the requirement to be solved, the purpose of the solution, terminology, information, data, tools ([67)] , [36], [21]) 2.1.2 Teaching by modelling Henry Pollak is one of the pioneers in the field of application and modelling in mathematics education Teaching by modelling makes students' interest in math become lasting [94] Modelling plays an important role in the development of learners' critical thinking and problem-solving ability in real-life situations [16] At the undergraduate level, modelling has linked mathematics to almost every field Modelling should be taught in open-ended situations, research, analysis, and prediction of problems, which will be appropriate to the student's level and learning objectives ([71], [36], [39]) Many studies have shown the application of IT in modelling teaching ([71], [47]) The basic goals in the process of teaching mathematics by modelling are behavior; progress; influence; and perception [76] For teachers: In order to implement modelling teaching effectively, it is necessary to identify the class characteristics, teaching purposes [47], and choose an appropriate topic among many practical situations [39] For learners: Most learners who participate in the process of acquiring knowledge through modelling teaching think that it is effective ([53], [80]) Learning opportunities in this environment are said to be more positive than in other teaching methods [59] Requirements on teachers’ competencies: teachers must experience the whole process of mathematical modelling and the teacher's competence plays an important role in guiding learners to approach the process of modelling at each level ([2], [49], [36]) Teachers need to design appropriate modelling activities ([30], [87], [96]) In the process of teaching modelling, the attitude of the teacher has a great impact on the learners [53] At the university level or higher, teachers need to supplement their knowledge of social fields and tools supporting the modelling teaching process to help students understand the nature of each element in the modelling process 36] Requirements on learners’ competencies: The level of modelling competence manifests itself in the knowledge and understanding of the modelling process [36] Besides IT support, learners must focus on understanding formulas, setting parameters and adjusting models as needed [47] To what extent learners reach in the modelling process depends on the mathematical knowledge they already have [79] The problem identification ability of students assesses the level of implementation of the modelling process [59] Choosing a solution and making a final conclusion requires learners to think logically and analyze the relationship between mathematics and reality ([96], [30]) 2.2 Research works related to the teaching of Probability and Statistics 2.2.1 The issues of learning Probability and Statistics Through building daily computational models and scientific phenomena, we can build models based on probability-statistics Research by Svetlana Tishkovskaya et al [104] shows that: Researchers Garfield (1995) Garfield (1995), Verhoeven (2006) Garfield (1995), Garfield & BenZvi (2002) Garfield & Ahlgren (1988) Research results Learners are not able to apply statistical knowledge to solve specific and discrete problems Concerns about statistical content The researchers state that there have not been many specific studies on the relationship between these two contents Probability and Statistics is quite difficult for students to learn Ignorance of basic statistics Verhoeven (2006) The statistics program is supposed to be taught independently, with no connection to other contents Gal (2002), Schield (2004), Verhoeven Learners are assessed as lacking knowledge of statistics and the ability to use statistics in practice Many studies have claimed that Statistics is one of the interesting and important subjects in high school and university programs Teachers need to pay attention to the selection of teaching methods and the design of learning activities based on the increasing knowledge contents and documents on statistics 2.2.2 Issues of teaching Probability and Statistics In his research [92], Pfannkuch reaffirmed that these two types of inference are connected According to statistics in [44], knowledge objectives at undergraduate and graduate level: Content knowledge is enhanced and presented in the form of application; Using IT as a support tool; The ability to choose and make decisions and to predict, Enhance understanding of the validity of statistics basing on comparisons of non-statistical and statistical problem analysis [104] The goal of teaching Probability and Statistics also contributes to the formation and development of vocational competence for students ([10]), [69]) The previous research works proposed pedagogical measures to improve the quality of teaching Probability and Statistics in the following directions: Contents of training programs; more exercises and examples of Probability and Statistics related to different areas of practice; Using IT as an effective means of support; Developing skills and competencies for learners 2.3 Research works on teaching mathematical modelling in Probability and Statistics Wilensky pointed out that the modelling environment is not limited to users’ orientations and purposes [107] Research work [51] specifically describes the activities of learners when solving situations Research work [111] presents a specific case of using mathematical modelling in teaching Probability and Statistics Research work [16] shows that through teaching mathematical modelling in Statistics, learners can develop statistical reasoning ability Research work ([81], p 155) gives an example of how to extend some probability-related situations by modelling Most of the published research works approach teaching mathematical modelling Teaching mathematical modelling in Probability and Statistics is feasible and effective However, the research works have not really given a specific teaching process and only approached at a simple level corresponding to the program content and understanding of the learners at the high school level RESEARCH AIM The aim of the thesis is to propose some measures for teaching mathematical modelling in Probability and Statistics for students of Economics and Business Administration, to help students be able to solve professional and practical situations using knowledge of Probability and Statistics through the process of mathematical modelling RESEARCH MISSIONS 4.1 Theoretical research on the contents The process of mathematical modelling in Probability and Statistics; the process of teaching mathematical modelling; Components of mathmatical modelling competence in Probability and Statistics 4.2 Practical research - Knowledge of teachers and students about the process of mathematical modelling? Comments of teachers about the process of mathematical modelling in Probability and Statistics? - What is the status of students' mathematical modelling skills in Probability and Statistics? - What is the current status of teaching mathematical modelling in Probability and Statistics at universities in the field of economics business administration? 4.3 Presenting proposals - Propose effective pedagogical measures to teach mathematical modelling in Probability and Statistics based on theoretical basis and research situation, to help students implement the process of mathematical modelling to solve professional and practical situations using knowledge of Probability and Statistics 4.4 Pedagogical experiment Organize the pedagogical experiment to test the feasibility and effectiveness of the proposed measures RESEARCH SUBJECTS AND OBJECTS - Research object: The process of teaching Probability and Statistics at universities in the field of economics - business administration - Research subject: The process of teaching modelling and the process of mathematical modelling SCIENTIFIC HYPOTHESES Based on the goals and tasks of the subject of Probability and Statistics for students of Economics and Business Administration, if teaching mathematical modelling can be done, it will help students see the application of Probability and Statistics into professional practice, thereby being able to solve situations using knowledge of Probability and Statistics through the process of mathematical modelling RESEARCH SCOPE - The research has been done within the scope of the curriculum content of Probability and Statistics and a number of specialized subjects according to the training program of universities of economics - business administration Chapter THEORETICAL ISSUES OF TEACHING MODELLING IN PROBABILITY AND STATISTICS 1.1 Mathematical modelling and the mathematical modelling process 1.1.1 Model There are two views about models: first, a model is seen as a copy of the theoretical issue Second, a model means description, representation, simplification of a real system However, the two definitions above have the same purpose 1.1.2 Mathematical model According to Kai Velten, a mathematical model is a triad consisting of: a system; a system-related question; a set of mathematical statements that can be used to answer a question According to Ang Keng Cheng, a mathematical model is considered a mathematical form of practical problems (possibly complex) or real-world situations N.D.Nam defines a mathematical model as a mathematical structure consisting of symbols, mathematical relationships representing and describing the properties of the research subject According to L.T.H Chau, a mathematical model is the mathematical explanation of a system other than mathematics According to English et al., a mathematical model is used to understand real-life situations or non-mathematical situations in mathematical formats Mathematical models focus on the structural and functional properties of real-life subjects or situations Thus, according to the researcher, a mathematical model is a set of symbols and mathematical relationships that represent a situation, a practical phenomenon or a certain problem to be studied 10 Classification of mathematical models: Descriptive models Optimal models; Random model - Definite pattern; Linear and nonlinear models 1.1.3 Mathematical modelling Modelling: According to Griesel, modelling is the process of developing a model based on its application and use to solve problems According to Greefrath, modelling is a cycle between practice and mathematics and it is repeated many times According to Hestenes, the structure of a modelling cycle can be decomposed into four main phases, which can vary depending on the goals of the implementer Lesh et al consider modelling as a process in which conceptual systems exist and models are used to create and develop new models in new contexts According to N.D.Nam, modelling is the process of creating models to solve mathematical problems Thus, according to the researcher, modelling is a process consisting of steps that can be iterative: simplifying the problem/situation, building/using the model, working with the model, and verifying the results Mathematical modelling: Greer considers mathematical modelling as the transition between reality and mathematics Haines and Crouch describe mathematical modelling as a cyclical process According to Haines and Crouch, mathematical modelling is a cyclic process, going through stages but not necessarily going through all of them According to Tran Vui, mathematical modelling is the process of solving real-life problems using mathematical tools Galbraith and Stillman argue that there is a need to constantly compare the real-world context at all stages of the modelling process The researcher believes that mathematical modelling is a 11 transition from practice to mathematics and vice versa, always with adjustment and repetition of steps performed in the process 1.1.4 Mathematical modelling competence Competence: According to the researcher's point of view, competence is a combination of knowledge, skills, attitudes, behaviors and abilities of a specific individual or object to meet the requirements of a specific activity/task in different situations, and at the same time ensure the most effective operation or performance of the task Mathematical modelling competence: In this whole study, the researcher agrees with other studies that: Mathematical modelling competence is a set of competency components that can perform steps or stages of the mathematical modelling process to solve practical problems Levels of Modelling Competence: According to Greer and Verschaffel, the following levels of competence are proposed: Implicit; Explicit; Critical According to Herbert et al., mathematical modelling competence is developed at three levels According to the study by Ludwig and Xu, based on the modelling process of Blum and Leiß, the researchers proposed six levels of mathematical modelling competence 1.1.5 The process of mathematical modelling The process of mathematical modelling is usually done through steps and there is the existence of a reflection activity during the implementation of the mathematical modelling process: Step 1: Use language conversion to understand the practical problem presented through the mathematical problem; Step 2: Search for strategies to solve math problems to provide solutions and mathematical results corresponding to the identified mathematical problem; Step 3: Continue to use the language conversion to understand the solution and 12 results in practice; Step 4: Evaluate and select the solution suitable to the given practice 1.1.6 Significance of the mathematical modelling process The significance of the process of mathematical modelling can be examined in two aspects: which mathematical modelling is considered meaningful (effective) and how meaningful (effective) mathematical modelling is in the teaching process 1.2 Teaching mathematical modelling 1.2.1 The nature of teaching mathematical modelling The nature of teaching mathematical modelling is to teach students (learners) to solve practical problems/situations according to the process of mathematical modelling Therefore, the process of teaching mathematical modelling is carried out according to the following contents: Detect problems/situations; Set up math problems; find strategies for solving math problems; Transfer to real results; Evaluate the solutions 1.2.2 Difficulties of learners when performing the process of mathematical modelling According to the previous studies, at all stages of implementing the mathematical modelling process, students face difficulties Difficulties are mainly related to activities of identifying situations, converting languages, formulating solution strategies and evaluating problem-solving processes through mathematical modelling 1.3 Teaching mathematical modelling in Probability and Statistics 1.3.1 Training program of Probability and Statistics for students of Economics and Business Administration Probability helps to measure or quantify uncertainty about future outcomes Statistics are applied to situations where the research problem cannot be answered with certainty, usually because of variations in the data 13 The purpose of teaching Probability: to help learners understand the concept of probability, understand the probability of a number of complex events, and apply knowledge of probability to solve some practical problems The purpose of teaching Statistics: to help learners be able to make decisions in uncertain situations, to create a habit of looking at a problem from a statistical point of view Types of models commonly encountered in Probability and Statistics: probabilistic models and statistical models Possibilities for teaching mathematical modelling in Probability and Statistics: undergraduate students have acquired initial knowledge of statistical concepts, multivariable functions, calculus, society, etc when working with modelling problems ([90], p.54) During the implementation of mathematical modelling, students can use many different models for the same goal of solving problems, developing internally (repeat the steps to perform the mathematical modelling process) and externally (the role and meaning of each model in practice or potential application) knowledge about modelling ([36], p 45) The implementation of mathematical modelling in problem solving at university seems to motivate students to work with real-world problems 1.3.2 Mathematical modelling in Probability and Statistics 14 Figure 1.8 The process of mathematical modelling in Probability and Statistics 1.3.3 Mathematical modelling competence of students performing the process of mathematical modelling in Probability and Statistics Competency Identify the practical situation/problem Competency Define a goal to solve the problem Competency Set up a real model Competency Convert to the probabilistic model and statistical model Competency Work on the probabilistic model and statistical model Competency Expand, create, change the appropriate probabilistic model, the statistical model Competency Convert math results to real results Competency Test and evaluate the results in practice Competency Relate the problem to be solved to practice Competency 10 Predict the outcome Competency 11 Critical thinking 15 CONCLUSION FOR CHAPTER The difference in the process of mathematical modelling in Probability and Statistics is the transition from practice to real model, probability model, statistical model and corresponding mathematical problem Due to the characteristics of Probability and Statistics, the mathematical modelling process has an extension in the future prediction step Teaching mathematical modelling in Probability and Statistics will aim to help students carry out the process of mathematical modelling to solve practical problems related to probability-statistics Chapter PRACTICAL RESEARCH 2.1 Research Methods 2.1.1 Research purposes 2.1.2 Research questions Question 1: What is the understanding of teachers and students about the mathematical modelling process? What are the comments of teachers about the process of mathematical modelling in Probability and Statistics? Question 2: What is the current status of students' skills in applying mathematical modelling in Probability and Statistics? Question 3: What is the current status of teaching mathematical modelling in Probability and Statistics at universities of economics business administration? 2.1.3 Research sample The researcher selected a survey sample including students and teachers at universities of economics - business administration 2.1.4 Data collection methods 2.1.5 Data processing 2.1.6 Research tools 16 2.2 Data collection results 2.2.1 Training programs of Probability and Statistics for students of Economics and Business Administration In the block of natural knowledge, Probability and Statistics account for - credits, corresponding to 54 - 75 lecture periods The program structure generally includes Probability section and Statistics section The process of mathematical modelling in this subject simply consists of steps as follows: Hypothetical situation → Math problem → Mathematical result → Real result 2.2.2 The reality of teaching mathematical modelling in Probability and Statistics for students of Economics and Business Administration 2.2.2.1 Data on the knowledge of teachers and students about mathematical modelling 2.2.2.2 Data on students' skills in applying mathematical modelling 2.2.2.3 Data on the current situation of teaching and learning Mathematical modelling in the subject of probability-statistics 2.2.3 Discussions based on the collected data 2.2.3.1 The understanding of teachers and students about mathematical modelling 2.2.3.2 Students' skills in applying mathematical modelling 2.2.3.3 The current situation of teaching mathematical modelling in Probability and Statistics CONCLUSION FOR CHAPTER The investigation of the current situation shows that teaching mathematical modelling is effective for students if students understand the mathematical modelling process and have the necessary competencies to carry out that process; the coursebooks needs to be changed in terms of examples/exercises/applied situations 17 so that teaching mathematical modelling can have the opportunity to be clearly demonstrated; the teaching of mathematical modelling should help students orient to systematic problem solving by recognizing the application of Probability and Statistics in practice and profession; IT is an effective support tool for the implementation of mathematical modelling Chapter ORGANIZATION OF TEACHING MODELLING IN PROBABILITY AND STATISTICS FOR STUDENTS OF ECONOMY AND BUSINESS ADMINISTRATION 3.1 Orientations for building measures to organize teaching mathematical modelling in Probability and Statistics for students of Economics and Business Administration The thesis has proposed main orientations 3.2 Measures to organize teaching mathematical modelling in the subject of Probability and Statistics for students of Economics and Business Administration 3.2.1 Measure 1: Enhance practice situations to develop mathematical modelling skills for students Example 3.1 Lesson "Probability formulas" Example 3.2 Lesson "Correlation and Regression Analysis" 3.2.2 Measure 2: Build and implement a system of learning projects containing mathematical modelling situations associated with the practice of economics - business administration Example 3.3 Develop criteria for evaluating employee performance Example 3.4 Synthesize the forms of Probability and Statistics exercises related to the basis to make the final decision for a certain problem 3.2.3 Measure 3: Create opportunities to use IT in the process of implementing mathematical modelling for students 18 Example 3.5 The larger the sample size, the more random variables are asymptotically distributed Example 3.6 The binomial law and the Student's law can both be reduced to the normal law Example 3.7 Estimation problem Example 3.8 Find data sources, build practical situations CONCLUSION FOR CHAPTER Chapter has proposed measures based on theoretical bases and analysis of the current situation The teacher only plays the role of an initiator, guide, and initial orientation for students Teaching mathematical modelling is now a tool to help students connect mathematical knowledge with practice Chapter PEDAGOGICAL EXPERIMENT 4.1 Purpose, requirements, tasks, principles for organizing the pedagogical experiment 4.1.1 Purpose of the pedagogical experiment The pedagogical experiment was conducted to test the correctness of the scientific hypothesis proposed in the thesis 4.1.2 Requirements for pedagogical experiment 4.1.3 Pedagogical experimental tasks 4.1.4 Principles for organizing the pedagogical experiments 4.2 Pedagogical experiment contents - Observe experimental teaching corresponding to proposed measures, and conduct case study on students selected in experimental classes 19 - Teaching measures are carried out during the entire semester in experimental classes under the teaching of teachers who have been trained in teaching mathematical modelling - Students in the experimental group and the control group were given the same cognitive test before and after the experiment - Select the contents in the program which are general and convenient for clearly showing the teacher’s process of teaching mathematical modelling and the student’s process of implementing mathematical modelling 4.3 Organization of the experiment 4.3.1 Experiment participants and time The pedagogical experiment was carried out in 06/12 regular classes at the University of Economics and Business Administration (K16), including control classes and experimental classes and students of the three experimental classes Experimental time: The second semester of the 2019-2020 academic year from March 2020 to July 2020 4.3.2 Method of conducting and tasks of the experiment Provide training for lecturers; Organize teaching in experimental classes; Conduct interviews, collect notes and comments from teachers and students after the experiment has been completed 4.3.3 Methods of evaluating experimental results Evaluation contents: Students' ability to perform mathematical modelling process; Students' interest and positive attitude in the process of performing lessons under teaching mathematical modelling; The change in the competency components in the process of mathematical modelling of 20 students; Ability to recognize applications of Probability and Statistics and apply them into professions and practice Tools to evaluate pedagogical experiment results a) Written test; b) Evaluation form for lecturers; c) Case studies; d) Classroom Observation; e) Interview; f) Mathematical statistics 4.4 Experiment results 4.4.1 Results of student quality analysis before the experiment The quality of the experimental and control groups has almost no difference or big difference Therefore, it is possible to carry out teaching according to the proposed measures in the selected classes 4.4.2 Results of student quality analysis after the experiment Quantitative analysis results Table 4.4 Results of the T-test Control Group Mean 6,771689498 Variance 2,342130619 Observations 219 Hypothesized Mean Difference df 420 t Stat -8,086494489 P(T