Flipped classroom theory and application in teaching “combinatorics and probability”, 11th grade textbook

HANOI PEDAGOGICAL UNIVERSITY FACULTY OF MATHEMATICS ====== NGUYEN THI LY FLIPPED CLASSROOM: THEORY AND APPLICATION IN TEACHING “COMBINATORICS AND PROBABILITY”, 11th GRADE TEXTBOOK BACHELOR THESIS Major: Mathematics teaching methodology Hanoi, May 2019 HANOI PEDAGOGICAL UNIVERSITY FACULTY OF MATHEMATICS ====== NGUYEN THI LY FLIPPED CLASSROOM: THEORY AND APPLICATION IN TEACHING “COMBINATORICS AND PROBABILITY”, 11th GRADE TEXTBOOK BACHELOR THESIS Major: Mathematics teaching methodology Supervisor Dr Nguyen Ngoc Tu Hanoi, May 2019 THESIS ACKNOWLEDGEMENT First of all, I would like to express my sincere gratitude to Dr Nguyen Ngoc Tu for his guidance and encouragement His guidance and support mean a lot to my thesis and my life I also would like to thank all lectures of the Department of Mathematics, Hanoi Pedagogical University for their advices, comments My deepest gratitude goes to my family and my friends for their encouragement everytime They always believe and help me to pursue my dreams Hanoi, May 2019 Student Nguyen Thi Ly THESIS ASSURANCE My thesis is completed under the enthusiastic guidance of Dr Nguyen Ngoc Tu and my efforts In this research, I have consulted and inherited research results of scientists with respect and gratitude I assure that the data and the results of this thesis are true and not identical to other topics I also assure that all the help for this thesis have been acknowledged and results presented in the thesis have been identified clearly Hanoi, May 2019 Student Nguyen Thi Ly LIST OF ABBREVIATIONS Symbols Meaning ADL Advanced Distributed Learning AICC Aviation Industry Computer-Based Training Committee BL B-Learning CD-ROM Compact Disc-Read-Only Memory CMI Computer Managed Instruction DCMI Dublin Core Metadata Initiative EL E-Learning F2F Face-to-Face FC Flipped Classroom HTML Hyper Text Markup Language ICT Information and Communications Technology IDD Creating the Instructional Design Document IEEE Institute for Electrical and Electronics Engineers IMS Instructional Management Systems IT Information Technology LAN Local Area Network LMS Learning management system LOM Learning Object Metadata LTSC Learning Technology Standard Committee PDF Portable Document Format SCORM Sharable Content Object Reference Model TC Traditional Classroom UK The United Kingdom USA United States of American XML Extensible Markup Language CONTENTS PREFACE 1 Rationale Aims of the research Object and scope of the research .2 Scientific hypothesis .2 The main results of the thesis Research methods Task of the research Structure of the thesis CHAPTER 1: INTRODUCTION .3 1.1 E-learning .3 1.1.1 Definition the e-learning 1.1.2 The history of the e-learning .4 1.1.3 Characteristics 1.1.4 Structure 1.1.5 Classification 10 1.1.6 Standards 10 1.1.7 Steps to design the system e-learning .13 1.1.8 Advantages and disadvantages 14 1.18.1 Advantages 14 1.1.8.2 Disadvantages 17 1.2 B-learning 19 1.2.1 Definition the b-learning 19 1.2.2 The history of the b-learning 20 1.2.3 Structure 21 1.2.4 Principles 22 1.2.5 Models of the b-learning 23 1.2.6 Steps to design the system BL 25 1.2.7 Advantages and Disadvantages .27 1.2.7.1 Advantages 27 1.2.7.2 Disadvantages 28 Conclusion of chapter 30 CHAPTER 2: FLIPPED CLASSROOM 31 2.1 Introduction to the Flipped classroom .31 2.1.1 Definition the flipped classroom .31 2.1.2 History of flipped classroom 33 2.1.3 Characteristics 34 2.2 The importance of Flipped classroom 35 2.2.1 The difference between traditional and flipped classroom .35 2.2.1.1 Bloom’s taxonomy .35 2.2.1.2 Thinking skills 37 2.2.2 Advantages 37 2.3 Application flipped classroom to Vietnam school .39 2.3.1 Preparation 39 2.3.2 Models .40 2.3.3 Principles of the flipped classroom 41 2.3.4 Steps to design the flipped classroom .42 2.3.5 Challenge of the flipped classroom approach for Vietnam .44 Conclusion of chapter 46 CHAPTER 3: APPLYING THE FLIPPED CLASSROOM FOR TOPIC “COMBINATORICS AND PROBABILITY”, 11th GRADE TEXTBOOK 47 3.1 Teaching contents and structure 47 3.2 Learning outcomes and objectives .48 3.2.1 Combinatorics 48 3.2.2 Probability .51 3.2.3 Skills obtained after learning by Flipped Classroom 52 3.3 Preparation 53 3.3.1 Materials 53 3.3.2 Internet tools 54 3.4 Teaching plan .54 3.4.1 Combinatorics 55 3.4.1.1 Rules of counting 55 3.4.1.2 Permutations- Arrangements- Combinations .61 3.4.1.3 Newton’s binomial .65 3.4.2 Probability .69 3.4.2.1 Experiments and events 69 3.4.2.2 Probability of events 73 Conclusion of chapter 78 CONCLUSION 79 REFERENCES 80 APPENDIX LIST OF FIGURES AND TABLES Figure 1.1 Basic model of e-learning system (Nguyen Duy Hai, HNUE) Figure 1.2 The relationship between e-learning standards [7] 12 Figure 1.3 Describe the structure of the BL teaching model (Blearning.com) 21 Figure 1.4 Components of BL (Blearning.com) .22 Figure 1.5 Design a b-learning lesson (Norwegian Business School) 26 Figure 2.1 Bloom’s Taxonomy (By the Vanderbilt University Center for Teaching) 36 Figure 2.2 Part flipped design – Clipart MS Word 7/2010 .42 Table 3.1 Contents structure of chapter “Combinatorics and Probability” 47 PREFACE Rationale In the last few decades, when the trend of globalization has developed strongly, the human resources of Vietnam is required to be able to compete with other countries Moreover, 21st Century Skills requires oral and written communication; teamwork and collaboration; applying technology and critical thinking and problem solving, etc., [13] Therefore, education plays a more important role than ever Education not only transmits knowledge as before but must trains a comprehensive human knowledge, capacity In the face of that challenge, reforming comprehensive education is necessary By oriented development of education innovation, students must be the center of the teaching and learning process, thereby developing the abilities of the students themselves Moreover, with strong development of information technology, students are now easy to access new sources of knowledge (internet, books, media, etc.), not just in textbooks That poses an urgent need for a new teaching method to meet the needs to promote the positive in teaching and learning In recent years, the Flipped Classroom teaching method has begun to show its effectiveness in schools and universities in the United States of American (USA) Specifically, it is said that the online learning program of this method helps students actively learn new knowledge before the help, guidance promptly of teachers This is an interesting method and I want to research and apply to a subject in high school in Vietnam I think Combinatorics and Probability are a close topic, useful in life and are appropriate to apply Flipped classroom to teach Under the guidance of Dr Nguyen Ngoc Tu, I decided to choose “Flipped Classroom: Theory and application in teaching “Combinatorics and Probability”, 11th grade textbook” for my research Aims of the research Research the theoretical basis of E-Learning (FL), B-Learning (BL); Flipped Classroom (FC) and apply FC method to “Combinatorics and Probability” to the conditions of Vietnamese education This is to improve the quality and effectiveness of studying mathematics in high school This research is tend to answer the following questions: - What is Flipped classroom (definition, history, characteristics, the advantages and disadvantages, applications)? 10 minutes - T guides S to exercise page 63 a) A: The number of dots on the face a) Q: How many can you have appear may: 1, 2, 3, 4, 5, the number of dots on the face A: The sample space: of the die?  = {(1,1) , (1, ) , , (1,6 ) , Q: What sample space you ( 2,1) , ( 2, ) , , ( 6,6 )} have? b) A: Event A has the number of dots on the face of the first die always b) Q: What characteristics of equal to events A, B, C ? Event B has the total number of dots - T requires S state the events in on the face that appear of two dies the form of proportions equal to Event C has the same number of dots on the face of two die A: “The first roll appeared face dots” “Total the number of dots of roll equal to 8” “The number of dots of roll is equal” 10 minutes - T requires S to exercise S: A1 is even: “The first shooter hits page 64 the target” - T checks answers A2 is even: “The second shooter hits the target” A1 is even: “The first shooter sliding shoot” A2 is even: “The second shooter sliding shoot” 72 A = A1  A2 B = A1  A2 C = ( A  A2 )  ( A1  A2 ) D = ( A  A2 )  ( A1  A2 )  ( A1  A2 ) 10 minutes - T requires S to exercise  =  H , TH , TTH , TTTH , TTTT  S:  A =  H , TH , TTH  page 64 b = TTTH , TTTT  - T checks answers (H- head and T- tail) Activity 4: Summary minutes - T repeated the center of - S records tasks knowledge and reminds students to the textbook exercises 3.4.2.2 Probability of events Teacher’s name: Date: Course: High School Mathematics Duration: Out of class and in class 45 minutes Subject/Unit: Analysis and Algebra Level: 11/12 Topic: Probability of events Learning outcomes: At the end of the lesson, students should be able to: Knowledge - Forming concept of probability of events - Understand and use the classic definition of probability - Know the nature of probability; the addition probability and the multiplication probability theories - Know how to calculate the probability of specific problems and understand their meaning Skills 73 - Applying the addition probability and the multiplication probability theories for specific problems - Use calculator to calculate probability of events Attitude - Be careful and exactly - Practice logic thinking Prepare Teacher - A teaching video about classical definition of probability - Find a video description of the meaning of probability in life - A quiz for online class - Multiple choice questions in appendix - Teaching tools and materials: die, teaching plan and textbook, PowerPoint… Student - Learning tools and materials - The contents of one into three tasks: classical definition of probability; properties of probability; independent events and multiplication formula for probability In this task, class was divided into groups by the teacher and assigned two groups to carry out the same content from the previous lesson Time Content & Teacher Activity Student Activity Activities before class Out class of - T posts the teaching file and examples; the test file; the video introducing simple experiments on probability and the video description of the meaning of probability in life on Edmodo - S read and understands contents of the lesson by online class - The contents of one into three tasks: classical definition of - T introduces a website which has some probability; properties of simple experiments on probability and probability; independent events their require and multiplication formula for 74 - T prepares multiple choice questions probability and a die for lesson in class Activities in class minute Activity 1: Stable class - T stabilizes class and check the number - Class president reports the of pupils 10 minutes minutes number of pupils Activity 2: Summarize the content of the lesson - T divides the class into two zones A and B (in zone A or zone B have three groups that have different tasks assigned home) - T requires groups to paste their group's results on their respective A zone or B zone - T requires small groups to divide members into three smaller groups and group them with smaller groups in the partner group to form three temporary groups This is described as follows: - T introduces operating rules: Temporary groups will send speakers to each station: After minutes, these groups turned around After two transfer times, this activity is the end minutes - T observes and evaluates groups - The groups active - T summary the answers of all class and - 75 S listens and learns minutes comments 16 minutes experience Activity 3: Apply exercises - T requires S to exercise page 74 S: minutes  = {(1,1) , (1, ) , , (1,6 ) , ( 2,1) , ( 2, ) , , ( 6,6 )}  A = {( 6, ) , ( 6,5 ) , ( 6,6 ) , ( 5,6 ) , ( 4,6 )} - T checks answer  B = {( 5,1)( 5, ) , ( 5,3) , ( 5, ) , ( 5,5 ) , ( 5,6 ) , (1,5 ) , ( 2,5 ) , ( 3,5 ) , ( 4,5 ) , ( 6,5 )} minutes P( A) = A = ;  36 P( B) =  B 11 =  36 - T guides S to exercise page 74 Q: b = ?  = ? A: b  1, 2,3, 4,5,6 ;  = Q:  = ?  = b − 8; 0b2  b  3, 4,5,6 ;    b  2  b  1, 2 a) P1 = = b) P2 = = c) The equation has an integer solution when b = (after confirmed) P3 = 76 13 Activity 4: Confirm minutes minutes - T prepared a set of 15 multiple-choice - S to the task questions (PowerPoint) and one die T painted 15 steps on the board: - T divided the class into three groups and disseminated game rules: “The name of the game is Good Luck; All three groups start from number The groups will be choosing questions and answering in 30 seconds; then will roll die If the answer of the group is correct, the number of steps is equal to the number of dots on appear face of the die After 10 minutes, the groups that approach the 15th most boxes win” 10 minutes - T guides and manages class minute - T summary the game and comments minutes minutes - All of class plays game - S listens experience and learns Activity 5: Summary - T let students watch videos about the - S monitors and realizes meaning of probability in life and lessons for their self directional S realizes lessons for their self minute - T repeated the centre of knowledge and - S records tasks reminds students to the exercises 77 Conclusion of chapter In chapter 3, I have designed lesson plans for topic "Combinatorics and Probability" theme with the FC model This is an important topic having many practical applications By using an online class on Edmodo, I have provided students the simplest knowledge of this topic and prepared for effective classroom lessons I picked the first part of the theory lessons to post an online class with videos, lectures, and articles After that, students short tests in text or quiz format in the library After applying the FC model for "Combining and Probability", although there are many advantages in knowledge or motivating, I realized difficulties such as limited resources, elaborately designed and take a lot of time But problems are not irreparable General, up to this point, I found it is possible to apply FC on "Combinatorics and Probability" Other teachers can even better and give more topics not only in math but also in other subjects Continuous, the experiment is indispensable But in this thesis, I have not taken that step yet Through experimentation, we will see the holes that are currently not seen for this lesson plan But surely, a teacher with soft skills and hard skills is good, this class will succeed 78 CONCLUSION In the context of fundamental and comprehensive innovation of Vietnamese education, a key issue is innovating teaching methods IT plays an increasing important role in innovating methods This thesis indicates that the Flipped classroom and accompany of IT have supported effectively in content teaching "Combinatorics and Probability" Comparing with the task of the thesis, we have obtained results as follow: - Analyze and clarify e-learning and b-learning methods through concepts, structures, classification and proposing steps to choose materials - Study of teaching FC model and clarify the importance of this method to direct the development of skills: Oral and written communication, teamwork and collaboration, application of technology and critical thinking, etc is based on the study of definitions, characteristics, model and steps for designing an FC - Design and build lesson plans and Edmodo online classes (videos, short lectures, etc.) to teach the topic "Combinatorics and Probability", 11th textbook by the FC 79 REFERENCES In Vietnamese: [1] Bộ Giáo dục Đào tạo (2009), Hướng dẫn thực chuẩn kiến thức, kĩ mơn Tốn lớp 11, Nhà xuất Giáo dục Việt Nam [2] Bộ Giáo dục Đào tạo (2011), “Hướng dẫn thực điều chỉnh nội dung dạy học mơn Tốn, cấp THPT”, Kèm theo Công văn số 5842/BGDĐT-VP ngày 01 tháng năm 2011 Bộ Giáo dục Đào tạo [3] Bộ Giáo dục Đào tạo (2011), Bài tập Đại số Giải tích lớp 11, Nhà xuất Giáo dục Việt Nam [4] Bộ Giáo dục Đào tạo (2016), Đại số Giải tích song ngữ Việt- Anh lớp 11, Nhà xuất Giáo dục Việt Nam [5] Nguyễn Duy Hải, Nguyễn Văn Hiền (2018), “Thiết kế, xây dựng khóa học elearning (dạy học đa phương tiện)”, Báo cáo hội nghị nâng cao lực bồi dưỡng giáo viên qua mạng, Hạ Long, 8-2018 [6] Nguyễn Minh Tuấn (2017), Luận án "Xây dựng học liệu E-learning đáp ứng yêu cầu phát triển chuyên môn, nghiệp vụ giáo viên tiểu học", Viện khoa học Giáo dục Việt Nam In English: [7] A M Bianco, A De Marsico, M Temperini (2005), Standards for elearning,Tisip,Norway [8] Epignosis LLC (2014), E-learning concepts, trends, applications, United States of American [9] FHSST Authors (2008), The Free High School Science Texts: textbooks for high school students studying the sciences mathematics grades 10-12, The Free High School Science Texts, Free Software Foundation [10] Gina Saliba, Lynnae Rankine and Hermy Cortez (2013), Fundamentals of Blended Learning, University Western Sydney [11] Khandve P V & Dr Shelke M E (2016), Blended learning: The future of education industry, India Society for Technical Educationm 45th Annual National Convention [12] Marjut Mäenpää, John Owen, Michael Haese, Robert Haese, Sandra Haese, Mark Humphries (2009), Mathematics for the international student, Raksar Nominees Pty Ltd, Australia 80 [13] National Geographic Learning (2017), ETEP Training- Flipped Classroom, Vietnam [14] Patricia Lynn Tétreault B.A., Simon Fraser University (2006), The Flipped Classroom: Cultivating Student Engagement, University of Victoria [15] Rosen Kenneth H (2012), Discrete Mathematics and Its Application, McGrawHill, New York [16] William Horton (2006), E-learning by Design, Pfeiffer, United States of American [17] Yan-Mei Song (2016), “Characteristics and Advantages of Flipped Class”, 2nd Annual International Conference on Social Science and Contemporary Humanity Development (SSCHD 2016), page 226-229 On websites: [18] lợi ích việc học trực tuyến https://tuoitre.vn/8-loi-ich-cua-viec-hoc-truc-tuyen-388629.htm accessed on March 8, 2019 [19] Blended learning course design https://www.bi.edu/globalassets/forskning/learninglab/teaching-excellence/blendedlearning-course-design-learninglab2018.pdf accessed on March 25, 2019 [20] E-learning cách học truyền thống https://studylib.net/doc/7266097/e-%E2%80%93-learning-v%C3%A0-c%C3%A1chh%E1%BB%8Dc-truy%E1%BB%81n-th%E1%BB%91ng accessed on March 8, 2019 [21] The history and state of blended learning https://www.researchgate.net/publication/313751703accessed on March 8, 2019 [22] Victoria L Tinio (2002), ICT in Education file:///E:/quan%20trong/Tai%20lieu%20KLTN/ICT_in_Education.pdf accessed on March 16, 2019 [23] Blended Learning Models https://elearningindustry.com/6-blended-learning-models-blended-learningsuccessful-students accessed on March 8, 2019 81 APPENDIX Appendix Multiple choice questions of topic “Experiments and events” Question 1: How many numbers have 4-digit can you make from 2,3,4,5? A 256 B 120 C 24 D 16 Question 2: Give a set 1,5,6,7 How many natural numbers have 4-digit which distinguish can you be made from the set? A 12 B 24 C 64 D 256 Question 3: What is the number of natural numbers that less than 100 and divided by and 3? A 12 B 16 C 17 D 20 Question 4: Given sets A = a, b, c, d  ; B = c, d , e Choose the false statement in the following statements: A N ( A) = B N ( B ) = C N ( A  B ) = D N ( A  B ) = Question 5: You would like to buy a pen and a pencil There are color pens and color pencils How many choices you have? A 64 B 16 C 32 D 20 Question 6: How many 5-digit numbers that divided by 10 you have? A 3260 B 3168 C 9000 D 12070 Question 7: To go from the city A to the city B, we have ways and we have ways to go from the city B to the city C How many ways can you go from the city A to the city C? A 42 B 13 C 20 D 40 Question 8: How many ways to arrange people A, B, C, D into buffets which have seats you have? A 81 B 64 C 12 D Question 9: In the football competition, 20 teams joined and played round Two teams played each other one time How many football matches you have? A 190 B 182 C 380 D.194 Question 10: How many 3- digit natural numbers you have? A 900 B 901 C 899 D 999 Appendix Learning ballot Applying Order Problems Answer p Arrange people A, B, C, D, E, F into a long-chair How many arrangements you have? Write 15 names of 15 students and put into a box a c Choose students to take a trip How many choices you have? Find the false statement 11 A C143 = C14 B C40 + C41 + C42 + C43 + C44 = 16 4 C C10 + C10 = C11 4 D C10 + C11 = C11 Let a set including elements What is the number of 3-elements subsets? Let B = {1, 2, 3, 4, 5, 6} How many natural numbers 4-digit you have? Remark: p- permutations; a- arrangements; c- combinations Require: Fill Y (yes) in the applicable column if the solve corresponding problem use contents of these parts Appendix The contents of topic “Newton’s binomial” have error Newton’s binomial formula (a + b) n n −1 n = C a + C a b + + C a b n n k n k n−k n −1 n + + C ab n −1 n + C b =  Cnk a k b n −k (*) n n n Corollary = Cn0 + Cn1 + + ( −1) Cnk + + Cnn k Note In the expression on the right side of formula (*): The number of terms is n; The k th term is Cnk a n−k b k , k = 0,1, , n (Convention a = with a  ) Terms with the exponents of a increase gradually from to n and those with the exponents of b decrease gradually from n to n , but the sum of the exponents of a and b in each term is always n ; The coefficients of each pair of terms equidistant from the first term and the last term are equal Pascal’s Triangle Cnk−−21 + Cnk−1 = Cnk ,1  k  n − n=0 n =1 n=2 n=3 n=4 n=5 n=6 n=7 … 1 6 10 15 21 1 10 20 35 15 35 … 1 21 Appendix Multiple choice questions of topic “Probability of events” Question 1: Roll a die, what is the probability of getting even faces? A 0,2 B 0,3 C 0,4 D 0,5 Question 2: Roll a die, what is the probability of getting 6-dot face? A B C D Question 3: Toss a coin and a die, what is the number of elements in sample space? A 24 B 12 C D Question 4: Roll two dice Consider the product between faces of dies What is the number of elements in sameple space? A B 18 C 29 D 39 Question 5: Roll a die times What is the number of elements in sample space? A 36 B 40 C 38 D 35 Question 6: Consider events that have sample space  = 1, 2,3, 4,5,6 Find nonopposite pair of events? A A = 1 , B = 2,3, 4,5,6 B C = 1, 4,5 , D = 2,3,6 C E = 1, 4,6 , F = 2,3 D ;  Question 7: Consider an event tossing coins What is the number of elements of sample space? A {NN, NS, SN, SS} B {NNN, SSS, NNS, SSN, NSN, SNS} C {NNN, SSS, NNS, SSN, NSN, SNS, NSS, SNN} D {NNN, SSS, NNS, SSN, NSS, SNN} Question 8: Consider an event tossing coins What is the probability of at least head faces? A 10 B 11 12 C 11 16 D 11 15 Question 9: Toss a coin times What is the number of elements in sample space? A B C D Question 10: Consider gunners The probability of the first gunner is 0.9 and the probability of the second gunner is 0.8 Choose randum a gunner takes an event, what is the probability of taking correct goal? A P ( A) = 0, 4124 B P ( A) = 0,842 C P ( A) = 0,813 D P ( A) = 0,85 Question 11: A box has 10 marbles that red marbles, green marbles, yellow marbles, white marble Consider of a randomly chosen marbles What is the probability of getting same color marbles? A P ( A ) = B P ( A ) = C P ( A ) = D P ( A ) = Question 12: Toss a coin times Find the probability of the event A: “the result of times is the same” A P ( A ) = B P ( A ) = C P ( A ) = D P ( A ) = Question 13: The probability of taking boy baby is 0.51 Consider times taking babies, what is the probability of getting at least a boy baby? A P ( A)  0,88 B P ( A)  0, 23 D P ( A)  0,32 C P ( A)  0,78 Question 14: Let A be an event of experiment T What is the true statement? ( ) A P ( A) is greater than B P ( A ) = − P A C P ( A) =  A =  D P ( A) is less than Question 15: Toss a coin times What is the probability of the event that the tail face gets at least time? A B C D ... important in teaching? - How to adapt Flipped classroom in teaching the topic “Combinatorics and Probability” Object and scope of the research Flipped classroom and apply to “Combinatorics and Probability”,. .. Chapter Introduction Chapter Flipped classroom Chapter Applying the flipped classroom for teaching “Combinatorics and Probability”, 11th grade textbook CHAPTER INTRODUCTION 1.1 E-learning 1.1.1 Definition... ====== NGUYEN THI LY FLIPPED CLASSROOM: THEORY AND APPLICATION IN TEACHING “COMBINATORICS AND PROBABILITY”, 11th GRADE TEXTBOOK BACHELOR THESIS Major: Mathematics teaching methodology Supervisor