Dạy học chủ đề giới hạn cho học sinh ở trường trung học phổ thông theo hướng phát triển tư duy bậc cao tt tiếng anh

THAI NGUYEN UNIVERSITY UNIVERSITY OF EDUCATION NGUYEN THI QUOC HOA TEACHING THE CONTENT OF LIMIT TO HIGH SCHOOL STUDENTS IN THE ORIENTATION OF DEVELOPING THEIR HIGHER - ORDER THINKING Major: Theory and Methodology of Mathematics Teaching Code: 9140111 DISSERTATION SUMMARY THAI NGUYEN - 2019 The dissertation is completed at: Thai Nguyen University - University of Education Supervisors: Assoc Prof Dr Dao Thai Lai Assoc Prof Dr Cao Thi Ha Reviewer 1: ……………………………………… Reviewer 2: ……………………………………… Reviewer 3: ……………………………………… The dissertation will be defended in the university committee: Thai Nguyen University - University of Education Time: ……………… Date: ………………………… The dissertation can be read at: National Library of Vietnam Thai Nguyen University - Learning Resource Center Library of University of Education THE AUTHOR’S PUBLICATIONS RELATED TO THE DISSERTATION TOPIC Cao Thi Ha, Hua Anh Tuan, Nguyen Thi Quoc Hoa (2014), "Training the skills of applying Maths into reality for high school students" Journal of Education, special issue, July 2014; pp.159-161 Nguyen Thi Quoc Hoa (2016), Some perspectives on higher-order thinking in teaching at high school, Journal of Educational Science Vietnam Academy of Educational Sciences, No 131, August 2016, pp 24 - 27 Cao Thi Ha, Nguyen Thi Quoc Hoa (2017), Higher-oder thinking - its concepts and components, Journal of Educational Science - Vietnam Academy of Educational Sciences, No 138, March 2017, pp 25-27 Nguyen Thi Quoc Hoa (2018), Fostering learners’ critical thinking and metacognitive skills in teaching “Finite limit of sequences” (Algebra and calculus 11), Vietnam Journal of Education; Vol 5, 2018, pp 71 - 75, Special Issue for the 1st ICME at Hanoi National University of Education Nguyen Thi Quoc Hoa, Cao Thi Ha (2019), Designing teaching activities for the content of “Limit” towards developing higher-order thinking for high school students, Journal of Educational Science Vietnam Academy of Educational Sciences , No 18, June 2019, pages 66 - 71 PART I INTRODUCTION Reason for choosing the research topic At the end of the twentieth century, the innovations in educational science, whose nature stems from the perspectives of changing teaching and learning in schools, took place quite strongly all over the world These reforms require teachers to change their teaching strategies, focusing on learning by discovery, enhancing experiential learning and developing thinking skills for students At the beginning of the 21st century, one of the research trends in thinking that has attracted the attention of many researchers is the study of classifying thinking in two types: lower-order thinking (LOT) and higher-order thinking (HOT) Typical studies in this direction are carried out by such researchers as Resnick, FJ King, Ludwika Goodson, Faranak Rohani, Susan M Brookhart Mathematical thinking and reasoning capacity is one of the five mathematical competencies that the Math program in general education program 2018 focuses on forming and developing for students (General education program issued by the Ministry of Education and Training on December 26, 2018) Currently, in Vietnam, there are a number of reserachers who have studied thinking, HOT and the development of thinking for students in teaching Typical reserachers are Phan Dung, Le Hai Yen and Phan Thi Luyen, Phung Ha Thanh, Le Trung Tin, However, there has been no research on the structure, manifestations, process, measures, teaching techniques to develop HOT for high school students in teaching Math For the above reasons, we choose the topic: "Teaching the content of limit to high school students in the orientation of developing their higher-order thinking" for the research Aims of the research Contribute to clarifying the theoretical and practical basis for HOT; propose some methods of teaching the content of “limit” (Algebra and Analysis Grade 11) in the orientation of developing HOT for high school students Research subject and object 3.1 Research subject The process of teaching the content of “limit” in the orientation of developing HOT for high school students 3.2 Research object The process of teaching Math in high schools Scientific hypotheses If the elements and specific manifestations of HOT are identified, and if methods of teaching the content of “limit” are proposed in the orientation of developing HOT, then HOT will be developed for students, contributing to improving their learning outcomes Research tasks and scope 5.1 Study the theoretical basis, structure and manifestations of HOT 5.2 Investigate the reality of teaching about “limit” in the orientation of developing HOT for students in some high schools 5.3 Propose some teaching methods to develop HOT for students through teaching the content of “limit” (Algebra and Analysis 11) 5.4 Carry out pedagogical experiment to evaluate the scientific hypotheses as well as the effectiveness of the teaching process and measures proposed in the thesis Research methods 6.1 Theoretical research 6.2 Practical research 6.3 Expert consultation 6.4 Case study 6.5 Mathematical statistical methods 6.6 Pedagogical experiment Contributions of the thesis 7.1 Contribute to further clarifying the theoretical basis for HOT in terms of its concepts, elements and typical manifestations 7.2 Propose methods of teaching the content of “limit” towards developing HOT for high school students The arguments to be defended 8.1 Concepts, elements and typical manifestations of HOT 8.2 Methods of teaching the content of “limit” towards developing HOT for high school students Structure of thesis In addition to the Introduction, Conclusion, Recommendations, References, Published works and Appendices; the thesis consists of chapters: Chapter Theoretical and practical basis; Chapter Teaching the content of “Limit” towards developing HOT for high school students; Chapter Pedagogical experiment PART RESEARCH RESULTS Chapter THEORETICAL AND PRACTICAL BASIS 1.1 Overview of research results on thinking and HOT 1.1.1 Research on thinking Thinking - the core component of the intellect is a rich and complex activity in psychology, one of the very few areas mentioned from the earliest days of educational psychological science So far, there have been many studies on the nature, the laws of initiation and the development of thinking Typical researchers are D.Ghatli, O.Denxơ, K Biulơ, J Watson, B Ph Skinner, J Piaget, J.C Guilford, V.A Cruchetxki D.N Perkins, R Sternberg, …; many revolutionary teaching programs have been built on the science of intelligence and thinking, but research on intelligence in general and thinking in particular is still being discussed in many forums of psychological science and education 1.1.2 Research on HOT So far, there has been a lot of research done by many authors on HOT Overall, there are three main trends in studying HOT: Trend Some researchers have tried to give definitions or describe manifestations to identify HOT Trend Examine a number of types of thinking that fall into HOT and recognize HOT as including HOT skills Representatives of this group are FJ King, Ludwika Goodson, M.S.Faranak Rohani Accordingly, critical thinking, logical thinking, metacognition and creative thinking are HOT elements Trend 3: Examine HOT from a cognitive perspective In this approach, Barak Miri or Anat Zohar and many other researchers have considered "analysis, synthesis, and evaluation" in Bloom's perception scale or "analysis, evaluation, creativity" in the rating scale of Anderson and Krathwohl as a high level of thinking 1.2 Thinking 1.2.1 Definition Although the definitions of thinking are not consistent and there are different expressions, there are some points in common: - Thinking is the product of the human brain and is a positive process of reflecting the world on the brain - Thinking only arises when encountering problematic situations, so it is generalized and closely related to emotional awareness The product of thinking manifests itself in concepts, judgment and inference 1.2.2 Taxonomy of thinking Depending on the approach, there are different classifications of thinking In this study, we approach the taxonomy of hierarchies of Fred Newmann, Resnick and Krathwohl, whereby thinking consists of two types: Lowerorder thinking (LOT) and  Higher-order thinking (HOT); 1.2.3 The formation and development of thinking According to Plantonov, thinking is an intellectual activity process consisting of four stages:  Receive the problem and express it as a task of thinking;  Mobilize knowledge, experience, association and formulate hypotheses;  Verify the correctness of the hypothesis If the hypothesis is correct, then go to the following step; if it is false, negate it and form a new hypothesis;  Evaluate the results and put them into use 1.3 Cognition and metacognition Cognition consists of many phases, stages and takes different forms, in which emotional cognition and rational cognition (thinking) are two different stages of the same unified cognitive process Metacognition is not merely a description or mere thought about the thinking process but it requires a rethinking of the thinking process at a higher level associated with self-evaluation and criticism Basically, cognition is the basis of metacognition; without emotional cognition, there would be no thinking or metacognition Thus, thinking, cognition and metacognition have close relationships with one another, go together and promote one another in the process of human activities As a result, each individual can accomplish cognitive tasks and achieve cognitive goals 1.4 Higher-order thinking (HOT) 1.4.1 Definition According to Section 1.1.2 there are three research trends in HOT; the differences of these three trends stem from the different approaches to the concept of HOT Approaching HOT following the first trend and inheriting the research results of the authors FJ King, Resnick, Lewis and Smith, Lindsey Engle, Goethals , we believe that: HOT is the process of rearranging existing information in a system of relationships, and then comparing (similarity and contrast) those systems to build new relationships (similarities, difference or cause and effect ), and at the same time combining with new information to make inferences, propose solutions to problems or put forward new theories based on the newly established relationships 1.4.2 HOT elements Based on Plantonov's research on the thinking process and other studies on critical thinking, creative thinking and metacognition; with a approach to describing HOT as including the combination of important features of critical thinking, creative thinking, metacognition, which are always intertwined, cohesive, supporting and promoting each other, we think that HOT consists of the following five elements and groups of elements:  Receive information selectively; classify and organize information into systems (R);  Propose hypotheses (H) based on the generalization of many perspectives;  Process information (P);  Make decision (M) and  Evaluate and self-assess products and views critically; and at the same time, propose adjustment plans (E) 1.4.3 Manifestations and levels of HOT In the process of teaching towards developing HOT, it is necessary to specify the specific manifestations of each HOT element with different levels of manifestation These are clear and detailed instructions for teachers to apply in assessing the achievement level of HOT in teaching situations When HOT takes place in an individual's brain, problematic situations are solved not only effectively but also thoroughly In addition, individuals can develop new ideas or have more general solutions to new situations In each specific situation and each specific stage of HOT there will be different manifestations, but they are all exposed to the outside so that we can identify them (Table 1.1) Table 1.1 Manifestation levels of each HOT element Elements R: Receive information selectively; classify and organize information into systems H: Propose hypotheses based on the generalization of many view points Manifestation R1: Receive and identify some necessary but unfocused information; initially know how to classify and sort information R2: Receive and identify most information but not comprehensively Classify and organize information in groups R3: Proactively search and select sufficient information to solve the problem; Organize information in groups and identify the relationship between them R4: Proactively search and select sufficient information to solve the problem; Organize information into systems according to relationships H1: Ask questions that revolve around issues but they may not be central H2: Ask general questions and propose hypotheses; however, the content of the hypothesis has not yet reached the focus of the problem H3: Propose the exact hypothesis to solve the problem H4: Propose the exact hypothesis to solve the problem and Level M1 M2 M3 M4 M1 M2 M3 M4 P: Process information Elements P1: Analyze information in an oriented and critical manner through synthesis P2: Compare and contrast systems against each other (similar or different) and from different perspectives to find new relationships M: Make decision P3: Reason (inductively or deductively) and build a reasoning system as a basis for conclusions M1: Apply criteria to propose and select different strategies for creative problem solving M2: Propose ideas / new ways or many solutions for a problem and choose an effective solution E: Evaluate and selfassess products and views Manifestation propose new hypotheses for related issues P11: Analyze information on purpose (determine the relationship between what is known and what to look for); Preliminarily evaluate the value of the information P12: Analyze information on purpose (determine the relationship between what is known and what to look for); Assess the value of information critically P13: Analyze information on purpose (determine the relationship between what is known and what to look for) Synthetize and evaluate the value of information critically P14: Analyze information on purpose (determining the relationship between what is known and what to look for) Synthetize and assess the value of information in a critical and multi-dimensional manner P21: Compare and contrast systems against each other (similar or different) based on some available criteria P22: Compare and contrast systems against each other (similar or different) based on the available set of criteria P23: Point out some criteria for comparing systems with each other (similar / different) P24: Develop a set of criteria to compare and contrast the systems with each other (similar or different) and find new relationships P31: Reason (inductively or deductively) to explain and draw conclusions P32: Reason (inductively or deductively) to explain and draw exact conclusions P33: Reason (inductively or deductively) to explain and draw conclusions Build a reasoning system as a basis for conclusions P34: Reason (inductively or deductively) to explain and draw conclusions Build a reasoning system as a basis for conclusions and propose new ideas M11: Apply criteria to choose the right strategy for problem solving M12: Create a strategic proposal plan (according to a certain criteria) for problem solving M13: Plan to propose multiple strategies (according to different criteria) for problem solving M14: Plan to propose many strategies (according to different criteria) to solve problems creatively (not in a routine) M21: Propose ideas to solve a problem M22: Propose many measures / ways to solve a problem M23: Propose many measures / ways to solve a problem and choose an effective solution M24: Propose new ideas / ways or many solutions / ways to solve a problem and choose an effective solution E1: Evaluate products and views critically E2: Evaluate and self-assess products and views critically Level M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 M3 M4 M1 M2 11 perceive things and phenomena in the objective world 2.2.1.3 Classification of questions There are many types of questions; based on students' cognitive abilities, there are several ways to classify as follows: Method 1: Based on Bloom's taxonomy and Krathwohl's and Anat Zohar's view, questions can be divided into two types: low level questions and high level questions Method 2: According to Tran Ba Hoanh, there are five types of questions:  Questions which stimulate observation and attention;  Questions which require comparison and analysis;  Questions which require synthesis, generalization and systemization;  Questions which require a relation to reality;  Questions which stimulate creative thinking and guide students to raise problems and propose hypotheses; Method 3: According to Benjamin Bloom, there are six types of questions corresponding to six levels of cognition:  Know;  Comprehend;  Apply;  Analyse; ; Evaluate;  Create Method 4: Based on Boleslaw Niemierko’s thinking levels, there are four types of questions:  Knowledge questions;  Comprehension questions;  Low-level application questions;  High-level application questions; Method 5: Based on the finiteness level of the answer, there are two types of questions:  Single-answer questions (convergent questions, closed-ended questions);  Multi-answer questions (divergent questions, open-ended questions) 2.2.1.4 Question quality criteria The question is rated as having quality when meeting the following requirements:  The question must create a wide range of answers (a set of answers to a question);  Mobilize many intellectual operations necessary to answer the question;  The question must be in depth: in order to fully answer the requirements of the question, the respondent must mobilize maximum intellectual activities to fully answer;  Ability to engage students in answering the questios: Questions should stimulate curiosity, inquiry, discovery in each student and stimulate many students to answer or comment on the answers of other students 2.2.1.5 Train questioning skills for students Based on the psychological rules of the cognitive process and the structure of the question, we propose a question-building process of steps:  Define lesson objectives;  Analyze the lesson content structure;  12 Find what to be questioned (determine the ability to encode the content into questions);  Put what needs to be questioned into a question;  Edit and complete the question Develop questioning skills for students is essentially a process where teachers train students to perform the steps of the following two procedures: + The process of developing questioning skills for students who not have questioning skills, including five steps:  Identify opportunities to develop questioning skills, learn the theory of question formulation; Teacher models and implements the question-making process; Formulate an exercise for students to practice the questionbuilding process;  Develop a system of exercises to develop questioning skills; organize discussions and assess the results of implementing the exercise system;  Create opportunities and encourage students to apply creativity to gradually improve the proficiency of the skill Details of the process are described in Table 2.1 + The process of developing questioning skills for students who already have the skills to ask questions, but at a low level, including steps:  The teacher raises a focal question;  Students themselves ask all possible questions;  Students improve their own questions;  Students choose among their questions;  The teacher and the students decide the next steps;  Students reflect on their own thinking processes For example: Step 1: The teacher raises a focal question to help students revise the content of “Limit” after finishing the Analysis program in grade 12 textbook: “Limit” is the opening topic and it plays an important role in the Analysis section of the mathematics program in high school, what is your opinion? Step 2: Students themselves ask questions related to the teacher's focal question, and then they will need to think, exchange, discuss and ask all possible questions, such as: - What is Limit? How many types of Limit? - Why is Limit the opening topic of the Analysis section? - Why is Limit an important content of the Analysis section in high school mathematics program? - What practical applications does Limit have? 13 - Without the concept of Limit, which concepts in high school Math program would not have a basis for definition? Step 3: Students can improve the questions, for example, the second question in step can be replaced by the question: What is the history of Limit? The fourth question in step can be replaced by a new question: What are the applications of the Limit in both theory and practice? Step 4: Once the student has identified the role and position of the Limit topic, the teacher can suggest so that students can ask additional questions: - To grasp the content of Limit, what we need to do? - Resystematize the concepts and types of exercises of Limit in a mind map? Step 5: In case the skill does not meet the set goals, students can take their own example and repeat the process to train again; if the students meet the requirements, they can continue to perform the next tasks of the learning process Step 6: In order for students to reflect on their thinking processes, they may ask: When learning the topic of Limit, what mistakes we often make? Give examples and explain the mistakes? 2.2.2 Measure 2: Design and use the system of teaching situations in the orientation of developing HOT for students 2.2.2.1 Purpose of the measure Teachers create teaching situations and organize teaching based on the teaching situations to put students in problematic situations Facing problematic situations, students are required to mobilize all knowledge and thinking ability to find ways to solve problems and complete learning tasks Through problem detection and solving students will both gain knowledge and train HOT 2.2.2.3 Method of implementing the measure To implement the measures, we focus on three implementation stages:  Design situations;  Organize teaching based on the situations;  Evaluate- adjust the designed situations There are types of teaching situations: development situations and consolidation situations A situation-based teaching lesson usually has three parts: (1) Introduction: Briefly describe the context of events in the situation (2) Content: Describe the events in the situation (facts) (3) Issues, requests, suggestions that need to be addressed We have built 14 nineteen situations for teaching the content of “Limit” to apply in the teaching process to develop HOT for high school students The following is a partial illustration of a teaching situation: Situation 2: Construct a concept of a finite number sequence (Development situation) Activity 1: Encourage motivation - Approach the learning situation Part 1: Teacher creates groups, giving students guidelines for group activities Step 1: Establish a study group + Divide the class into groups of students + Leader of each group asks members to draw one of three colored cards: yellow, blue, red + Student with Yellow card performs requirement 1; Student with Blue card fulfills request 2; Student with Red card fulfills requirement Step 2: Students who receive the same color card transfer to a new group to perform the task on their A3 paper Step 3: Students go back to the original group and fulfill requirements and on the supplementary board Once completed, paste the results representing each request Part 2: Teacher asks students to fulfill the requirements in worksheet WORKSHEET Problem: Given the sequence number (sn) determined by: s1  ; 1 s2   ; 2 1 s3    ; 2 1 1     n ; 2 2 Use a shape (such as a square with sides equal to one unit long) and represent the first few terms of the sequence (sn) by dividing that shape sn  1 , , into parts with an area of 2 , respectively Then comment the characteristic of this sequence? 15 s ,s ,s ,s Please show the terms on the number line and predict the position of sn on the number line Find the formula for the general term of the sequence (sn) and create a new sequence (vn): = 1-sn Find the limit (if any) of the sequence (vn)? Let's generalize the definition of the (un) sequence with a finite limit L Activity 2: Address the situation Students: fulfill specific requirements on the worksheet Teacher: Anticipate student results: + Represent pictures + Characteristics of the sequence: the sequence is increasing; the value of the terms of the sequence is increasingly larger and closer to the value s ,s ,s ,s + Represents the term on the number line and predicts the position of sn on the number line The general formula of (sn) is: n �1 � 1 � � n 2� �1 � � sn   1 � � 1 �2 � n �1 �   sn  � � �2 � Then, the new (vn): n �1 � lim  lim � � �2 � Find the limit of the sequence (vn): We have 16 Teacher: Correct exercises for groups and give comments - In this activity, when performing the first requirement of the worksheet, students may fail to represent, or represent incorrectly Teachers need to guide students promptly In addition to the representation above, students may represent in the other ways as shown below: or In addition, students can also use an isosceles triangle with an area of and a circle with an area of to represent The teacher can ask the groups to present their own representation rules or ask one group to ask questions to the other groups Teacher suggests: We can represent squares with area values of s1 , s2 , s3 , , sn , There are countless such squares but the area of these squares is always equal to (Details of other situations are in Appendix 07 of the thesis) 2.2.3 Measure 3: Project-based teaching to develop HOT for students 2.2.3.1 Purpose: Put students in problematic situations and solve problems that appear in the project In the course of implementing a learning project, students must ask research questions themselves, set goals, develop a plan, search for materials, propose tasks, create products, report and review the product of the project 2.2.3.2 Basis of the measure: According to cognitive theory, the purpose of teaching is to create the ability for learners to understand the 17 real world The projects put into teaching for students often stem from issues that need to be learned in real life In order to implement a project, learners must ask their own research questions, identify specific goals, tasks, and products that need to be targeted for each member and the whole group The environment for project activities must be guaranteed to be an open environment, enabling learners to express and develop their own capacity for thinking and creativity Project-based teaching ensures the educational goals set out which are oriented towards developing students’ capacity Through projectbased teaching, students have the opportunity to demonstrate and develop common, specialized competencies including HOT elements 2.2.3.3 Method of implementing the measure To implement the measure, based on the project-based teaching theory presented in Chapter 1, we propose the process of designing and organizing project-based Math teaching at high school as follows: a) The procedure of developing a learning project Step 1: Identify the project name for the teaching topic Step 2: Build the concept map Step 3: Anticipate and look for material sources Step 4: Anticipate learning activities Step 5: Anticipate evaluation b) Organize project-based teaching Project-based teaching activities are a combination of organizational activities of teachers and diverse learning activities of students in many different learning environments (which can take place in classrooms, schools and community) The interaction between the teacher and students can be direct or indirect in many different forms The activities are described in five steps:  Organize the class;  Introduce the project;  Assign project implementation tasks;  Implement the project;  Report the project implementation results;  Evaluate project implementation results 18 The teaching measures proposed in the thesis aim to impact on the HOT elements as shown in Figure 2.1: MEASURE MEASURE R: Receive selectively; classify and organize information into systems H: Propose hypotheses based on the generalization of many view points P1: Analyze information in an oriented and critical manner through synthesis P2: Compare and contrast systems (similarity or difference) from different perspectives to find new relationships P3: Reason (inductively or deductively) and build a reasoning system as a basis for conclusions MEASURE M1: Apply criteria to propose and select different strategies to solve a problem creatively M2: Propose a new solution or many solutions to a problem and choose an effective solution E: Evaluate and self-assess products and views critically; at the same time, propose adjustment plans Figure 2.1 The impact of the measures on the development of HOT in teaching towards developing HOT for high school students Chapter PEDAGOGICAL EXPERIMENT 3.1 Experiment purposes 19 Verify scientific hypotheses; evaluate the feasibility and effectiveness of the teaching process and measures proposed in the thesis 3.2 Experiment participants Grade 11 high school students at Chu Van An High School in Thai Nguyen province 3.3 Experiment time and plan 3.3.2 Official experiment: From January to February 2018, on 48 students 3.4 Experimental content Implement teaching plans (lesson plans) with a duration of 15 periods on the topic “Limit” (Advanced Algebra and Analysis Grade 11) 3.5 Experimental results and discussion 3.5.1 The assessed dimensions Quantitative assessment: Based on the results of the Math knowledge tests and the achievement level of HOT of 48 students (including students in the case study at Good - Fair - Medium – Weak level) Qualitative assessment: assess the achievement level of HOT of students through external manifestations in terms of initiativeness, creativity in study, receiving and gathering information; analyzing information; proposing hypothesis; making decisions (choose strategies, propose solutions); ability to listen and adjust 3.5.2 Experimental results analysis and discussions 3.5.2.1 Results of quantitative analysis of the entire experimental sample a) Development level of HOT through experimental lesson plans To assess the degree to which students form and develop HOT through experimental lesson plans (LP), we conduct data collection and data processing using SPSS 22.0 software Experimental results are evaluated based on descriptive statistics such as: mean, error, median, dominant, standard deviation, variance, minimum value, maximum value Descriptive statistical results are presented in Table 3.3 Table 3.3 Descriptive statistics of the average scores of HOT of students through experimental lesson plans       Statistical parameters Valid value Mean Standard deviation Variance Smallest value Greatest value 48 4,74 0,43 0,18 3,75 6,33 48 5,72 0,43 0,18 5,13 7,46 48 6,15 0,31 0,10 5,33 7,21 Lesson plans 48 48 48 6,23 6,98 7,44 0,39 0,37 0,32 0,15 0,14 0,10 5,50 6,00 7,75 6,92 7,67 8,00 48 7,49 0,33 0,19 5,50 8,17 48 7,42 0,31 0,17 5,92 8,33 48 7,64 0,26 0,13 6,19 8,37 20 Note: The achieved score of HOT is the average of the scores of the assessed elements in each experimental lesson plan Percentage (% ) 100 100 90 80 70 60 50 40 30 20 10 100 100 100 95.84 93.75 87.5 83.33 79.17 20.83 4.16 6.25 0 0 12.5 16.67 0 LP 402LPLevel 0 LP 70 4LP 80 LP 90 LP01 LPLevel 02 LP103 Level 05 LP036 Level 0 Figure 3.1 The HOT differentiation level of students through experimental lesson plans Thus, after experimental lesson plans, students' HOT mostly reached level (83.33%), the proportion of students achieving HOT at level is still relatively low (16,67%) By analyzing the data at Level 3, we found that up to 20.83% of students achieved HOT scores from 7.75 points to 7.88 points (asymptotic level 4) Hence, we believe that it is necessary to continue training the HOT elements in other topics of the mathematics program and other subjects to continue training, consolidating and improving HOT for students Correlation test results (Pearson, sig