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

UNIVERSITY OF EDUCATIONNGUYEN THI QUOC HOA TEACHING THE CONTENT OF LIMIT TO HIGH SCHOOL STUDENTS IN THE ORIENTATION OF DEVELOPING THEIR HIGHER - ORDER... 5 Nguyen Thi Quoc Hoa, Cao Thi H

UNIVERSITY OF EDUCATION

NGUYEN THI QUOC HOA

TEACHING THE CONTENT OF LIMIT TO HIGH SCHOOL STUDENTS IN THE ORIENTATION OF DEVELOPING THEIR HIGHER - ORDER

Thai Nguyen University - University of Education

Supervisors:

1 Assoc Prof Dr Dao Thai Lai

2 Assoc Prof Dr Cao Thi Ha

The dissertation can be read at:

1 National Library of Vietnam

2 Thai Nguyen University - Learning Resource Center

3 Library of University of Education

RELATED TO THE DISSERTATION TOPIC

1 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

2 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

3 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

4 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 NationalUniversity of Education

5 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

1 Reason for choosing the research topic

At the end of the twentieth century, the innovations in educationalscience, whose nature stems from the perspectives of changing teachingand 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 anddeveloping thinking skills for students

At the beginning of the 21st century, one of the research trends inthinking that has attracted the attention of many researchers is the study

of classifying thinking in two types: lower-order thinking (LOT) andhigher-order thinking (HOT) Typical studies in this direction arecarried out by such researchers as Resnick, FJ King, Ludwika Goodson,Faranak Rohani, Susan M Brookhart

Mathematical thinking and reasoning capacity is one of the fivemathematical competencies that the Math program in general educationprogram 2018 focuses on forming and developing for students (Generaleducation program issued by the Ministry of Education and Training onDecember 26, 2018)

Currently, in Vietnam, there are a number of reserachers who havestudied thinking, HOT and the development of thinking for students inteaching Typical reserachers are Phan Dung, Le Hai Yen and Phan ThiLuyen, Phung Ha Thanh, Le Trung Tin, However, there has been noresearch on the structure, manifestations, process, measures, teachingtechniques 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 theirhigher-order thinking" for the research

2 Aims of the research

Contribute to clarifying the theoretical and practical basis for HOT;propose some methods of teaching the content of “limit” (Algebra andAnalysis Grade 11) in the orientation of developing HOT for highschool students

3 Research subject and object

3.1 Research subject

The process of teaching the content of “limit” in the orientation ofdeveloping HOT for high school students

5 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 ofdeveloping HOT for students in some high schools

5.3 Propose some teaching methods to develop HOT for studentsthrough teaching the content of “limit” (Algebra and Analysis 11).5.4 Carry out pedagogical experiment to evaluate the scientifichypotheses as well as the effectiveness of the teaching process andmeasures proposed in the thesis

7 Contributions of the thesis

7.1 Contribute to further clarifying the theoretical basis for HOT interms of its concepts, elements and typical manifestations

7.2 Propose methods of teaching the content of “limit” towardsdeveloping HOT for high school students

8 The arguments to be defended

8.1 Concepts, elements and typical manifestations of HOT

8.2 Methods of teaching the content of “limit” towards developingHOT for high school students

9 Structure of thesis

In addition to the Introduction, Conclusion, Recommendations,References, Published works and Appendices; the thesis consists of 3chapters: Chapter 1 Theoretical and practical basis; Chapter 2.Teaching the content of “Limit” towards developing HOT for highschool students; Chapter 3 Pedagogical experiment

PART 2 RESEARCH RESULTS Chapter 1 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 andcomplex activity in psychology, one of the very few areas mentionedfrom the earliest days of educational psychological science So far, therehave been many studies on the nature, the laws of initiation and thedevelopment of thinking Typical researchers are D.Ghatli, O.Denxơ, K.Biulơ, J Watson, B Ph Skinner, J Piaget, J.C Guilford, V.A Cruchetxki vàD.N Perkins, R Sternberg, …; many revolutionary teaching programshave been built on the science of intelligence and thinking, but research

on intelligence in general and thinking in particular is still beingdiscussed 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 onHOT Overall, there are three main trends in studying HOT:

Trend 1 Some researchers have tried to give definitions or describe

manifestations to identify HOT

Trend 2 Examine a number of types of thinking that fall into HOT

and recognize HOT as including HOT skills Representatives of thisgroup are FJ King, Ludwika Goodson, M.S.Faranak Rohani .Accordingly, critical thinking, logical thinking, metacognition andcreative thinking are HOT elements

Trend 3: Examine HOT from a cognitive perspective In this

approach, Barak Miri or Anat Zohar and many other researchers haveconsidered "analysis, synthesis, and evaluation" in Bloom's perceptionscale or "analysis, evaluation, creativity" in the rating scale of Andersonand Krathwohl as a high level of thinking

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: Lower-order thinking (LOT) and  Higher-order thinking (HOT);

1.2.3 The formation and development of thinking

According to Plantonov, thinking is an intellectual activity processconsisting of four stages:  Receive the problem and express it as a task

of thinking;  Mobilize knowledge, experience, association and formulatehypotheses;  Verify the correctness of the hypothesis If the hypothesis iscorrect, then go to the following step; if it is false, negate it and form a newhypothesis;  Evaluate the results and put them into use

1.3 Cognition and metacognition

Cognition consists of many phases, stages and takes differentforms, 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 thethinking process but it requires a rethinking of the thinking process at ahigher level associated with self-evaluation and criticism

Basically, cognition is the basis of metacognition; withoutemotional cognition, there would be no thinking or metacognition.Thus, thinking, cognition and metacognition have closerelationships with one another, go together and promote one another inthe process of human activities As a result, each individual canaccomplish cognitive tasks and achieve cognitive goals

1.4 Higher-order thinking (HOT)

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 otherstudies on critical thinking, creative thinking and metacognition; with aapproach to describing HOT as including the combination of importantfeatures of critical thinking, creative thinking, metacognition, which arealways intertwined, cohesive, supporting and promoting each other, wethink that HOT consists of the following five elements and groups ofelements:  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 isnecessary to specify the specific manifestations of each HOT elementwith different levels of manifestation These are clear and detailedinstructions for teachers to apply in assessing the achievement level ofHOT in teaching situations

When HOT takes place in an individual's brain, problematicsituations are solved not only effectively but also thoroughly Inaddition, individuals can develop new ideas or have more generalsolutions to new situations In each specific situation and each specificstage of HOT there will be different manifestations, but they are allexposed to the outside so that we can identify them (Table 1.1)

Table 1.1 Manifestation levels of each HOT element

R: Receive information

selectively; classify and

organize information into

M3

R 4 : Proactively search and select sufficient information to solve

the problem; Organize information into systems according to relationships.

M4 H: Propose hypotheses

M2

H 3: Propose the exact hypothesis to solve the problem. M3

H 4: Propose the exact hypothesis to solve the problem and M4

Elements Manifestation Level

propose new hypotheses for related issues.

P 1 : Analyze information on purpose (determine the relationship

between what is known and what to look for); Preliminarily evaluate the value of the information.

M1

P 1 : Analyze information on purpose (determine the relationship between what is known and what to look for); Assess the value of information critically. M2

P 1 : Analyze information on purpose (determine the relationship between what is known and what to look for) Synthetize and evaluate the value of information critically.

M3

P 1 : 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.

P 2 : Compare and contrast systems against each other (similar

or different) based on some available criteria. M1

P 2 : Compare and contrast systems against each other (similar

or different) based on the available set of criteria. M2

P 2 :Point out some criteria for comparing systems with each

P 2 : Develop a set of criteria to compare and contrast the systems

with each other (similar or different) and find new relationships. M4

M3

P 3 :Reason (inductively or deductively) to explain and draw conclusions Build a reasoning system as a basis for conclusions and propose new ideas.

M 1: Create a strategic proposal plan (according to a certain

M 1: Plan to propose multiple strategies (according to different criteria) for problem solving. M3

M 1: Plan to propose many strategies (according to different criteria) to solve problems creatively (not in a routine). M4

M 2: Propose ideas to solve a problem. M1

M 2: Propose many measures / ways to solve a problem. M2

M 2: Propose many measures / ways to solve a problem and

M 2: Propose new ideas / ways or many solutions / ways to solve a problem and choose an effective solution. M4E: Evaluate and self-

assess products and views E 1 : Evaluate products and views critically M1

E 2: Evaluate and self-assess products and views critically. M2

Elements Manifestation Level

critically; at the same

time, propose adjustment

plans.

E 3: Assess and self-assess products and views critically and

E 4: Evaluate and self-assess products and views critically; at the same time, propose adjustment solutions with high efficiency. M4

1.5 Develop HOT for students in teaching mathematics at high schools

1.5.1 The need to form and develop HOT for high school students

1.5.1.1 The role of HOT in teaching

Teaching in the orientation of developing HOT will keepstudents from passive learning, making them in need of learningand being active learners Students will be awakened and interested

in the learning content

1.5.1.2 Teaching opportunities to develop HOT for high school students

Limit is the first concept of Analysis, so students will be quitesurprised and find it difficult to approach If a teacher can takeadvantage of the concept of limit, it will not only inspire students togain knowledge enthusiastically, but also help them practice critical,flexible, creative abilities and always know how to recognize and re-evaluate their own thinking process of oneself That is to help studentstrain and develop HOT

1.5.2 General orientation on teaching to develop HOT

1.5.1 In teaching in the orientation of developing HOT, teachers need

to perform well some of the following tasks:  Encouraged students toask questions  Allow students to solve problems in learning activities

 Create a friendly environment and encourage discussion in theclassroom  Encourage students to study; students need to not onlyknow but also experience  Train and develop HOT for students at anytime and anywhere

1.5.3 Some active teaching methods which are applied in teaching to develop HOT

To achieve the goal of teaching in the orientation of developingHOT for students, teachers need to make good use of the followingteaching methods:  Problem-based learning;  Project-based learning;

 Cooperative learning;  Learning by discovery;  based teaching

Situation-1.5.4 Organize teaching to develop HOT for high school students

The process of organizing teaching towards developing HOTshould perform well the following two stages:  Design teaching plans;

 Organize the implementation of the teaching plans The relationshipbetween the teacher and the students in the two above stages isspecified in Figure 1.3

1.6 Current situation of training and developing HOT for students in teaching Math in general and “Limit” in particular at high schools

A survey was carried out on 56 teachers of Mathematics and 191 highschool students at Grade 11 at 32 high schools in Thai Nguyen, Hanoi,Hoa Binh and Hai Phong The results are as follows:

1.6.1 Teacher survey results

+ 100% of the surveyed teachers know and know well the concept

of thinking, mathematical thinking, logical thinking, but up to 23.21% ofteachers do not know the concept of dialectical thinking; 1.79% do notknow about the concept of creative thinking; 30.36% do not know aboutcritical thinking; 64.29% do not know about metacognition and 37.50%

do not know about HOT

+ 100% of surveyed teachers are fully aware of the role of teaching

to develop thinking in general and HOT in particular for students.However, most teachers currently do not pay much attention to teachingtowards developing HOT for students

+ The percentage of teachers surveyed using teaching methods andtechniques that promote students' activeness is very low: 78.57%regularly use presentation methods, 62.50% often use open oralquestions, 25,00% teachers often use collaborative teaching methods,19.64% regularly use teaching-by-discovery techniques, 5.36% regularlyuse project-based teaching, 3.57% regularly use programmed teachingmethod The percentage of teachers who do not use these methods andtechniques is relatively high at 33.93%, 44.64% and 73.21%,respectively

+ 60.71% of the teachers surveyed said that teaching in the orientation

of developing HOT for students would face many difficulties; forexample, the knowledge content of each lesson is too much; 80.36% saidthat the students' education level was still low and 57.14% to 73.21% ofteachers thought that creative and critical thinking was still strange tostudents However, 83.93% of teachers do not know how to train thinkingfor students

To sum up, the majority of surveyed teachers do not fully exploit thecontent of knowledge in textbooks and other documents; they haven'tapplied thoroughly and creatively teaching methods, measures andtechniques which have many opportunities to develop HOT for students

Students master knowledge, formulate and

develop HOT

STUDENTS

Prepare a new lesson following the teacher's instructions

1 Define lesson objectives

2 Identify key knowledge

3 Identify the knowledge circuit

4 Identify relevant knowledge

5 Supporting documents

Self-think/exchange, discuss, handle situations presented by classmates or the teacher when reporting learning results and draw experiences, self- assess, self-adjust.

Take tests, evaluate other tasks to prepare for the next lesson.

Receive tasks and develop a plan to perform the assigned

tasks

Perform learning tasks according

to the plan and the teacher's requirements

P a s s

Identify key knowledge of the lesson and

opportunities to develop HOT for students

Define lesson objectives, HOT

elements which should be trained

Choose appropriate teaching

methods, techniques and facilities

Develop teaching situations

Orient the student's learning tasks for

the next lesson

Activate and create learning

motivation for students

Provide students with access to

learning situations (group/individual)

Guide students to solve situations to

explore knowledge, develop HOT;

such as cooperative teaching methods, project-based teaching methods inteaching maths to achieve a dual goal: students both acquiremathematical knowledge and develop HOT and other competencies.

1.6.1.2 Student survey results

The majority of students surveyed are still quite passive in learning,hesitant to give opinions, questions and lack creativity and practicalapplication; their ability to apply the learned knowledge to related issuesmuch is not good

Chapter 2 TEACHING THE CONTENT OF “LIMIT” IN THE ORIENTATION OF DEVELOPING HOT FOR HIGH SCHOOL

STUDENTS 2.1 General principles in proposing teaching methods in the orientation of developing HOT for high school students

The pedagogical measures proposed in the thesis are based on thefollowing principles:

2.1.1 Ensure the objectives of teaching Mathematics while training and developing HOT for high school students

2.1.2 Ensure the activeness of learners through assigning tasks and creating conditions for learners to self-study and proactively master the knowledge

2.1.3 Ensure the feasibility of the methods in the current practical conditions

in Vietnam to help teachers apply them in teaching at high schools

2.2 Some teaching methods to develop HOT for high school students

2.2.1 Measure 1 Develop questioning skills for students in teaching

in the orientation of developing HOT

2.2.1.1 Purpose of the measure: Provide students with opportunities to

express HOT manifestations by asking questions to stimulate students

to brainstorm when participating in discussions, explore keyideas/content of the lesson in a logical order and find ways to solveproblems

2.2.1.2 Scientific basis of the measure: Questions and exercises are a

logical tool for modeling objective and subjective contradictions,turning objective objections into subjective contradictions, which helpslearners to be aware of research objects It can be said that the question

is both a starting point and a product, both a medium and a bridge to