Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.Vận dụng lí thuyết siêu nhận thức vào dạy học môn Toán trung học cơ sở theo hướng phát triển năng lực toán học cho học sinh.ĐỀ CƯƠNG NGHIÊN CỨU PAGE MINISTRY OF EDUCATION AND TRAINING HA NOI NATIONAL UNIVERSITY OF EDUCATION NGUYEN THI HUONG LAN APPLYING METACOGNITIVE THEORY IN TEACHING MATHEMATICS IN SECONDARY SCHOOLS IN T.
Trang 1HA NOI NATIONAL UNIVERSITY OF EDUCATION
NGUYEN THI HUONG LAN
APPLYING METACOGNITIVE THEORY IN TEACHING MATHEMATICS IN SECONDARY SCHOOLS IN THE DIRECTION OF DEVELOPING MATHEMATICAL
COMPETENCE FOR STUDENTS
Major: Theory and Methods of Teaching Mathematics
Code: 9 14 01 11
SUMMARY OF DOCTORAL THESIS
IN EDUCATIONAL SCIENCES
Hanoi - 2022
Trang 2AT HANOI NATIONAL UNIVERSITY OF EDUCATION
Scientific supervisor: Prof Dr Bui Van Nghi
Reviewer 1: Assoc.Prof Dr Nguyen Huu Hau
Hong Duc University
Reviewer 2: Assoc.Prof Dr Le Van Hien
Hanoi National University of Education
Reviewer 3: Assoc.Prof Dr Nguyen Tien Trung
Vietnam Journal of Education
The dissertation will be defended in front of the Dissertation Defense Jury
at Hanoi National University of Education
Time: ……… Date: ………
The dissertation can be found at:
- National Library, Hanoi
- Library of Hanoi National University of Education
Trang 31 Rationale for choosing the research topic
In the context of the Fourth Industrial Revolution, education in Vietnam faceschallenges and negative impacts To address these challenges, it is necessary to changeeducational policies, contents and methods of training to create human resources capable
of following new technological production trends
Around the world, policymakers are making efforts to reform the education system
in general and Maths education in particular to create a fundamental transformation inthe content, programs and methods of Maths learning of students
Metacognition is increasingly attracting the research interest of psychologists andeducators Studies on the role of metacognition in the development of students'competencies focus on two basic components: individual’s knowledge of their thinkingprocesses and the monitoring and control of individual activities in the learning process.Teaching with metacognition (serving as a tool – a method of higher-order thinking incognitive processes) will contribute to the development of students' competencies andhelp promote a more positive and effective learning environment
There have been several research works on metacognitive skills in the process ofteaching Maths such as doctoral theses by Hoang Xuan Binh, 2019; Le Binh Duong,2019; Hoang Thi Nga, 2020; Le Trung Tin, 2016; Phi Van Thuy, 2021
Research works on metacognition in Maths teaching in Vietnam mainly focus ontraining metacognitive skills through Maths The problem of understanding the influence
of metacognition on the formation and development of mathematical competence ofsecondary school students through Maths has not been researched specifically.Therefore, conducting research in this direction to find out how to apply metacognitivetheory to contribute to the development of mathematical competence for students inteaching Maths in secondary schools is necessary
For the above reasons, the researcher chose the research topic: “Applying
metacognitive theory in teaching Mathematics in secondary schools in the direction of developing mathematical competence for students”.
2 Research aims
On the basis of studying the impacts of metacognitive activities on themathematical competence of secondary school students, we have proposed measures forapplying metacognitive theory in teaching secondary school Mathematics in thedirection of developing mathematical competence for students
3 Research questions
The research question is "How can the application of metacognitive theory inteaching secondary-school mathematics contribute to the development of students'
Trang 4mathematical competence?" To answer this research question, it is necessary to answerthe following specific questions:
1 What is the theoretical basis for the application of metacognitive theory inteaching secondary school Mathematics to contribute to the development ofmathematical competence for students?
2 What is the current situation and effectiveness of organizing metacognitiveactivities for students in the direction of fostering mathematical competence inMathematics at secondary schools today?
3 How do metacognitive activities in math learning affect the formation anddevelopment of mathematical competence for secondary school students?
4 How to apply metacognitive theory in teaching secondary school Mathematics tocontribute to the development of mathematical competence for students?
4 Research subjects and objects
+ Research subjects: Measures for applying metacognitive theory in teaching
secondary-school mathematics to contribute to the development of mathematicalcompetence for students
+ Research objects: The process of teaching and learning Mathematics of teachers
and students in secondary schools
5 Scientific hypothesis
If the impacts of metacognitive activities on students' mathematical competence insecondary-school Maths are clarified and measures for applying metacognitive theory inteaching secondary school mathematics in the direction of developing mathematicalcompetence for students are implemented, they will contribute to improving theeffectiveness of teaching and the development of mathematical competence for students
6 Research tasks
+ Review related research issues on metacognitive theory and mathematicalcompetence in the field of mathematics education
+ Analyze the impacts of organizing metacognitive activities in teaching Mathematics
on the development of mathematical competence for secondary school students
+ Investigate the current situation of applying metacognitive theory in teachingMathematics in the direction of developing mathematical competence for secondaryschool students today
+ Propose measures to apply metacognitive theory in teaching secondary schoolmathematics in the direction of developing mathematical competence for students
+ Organize experiments to test the feasibility and effectiveness of the measures
7 Research Methods
Theoretical research method
Survey method
Trang 5 Pedagogical experiment method
Case study method:
Mathematical statistical method
8 Research scope
- Programs and contents of secondary school Mathematics
- Methods of teaching secondary school mathematics in the direction of developingmathematical thinking and reasoning competence and mathematical problem-solvingcompetence for students through typical situations in teaching secondary school mathematics
9 New contributions of the thesis
9.1 Theoretical contributions
The thesis has:
+ Reviewed studies on applying metacognitive theory in teaching towardsdeveloping mathematical competence for secondary school students
+ Identified and clarified the role of metacognitive activities in developing students'mathematical competence in the process of teaching Mathematics
+ Proposed measures to apply metacognitive theory in teaching secondary schoolmathematics in the direction of developing mathematical competence for students
The above results contribute to the theory and teaching methods of Mathematics
9.2 Practical contributions
+ The thesis has reflected part of the current situation of teaching Mathematics inthe direction of developing mathematical competence for students in secondary schools.+ The results of the thesis contribute to innovating teaching methods of Mathematics andimproving the effectiveness of teaching Mathematics in secondary schools
10 Arguments that will be protected
(1) Metacognition plays an important role in developing students' mathematicalcompetence through secondary-school mathematics
(2) The measures for applying metacognitive theory in teaching secondary schoolmathematics in the direction of developing mathematical competence for studentsproposed in the thesis are feasible and effective
11 Structure of the thesis
In addition to the introduction, conclusion and appendices, the thesis consists of 3chapters:
Chapter 1 Theoretical basis
Chapter 2 Practical basis
Chapter 3 Measures for applying metacognitive theory in teaching school mathematics in the direction of developing mathematical competence for studentsChapter 4: Pedagogical experiment
Trang 6secondary-CHAPTER 1 THEORETICAL BASIS
1.1 Literature Review
1.1.1 Research on metacognition
1.1.1.1 Research on metacognition in the world
Metacognition has been interested in research since the 70s of the twentieth century
in the work of Flavell (1979) Although there are many different definitions of the term
"metacognition", in general, these definitions provide a unified meaning of this concept
The large-scale research works on metacognition in education were conducted in
the late twentieth century and early twenty-first century, more or less related tocomprehensive assessment programs to understand the role of effective teachingmethods in schools
1.1.1.2 Research on metacognition in Vietnam
In Vietnam, in the field of Psychology and Education, there are some authors
researching metacognition, for example, Hoang Thi Tuyet with the research
"Strategies for teaching nature-society in primary school"; Ho Thi Huong (2013) withthe research "A study on metacognitive theory and its applications in secondaryschool education", institute-level project, Vietnam Institute of Educational Sciences;Hoang Xuan Binh, Phi Van Thuy (2016) had research articles on "The role ofmetacognition in teaching Mathematics in high schools" and "Developingmetacognitive skills for students through solving geometry problems in high school”
In these articles, the authors have analyzed and clarified the role of metacognition inthe process of teaching mathematics in high schools, and concretized the fostering ofmetacognitive skills in teaching spatial geometry
In this thesis, with the aim of applying metacognitive skills in teaching school Maths in the direction of developing mathematical competence for students, wechose 3 component metacognitive skills corresponding to 3 metacognitive activities,which are orientation and planning, monitoring and adjusting, and evaluating to focus onorganizing for students to apply metacognition when learning Math, thereby affecting 5components of mathematical competence that need to be developed through Math
secondary-1.1.2 Research on Mathematical competence
1.1.2.1 Overview of research on mathematical competence around the world
The concept of competence
There have been many studies abroad on mathematical competence from differentaspects, such as: V.A Krutecxki; A.N Kolmogorov (refer to Pham Van Hoan et al.,pp.128-129); UNESCO (1973) announced 10 basic mathematical competence indicators;Morgen Niss (2003);
Trang 71.1.2.2 Overview of research on mathematical competence in Vietnam
The concept of competence
According to Nguyen Cong Khanh “Competence is the ability to master systems ofknowledge, skills, attitudes and operate (connect) them logically into successfullyperforming tasks or effectively solving problems in life Competence is a dynamic(abstract) structure, open, multi-component, multi-level, containing not only knowledgeand skills but also beliefs, values, and social responsibilities, etc., expressed in thewillingness to act in real conditions and changing circumstances"
Thus, it can be seen that “competence is seen as a combination of individualattributes that are suitable for the specific requirements of a certain activity, enabling theindividual to successfully perform certain activities, achieve desired results underspecific conditions”
Research on Mathematical competence
The Mathematical General Education Program in 2018 specifically identified the goal
of developing students' mathematical competence, including five components: (1)Mathematical thinking and reasoning competence; (2) Mathematical modeling competence;(3) Mathematical problem-solving competence; (4) Mathematical communicationcompetence; (5) Competence to use mathematical learning tools and means; and directly setrequirements for teaching Maths, focusing on the formation and development ofmathematical competencies for students, making an important contribution to thedevelopment of necessary competencies to continue studying and working in life
1.2 Metacognitive Theory
1.2.1 Cognition, cognitive activities, skills
1.2.2 Concepts and approaches of metacognition
Based on reference to research results on metacognition in the world and inVietnam (section 1.1.), in this thesis, with the aim of applying metacognition as a
"support means" for teaching Maths to approach the goal of developing students'mathematical competence, we define that “Metacognition is a form of cognition, a high-order thinking process, relating to human cognitive processes, reflecting theirunderstanding of the nature of the cognitive process and strategies for carrying outcognitive activities”
1.2.3 Features and functions of metacognition
According to John Flawell (1979), some of the main features of metacognition thatneed to be mentioned are “Awareness of one's own thinking process; Active andproactive monitoring of cognitive processes related to learning tasks; Learners find ways
to solve problems by themselves; Monitor and regulate one’s own cognition; Evaluatethe process and results achieved against the set goals”
Trang 8The functions of metacognition are “Awareness of one’s own cognition; Planning,monitor, and adjust the problem-solving process.”
1.2.5 Components of metacognition
Research on metacognition cannot fail to mention Flavell, who is considered one ofthe first to define "metacognition" The metacognitive components proposed by Flavellserve as the foundation for later metacognition-related research Flavell (1979, identifiedthe components of metacognition and specified their characteristics, includingMetacognitive knowledge; Metacognitive experiences; Cognitive goals; Activities andstrategies He argued that the ability of an individual to regulate cognitive outcomesdepends on the interaction between the components of cognitive strategy, cognitiveexperience, metacognitive knowledge and metacognitive experience
1.2.6 Metacognitive activities
According to the research by Tobias and Everson (2002), metacognition is acombination of factors such as skills, knowledge (understanding of cognition) in thecognitive process of learners as well as the control of the learning process according tothe following “pyramid” model:
Figure 1.1 The “pyramid” model of the metacognitive process (Tobias and Everson, 2002)
1.2.7 Metacognition in problem-solving
1.2.7.1 Problem-solving diagram
There have been many scholars outlining different models of problem-solving Fernandez, Hadaway and Wilson (1994) gave a problem-solving model (Figure 1.4) in the form of a circle representing "the management overseeing the entire problem-solving process", which Schoenfeld and Flavell (2000) have recognized as metacognition.
Trang 9Figure 1.4 The problem-solving model outlined by Fernandez, Hadaway and Wilson (1994)
1.2.7.2 Metacognitive activity during the Mathematical problem-solving process
To describe the metacognitive aspects of learners in solving mathematical problems,Garofalo and Lester (1985) have proposed four metacognitive activities related to solvingany mathematical task, including orientation, organization, implementation, andevaluation
1.2.7.3 Theoretical framework of metacognition in problem-solving processes
Artzt and Armor-Thomas (1992) provided a framework for the interrelationshipbetween metacognitive and cognitive processes in solving mathematical problems
Stages: 1- Read the problem (cognition); 2- Understanding the problem(metacognition); 3- Problem analysis (metacognition); 4- Devising a plan(metacognition); 5a-Exploration (cognition); 5b- Modification (metacognition); 6a-Implementation (cognition); 6b- Evaluation (metacognition); 7a- Revision (cognition);7b-Confirmation (metacognition); 8- Watch and listen (uncategorized)
1.2.7.4 The five metacognitive components of problem-solving
Howard, McGee, Shia and Hong (2000) have identified five learning strategies thatself-regulated learners use in a problem-solving context and considered them as 5metacognitive components to guide learners' cognitive activities in the problem-solvingprocess:
Trang 101.3 Cognitive and metacognitive activities in the process of developing mathematical competence for secondary school students`
1.3.1 Cognitive and metacognitive activities
1.3.2 Cognitive and metacognitive manifestations of secondary school students in 5 components of mathematical competence
Table 1.3 Cognitive and metacognitive manifestations of secondary school
students in 5 components of mathematical competence
Cognitive and metacognitive
competencies are demonstrated
through:
- Performing thinking operations such
as: compare, analyze, synthesize,
specialize, generalize, analogize;
induce, and interpret (cognition)
- Pointing out evidence and reasons
(cognition) and making reasonable
arguments before concluding
(metacognition)
- Explaining or modifying how to
solve the problem mathematically
(metacognition)
- Performing thinking operations, especiallyobserving (cognition), explaining similaritiesand differences in many situations(metacognition) and expressing the results ofobservation (cognition)
- Reasoning (cognition) logically(metacognition) when solving problems
- Asking and answering questions whenreasoning and solving problems; proving thatthe mathematical proposition is not toocomplicated (cognition)
Mathematical modeling competence is
demonstrated by:
- Identifying mathematical models
(including formulas, equations, tables,
graphs, etc.) for situations appearing in
practical problems (metacognition)
- Solving mathematical problems in
the established model (cognition)
- Demonstrating (cognition) and
evaluating (metacognition) the
solution in the actual context and
improving the model if the solution is
not appropriate (metacognition)
- Using mathematical models (includingmathematical formulas, diagrams, tables,drawings, equations, representations, etc.) todescribe situations appearing in somepractical problems which are not toocomplicated (cognition)
- Solving mathematical problems in theestablished model (cognition)
- Demonstrating mathematical solutions inpractical contexts (cognitive) and gettingused to verifying the correctness of thesolutions (metacognition)
Mathematical problem-solving
Trang 11competence is demonstrated by:
- Identifying and detecting problems
that need to be solved mathematically
(cognition)
- Selecting and proposing ways and
solutions to solve problems
(metacognition)
- Using relevant mathematical
knowledge and skills (including tools
and algorithms) to solve problems
(cognition)
- Evaluating the proposed solutions
and generalizing to similar problems
competence is demonstrated by:
- Listening, reading, understanding
and recording essential mathematical
information presented in mathematical
text or spoken or written by others
(cognition)
- Presenting and expressing (oral or
written) mathematical contents, ideas,
and solutions in interaction with others
(with appropriate requirements for
completeness and accuracy)
(cognition)
- Effectively using mathematical
language (digits, letters, symbols,
charts, graphs, logical links, .) in
combination with the common
language or body movements when
presenting (cognition), interpreting
and evaluating mathematical ideas in
interaction (discussion, debate) with
others (metacognition)
- Showing confidence when
presenting, expressing, asking
questions, discussing and debating
- Listening, reading and recording(summarizing) the basic and centralmathematical information in the text (in oral
or written form), and then analyzing,selecting, and extracting the necessarymathematical information from the text (inspoken or written form) (metacognition)
- Presenting and expressing (cognition),asking questions, discussing and debatingmathematical contents, ideas, and solutions ininteraction with others (at a relativelycomplete and exact level) (metacognition)
- Using mathematical language incombination with the common language toexpress mathematical content as well asdemonstrate evidence, methods and results ofreasoning (cognition)
- Showing confidence when presenting,expressing, discussing, debating, andexplaining mathematical contents in anumber of situations that are not toocomplicated (metacognition)
Trang 12content and ideas related to Maths.
(metacognition)
Competence to use mathematical
learning tools and means is
demonstrated by:
- Recognizing the names, effects,
usage rules, ways of preserving
common visual aids, tools, and
scientific and technological means
(especially those using information
technology), for Maths learning
(cognition)
- Using tools and means, especially
scientific and technological means to
explore, discover and solve Maths
problems (suitable to cognitive
characteristics by age) (cognition)
- Recognizing the advantages and
limitations of supporting tools and
means to have a reasonable use
(metacognition)
- Recognizing the names, effects, usage rules,and ways of preserving tools and means(plane and spatial geometric models,protractors, rulers, pictures, charts, etc.) ).(cognition)
- Show how to use Mathslearning tools andmedia to perform learning tasks or to expressmathematical arguments and proofs.(cognition)
- Using handheld computers, some computersoftware and learning aids (cognition)
- Pointing out the advantages and limitations
of supporting tools and means to have areasonable use (metacognition)
1.3.3 The influence and role of metacognition in learning Mathematics and developing mathematical competence for students
1.3.3.1 Metacognition helps students to have the ability to self-direct, choose strategies, adjust, monitor and evaluate in the process of thinking and reasoning, mathematical communication, solving mathematical problems, and mathematical modelling, etc in the Math learning process.
1.3.3.2 Metacognition helps students learn how to think effectively and independently; students can explain their ways of thinking and acting; as a result, others can learn from them.
1.3.3.3 Metacognition helps students have a better learning mentality, because metacognition helps them proactively identify what they know and what it takes to succeed, help them gain confidence in themselves, and develop their own mathematical competence.
1.3.4 Opportunities and orientations to apply metacognitive theory in teaching secondary school Maths towards developing students' mathematical competence
1.3.4.1 Opportunities and approaches
Trang 13Stemming from the study of the characteristics of the cognitive process, therelationship between cognitive and metacognitive activities, the role of cognitive skills
in learning mathematics - especially in mathematical thinking and reasoning activities,mathematical communication and mathematical modeling, in this thesis, applyingmathematical reasoning is understood as: On the basis of clarifying the effect ofmetacognition on the development of components of mathematical competence, buildmethods of teaching mathematics to exploit strengths and effects of metacognitiveactivities to affect students' self-study competences
1.3.4.2 Orientations for applying metacognitive theory in teaching secondary school Maths in the direction of developing mathematical competence for students.
- Evaluate the actual situation of organizing cognitive and metacognitive activities
in the direction of developing mathematical competence for secondary school students inteaching mathematics
- Study methods and techniques of teaching Mathematics in order to exploit theadvantages of metacognition for the goal of developing mathematical competence forstudents through Mathematics
- Develop measures to apply metacognition in teaching Secondary SchoolMathematics in order to develop mathematical competence for students
1.4 Summary of Chapter 1
In this thesis, applying metacognitive theory is understood as: On the basis ofclarifying the effects of cognitive thinking on the development of components ofmathematical competences, build measures of teaching mathematics to exploit thestrengths and effects of metacognitive activities to affect students' self-studycompetence
Many studies have shown that when students are taught how to learn and think,they can achieve higher levels of education; effective teachers often integrate teachingcontents with teaching strategies and metacognition information about choosingeffective strategies in their daily teaching activities
The comparison between cognitive activities and metacognitive activities can beseen in Table 1.2; The manifestions of cognition and metacognition in the 5 components
of mathematical competence for secondary school students can be seen in Table 1.3.The results of research and analysis show that there are many opportunities andways of applying metacognitive theory to develop mathematical competence forstudents In order to perform well this activity, it is necessary to add an assessment of theactual situation of applying metacognitive theory to the process of developing students'