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HANOI NATIONAL UNIVERSITY OF EDUCATION

-DO DUC BINH

TEACHING GEOMETRY IN LOWER-SECONDARY SCHOOLS WITHA FOCUS ON CURRICULUM DEVELOPMENT AT

THE CLASSROOM LEVEL

Major: Theory and Methods of Teaching MathematicsCode: 9.14.01.11

SUMMARY OF DOCTORAL THESIS OF EDUCATION SCIENCE

Hanoi, 2024

HANOI NATIONAL UNIVERSITY OF EDUCATION

Science instructors: Prof Dr BUI VAN NGHI

Reviewer 1: Prof Dr Trinh Thanh Hai

Thai Nguyen University of Sciences

Reviewer 2: Assoc.Prof Dr Nguyen Huu Hau

Hong Duc University

Reviewer 3: Assoc.Prof Dr Tran Viet Cuong

Thai Nguyen University of Education

The thesis is defended before the Ph.D Thesis Evaluation Council at theUniversity level

Location: Hanoi National University of Education at time … , date ……month …….2024

The thesis can be found at: - Vietnam National Library

- Library of Hanoi National University of Education.

RELATED TO THE THESIS

Do Duc Binh (2023), “Some solutions to develop a curriculum at the classroom level

for teachers in teaching Geometry at lower-secondary schools”, Vietnam Journal

of Education, ISSN 2354-0753, Special Issue – September 2023.

Do Duc Binh (2023), “The current situation of teachers' awareness about teaching

Geometry at lower-secondary schools with a focus on curriculum development at

the classroom level”, Vietnam Journal of Education, ISSN 2354-0753, Special

Issue - August 2023.

1. Do Duc Binh (2019), “Curriculum development at the classroom level (illustrated

with the main content of geometry)”, Vietnam Journal of Educational Sciences,

ISSN 2615-8965, January 2019, Volume 13, pp 76-81.

4 Do Duc Thai and Do Duc Binh (2019), “On Visual Geometry at the secondary

level in the new mathematics curriculum”, HNUE Journal of Science:Educational Sciences, ISSN 2354-1075, 2019, Volume 64, Issue 4, pp 3-16,

DOI: 10.18173/2354-1075.2019-0001.

5 Do Duc Thai and Do Duc Binh (2017), “Basic perspectives in determining and designing the main content of Geometry in the mathematics curriculum of

middle-school level in the new general education”, International Conference onScience and Mathematics Education (CoSMEd 2017), eISSN: 2600-7452,

SEAMEO RECSAM, Penang, Malaysia.

PREAMBLE1 Reasons of the topic

1.1 The national curriculum in Vietnam has been changed in response to societal transformations.

1.2 Over the past several decades, the development of national curriculum in the world and in Vietnam has undergone many significant changes.

1.3 Practice shows that numerous teachers have not allocated sufficient attention to the development of the Mathematics curriculum in general, and the main content of Geometry in particular.

1.4 There have been numerous studies related to curriculum development, but there are few works focusing on curriculum development at classroom level, especially lacking research on “teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level”

With the aim of identifying activities to engage teachers in the curriculum development process at classroom level, the topic selected is:

"Teaching Geometry in lower-secondary schools with a focus on curriculumdevelopment at the classroom level"

2 Research objectives

On the basis of the theory and practice of the problem of developing curriculum at the classroom level, it is suggested to propose activities for teachers in teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level, contributing to improving the quality of the teaching mathematics in lower-secondary schools.

3 Research entity, object and scope

- Research entity: The process of teaching Geometry at lower-secondary school.

- Research object: Activities in teaching Geometry at lower-secondary schools with a

focus on curriculum development at the classroom level.

- Scope of research: Focusing on teaching activities of Geometry in lower-secondary

4 Scientific hypothesis

On the basis of theory and practice on the development of the Mathematics curriculum at the classroom level, if teachers understand and implement classroom curriculum development activities right in the process of preparing lesson plans, studying lessons, in the process of teaching Geometry in lower-secondary schools, teaching results will be improved, and at the same time, practically contribute to the curriculum development at the classroom level.

5 Research tasks

The thesis has the task of answering the following scientific questions:

(1) What is the overview of the research conducted on this topic? (The research results worldwire and in Vietnam have studied to what extent, the thesis can contribute to the development of geometry curriculum in secondary schools)

(2) What is the rationale for the geometric curriculum development at the classroom level in lower-secondary schools? (What is the concept of in general and curriculum development at the classroom level in particular? What are the manifestations of curriculum development at the classroom level?)

(3) What is the current situation of teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level?

(4) What activities of the teacher contribute to the development of the geometric curriculum at the classroom level in lower-secondary schools?

(5) Are the proposed activities to answer question (4) feasible and effective?

7 New contributions of the thesis

7.1 In terms of theory: Clarifying the theory of curriculum development at the classroom

level; Proposing the teacher's activities in teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level.

7.2 In terms of practice:

- Reflects a part of the current situation of curriculum development at the classroom level in lower-secondary schools in Vietnam today.

- The activities proposed in the thesis contribute to curriculum development at the classroom level through teaching Geometry in lower-secondary schools in accordance with the actual conditions of the classroom, meeting the requirements of educational innovation and improving the quality of teaching Mathematics The examples and pedagogical experimental documents in the thesis can be considered as references for teachers when teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level.

8 Issues in defence

- Issue 1: The curriculum development at the classroom level in lower-secondary

schools has a theoretical and practical basis.

- Issue 2: The activities proposed in the thesis for teaching Geometry in

lower-secondary schools, with a focus on curriculum development at the classroom level, are both feasible and effective."

9 Structure of the thesis

In addition to the introduction and conclusion, the thesis consists of 4 chapters: Chapter 1 Theoretical basis

Chapter 2 The practical basis

Chapter 3 Proposing the teacher's activities in teaching Geometry in lower-secondary schools with a focus on curriculum development at the classroom level

Chapter 4 Pedagogical experiment

Chapter 1Theoretical basis1.1 Overview of research related to the topic

1.1.1 In the world

International studies on curriculum development can be divided into three areas, from general to specific: the study of general problems of curriculum development; array of studies on different levels of the curriculum; the study of curriculum development at the classroom level.

a) On general matters

Research on general issues of curriculum development can include the work of Kieran Egan, Robert Diamond and especially the work of Peter F Oliva In his work, Peter F Oliva discussed quite carefully the concepts related to the curriculum (chapter 1), the principles of curriculum construction (chapter 2); curriculum planning – a multi-level, multidisciplinary process (including classroom level, team and subject level, school level, local level, national level, international level - chapter 3), the roles of teachers, students, administrators, parents, etc in the development of the curriculum (chapter 4) In this work, the author mentions the curriculum building models, the curriculum's goals and objectives, the curriculum organization and implementation, and the curriculum evaluation.

Many other works can be mentioned such as the textbook “development of school curriculum”, monograph of Floyd G Robinson, John A Ross, Floyd White, Colin J Marsh and George Willis, Wentling Tim,

b) On different levels of the curriculum, some of the following works can be mentioned: Articles by Reid (1998), Michael Bezzina (1991) discuss the levels of curriculum development (national level, local level and school level) in the 90s of the twentieth century in Europe, America and Australia.

In the Netherlands, the work of the Netherlands Institute for curriculum development (SLO) summarized the theoretical basis for curriculum development, presented strategic frameworks and thinking about curriculum development from the national to the classroom level learn, introduce techniques applying international experience

In Asia, it is possible to mention the research works of Chenzhi Li, Feifei Shuai (2010), Chi-Chung Lam, Shirley S Y Yeun (2010), discussing the issue of school curriculum development in China, Korea, Taiwan.

c) Regarding the development of Geometry curriculum for lower-secondary schools

According to known research works, there has been no separate study on the development of the junior high school geometry curriculum, only a few works related to the geometry learning of junior high school students.

1.1.2 In Vietnam

In Vietnam, there have been a number of studies that delve into curriculum development for different levels of education At the preschool level, there are works by Nguyen Thi Thu Hien (2008), works by Tran Thi Minh Hue (2017); at the primary school level, there are works of Dau Dinh Hoan (2011), works of Vu Quoc Chung… followed by a number of projects by the Ministry of Education and Training on “Educational development program” at the primary level (2004), at the secondary level (2009).

A further study on the theory of curriculum development, including the works of Nguyen Huu Chau (2005), Tran Huu Hoan (2011) there have been a number of scientific conferences organized by the Ministry of Education and Training, focusing on innovation of general education curriculums, textbooks, current status of school curriculum development, such as scientific seminars "Evaluation of one year of pilot implementation of school

education curriculum development” (2014); scientific conference " Some common issues onbuilding general education curriculums after 2015 ", with 54 reports.

Thus, studies on curriculum development have been around since the 50s of the twentieth century most of these studies delve into general theory: concepts, processes, principles about curriculum development; there are very few works that guide or indicate specific solutions for curriculum development for a specific level of education

Meanwhile, there is an urgent immediate and long-term need for specific research to help teachers practice and implement curriculum development during the teaching process at general education levels This is also the goal and content that this thesis is aiming for.

1 2 General education curriculum

1.2.1 Some issues about the general education curriculum

1.2.1.1 About the term Curriculum

In this thesis, curriculum is understood as the general education curriculum.

1.2.1.2 Concept of the curriculum

According to Oliva (2005), there are different interpretations of the term curriculum:

“A curriculum is what is taught in school, is a set of subjects;Curriculum is the content taught in a course;

The curriculum is everything that happens in the school including teaching activities,extracurricular activities, planning "

According to Colin J Marsh and George Willis (2005, page 22): A curriculum is a set of plans and practical knowledge that a learner acquires under the guidance of a school The curriculum is the totality of practical knowledge provided to students so that they can gain knowledge and skills in many places Curriculum can include syllabus (curriculum of each course) and course of studies (curriculum of many courses) Elizabeth Vallance (1983)

commented: The field of curriculum is not clear at all, it seems both a subject and a practice, the curriculum lacks clear boundaries.

In this thesis we use the curriculum definition of Tim Wentling (1993): “A curriculumis an overall blueprint for a training activity (which may last a few hours, a day, a week oryears) That master design tells us all about the content to be trained, specifies what we canexpect from the learners after the course; it outlines the process required to deliver thetraining content; It also tells us about the training methods and the methods of testing andevaluating the learning outcomes and all of that is arranged according to a tighttimetable.”

1.2.1.3 Plan training curriculum Build and change curriculum

a) Curriculum planning – a multi-level, multidisciplinary process b) Who can participate in the development/change of the curriculum

Parents and many other individuals can express their views on the curriculum to principals and teachers: Parents' unions, the business community, trade unions, political parties, religious groups and many other organizations all have views on what children need to learn in school.

Participants participating in curriculum development/change according to curriculum levels from low to high can be as follows:

1 Classroom curriculum Teachers, professional groups 2 School curriculum Professional team, board of directors 3 Subject curriculum Ministry of Education and Training 4 Framework curriculum Ministry of Education and Training

1.2.1.4 Some type of general education curriculum

Depending on the concept of nature, method of curriculum design and implementation, researchers have many different ways of classifying curriculums For example: Classifying according to the hierarchy in curriculum development, highly centralized curriculums or decentralized curriculums (national, local, school level); or effective categorization and curriculum implementation progress

a) Intended curriculum, implemented curriculum, attained curiculumb) Framework curriculum and subject curriculum

c) Closed curriculum, open curriculum

d) National curriculum, local curriculum, school curriculum, classroom curriculum.

1.2.2 Classroom curriculum

1.2.2.1 Concept of the classroom curriculum

It can be said that the teacher is the person who is directly in contact with the contents of the general education curriculum, who is closely involved with the curriculum and the teacher's activities mainly take place within the classroom, with little connection to the curriculum Related to the national curriculum, the local curriculum, the school curriculum furthermore, the most important criterion for an educational curriculum is that the curriculum should be more relevant and meaningful to student learning, to the competence

of the teacher, and to the conditions of the classroom Therefore, the issue of both urgency and practicality is the need to pay more attention to the curriculum at the classroom level (classroom curriculum).

Classroom curriculum can be understood as an educational plan (teaching plan) of anindividual teacher that is built on the basis of regulations of the national curriculum, localcurriculum, school curriculum, based on practice education of the school, the classroom,the teaching and learning capacity of teachers and students.

According to Colin J Marsh, George Willis, when designing a classroom curriculum each teacher can make different decisions about the curriculum, what to teach, and how to teach This is the stage where the training curriculum proposed in the plan turns into a training curriculum that is implemented and tested The concept of the classroom curriculum above is consistent with the "openness" and "autonomy" of the curriculum Teachers can promote initiative and creativity in implementing and developing the curriculum.

1.2.2.2 The process of forming the classroom curriculum concept

According to Fullan, in the 1970s and 1980s, in Australia, the UK and the US, there were studies showing the role of teachers in curriculum development and affirming that teachers are not just "workers " or “ technicians” execute curriculums from central or local regulatory documents Since 2000, there have been studies on the classroom curriculum In the world, people have different names for the concept of classroom curriculum: “classroom curriculum”, “ curriculum in classroom”, “ curriculum for classrooms teaching”,… In Australia, since 2012, the Ministry of Education Queensland has developed a set of teaching materials to help teachers develop their own teaching plans for a class or group of classes, general students, special students or students taking classes remotely This kit is called “curriculum into classroom” or “C2C” In the US, teachers develop their own teaching plans, called "field guides", which are used as textbooks and workbooks for students Developing teaching plans of individual teachers in the US has become a regular task.

The Dutch Institute for Curriculum Development mentioned the levels of curriculum development as: SUPRA – international curriculums (for example, the Common European Framework of Reference for Languages); MACRO – national curriculum; MESO – school

curriculum; MICRO – classroom curriculum (e.g., lesson plans, lesson plans, teaching

materials; modules of lectures, etc.).

In Vietnam, Vu Quoc Chung (2015) mentioned four levels of educational curriculum as national curriculum, local curriculum, school curriculum, classroom curriculum In another work, N T Hong Nhung (2016) introduced the concept of the classroom curriculum: A classroom curriculum is a teacher's teaching plan that may include one/several lessons, used to guide educational activities in class or out of class, in school or outside the school.

1.3 Development of general education curriculum

1.3.1 Some approaches in the development of general education curriculums

1.3.1.1 General education curriculum development

In the dictionary sense (Hoang Phi, 1996): Development is change, making changes from few to many, narrow to wide, low to high, simple to complex.

According to dialectical point of view: Development is a philosophical category used to refer to the movement of things in an upward trend, from low to high, from simple to complex, from incomplete to perfect object Development has objectivity, universality, richness, diversity and inheritance.

We believe: Curriculum development is the process of changing the curriculum or making the curriculum more and more complete, more suitable for educational goals and with the development of society.

1.3.1.2 Curriculum development needs

In essence, the education/ training curriculum is a process of gradual improvement, which is always updated/refreshed, because it is a cyclically closed process and is increasingly advanced.

According to Peter F Oliva: Change of curriculum is necessary and unavoidable, because through life change comes growth and development; a school's curriculum is a product of the times; curriculum changes stem from changes in people.

1.3.1.3 Some approaches in the development of general education curriculums

In the past few decades, people often mention two main trends: - Content - based approach

- Outcome - based approach

Recently, from the second approach, a new approach trend has been noticed and

applied by many countries, which is the competency based approach.

1.3.2 Curriculum development at the classroom level

1.3.2.1 Concept about classroom-level curriculum development

School curriculum development is the process of concretizing and making the national curriculum consistent with local realities on the basis of ensuring the general requirements of the national curriculum; select and develop content (part for the school to determine); and determine implementation methods that reflect characteristics and are consistent with school practices, modern requirements and achievements (in educational science, technology, etc.); to meet the requirements of developing learners' qualities and abilities, effectively implementing educational goals.

According to Peter F Oliva, when talking about the rights and obligations of teachers

in participating in curriculum development, pointed out that: “It can be said that a teacher'slife would be extremely boring if they could not come up with a decision about thecurriculum If teachers espouse the axiom of “change is inevitable and never ending” theywill see the role first and foremost: they are the deciders.” Teachers participate in

curriculum development as soon as they prepare lesson plans: Write down objectives, select content, teaching methods, learning resources, lesson plans, etc to meet all the differences individually in the classroom This work includes curriculum evaluation.

In this thesis, classroom curriculum development is understood as transforming the school curriculum (or making the school curriculum change) more complete, more expansive, more appropriate, and more effective through activities design, building and implementing teachers' teaching plans.

The four characteristic signs of classroom curriculum development are described more specifically as follows:

- More perfect: more complete, better, no more mistakes, errors, or omissions.

- More extensive: more complete, richer, more diverse, from less to more, from simple to complex, from narrow to broad, from specific to general, from less common to more common

- More suitable: more suitable for students' psychology and cognitive ability, the knowledge fits together and is more interconnected; Attract more students to participate in learning activities, raise students' awareness level from low to high, help students solve problems from easy to difficult

- More effective: has a result more than what is desired or expected, has greater efficiency, creates a deeper, more vivid impression; complete a job or task better and faster; see more clearly the meaning and ability to apply mathematical knowledge in practice, better meeting the goals, requirements, and desires of the curriculum.

1.3.2.3 Analysis of international and Vietnamese experience in curriculum development atthe classroom level

The trend of curriculum reform in Western countries first comes from the concept: Instead of imparting and explaining knowledge, teachers need to pay attention to developing students' abilities, giving students opportunities and the ability to self-discover, self-possess knowledge, as well as have the ability to solve problems that arise in practice.

The process of curriculum reform gradually raises the need to reform the curriculum management institution, which is a major, revolutionary change in the design and management of a curriculum, depending on the design and use objects Curriculum is often interpreted at the following levels: National Curriculum, Local Curriculum, School Curriculum and Classroom Curriculum This is also the model chosen in many countries with developed market economies in the years since the 1970s.

As stated above, the term curriculum development has only been officially used in Vietnam in the past ten years However, along with the development of the country, the education sector in general and curriculum in particular have also had changes related to curriculum development, which are summarized in the form of educational experience This can be clearly seen through some of the following manifestations:

- Hoa Binh Socialist Labor Youth School with the method of "learning by doing" - "Bac Li drum sound" with the emulation movement "Two good"

- Guidance documents from the Ministry of Education and Training to increase the autonomy of localities and schools in implementing the Development Curriculum.

1.4 Conclusion chapter 1

Since the 50s of the twentieth century, the issue of curriculum development has been studied and interested by countries Up to now, general education curriculum development has become a discipline, a subject Vietnam has been interested in this issue since the early years of the twentieth century There have been many published works related to curriculum development.

Teachers have an important role in the development of the curriculum, which is reflected in specific lesson plans, so this thesis wants to focus on the object of participation in curriculum development who is the teacher, taking place in the classroom, and we call it classroom-level curriculum development.

Chapter 2Practical basis

2.1 The development of mathematics curriculum in Vietnam

2.1.1 Education reform and change in mathematics curriculum in Vietnam

In Vietnam, there have been four education reforms and two revisions to the general education curriculum Education reform four times: the first education reform in 1950, applied in the free zone during the anti-French resistance war; 2nd time in 1959 – changing towards socialist orientation, with a 10-year general education system; the third time in 1981, the 12-year general education system was deployed, applied nationwide; 4th time in 2002, implemented in accordance with the resolution 40 of the National Assembly, term viii, in accordance with the subdivision orientation Revised the general education curriculum twice in 2002 and 2018.

2.1.2 Curriculum development in Vietnam

Starting from the 2013-2014 school year, the development of the general school education curriculum was piloted according to the official dispatch No 791/HD-BGDĐT, dated June 26, 2013 of the Minister of Education and Training

2.1.3 Comment on some realities of current classroom-level curriculum development inVietnam

We have made considerable efforts to expand teachers' curriculum autonomy through

the policy of “a unified but flexible general education curriculum; the curriculum ensures auniform orientation and core educational contents, which are compulsory for studentsnationwide, and at the same time empowers local authorities and schools with initiative andresponsibility in selecting and supplementing a number of curriculums Educational contentand implementation of educational plans suitable to the educational subjects and conditionsof the locality, of the educational institution, contributing to ensuring the connection of theschool's activities with the family, the government and the society association" (resolution

TW 8)

2.2 Opportunities to teach Geometry at Middle School in the direction of classroomcurriculum development

2.2.1 Opportunities to develop classroom curriculum in teaching Geometry fromreviewing the content of Middle School Geometry knowledge in Vietnam and somecountries around the world before 2018

The content of Middle School Geometry knowledge in Vietnam and some countries around the world (before 2018) can suggest us some opportunities to develop curriculum at the classroom level in teaching Middle School Geometry in Vietnam Adding or removing a certain Geometry content in secondary schools to suit the reality at home and abroad will be issues that need to be discussed and calculated so that the curriculum becomes more and more perfect.

2.2.2 Opportunities to develop classroom curriculum in teaching Geometry from issuesin building the content of Middle School Geometry in 2018 in Vietnam

How much knowledge and content to introduce and at what level to balance between Visual Geometry and Plane Geometry is an issue that needs to be perfected, through experience from practice.

Innovating teaching methods for specific Geometry content is fertile ground that creates opportunities for teachers to constantly explore and discover during the teaching process Each innovation makes the lesson content more and more suitable for students, better meeting the requirements of the curriculum.

2.2.3 Opportunities to develop classroom curriculum in teaching Geometry fromapproaches when building Geometry content in the Middle School Mathematicscurriculum

When building geometry content in the 2018 curriculum, there are two trends, two approaches: The first approach "Presenting Geometry subject is mainly descriptive -experimental, based on intuition"; The second approach - "Geometry moves from descriptive - experimental to deductive science, although it is no longer too formal and abstract like in the period of modernization of Mathematics".

For each Geometry content taught in high schools, choosing an approach that is appropriate to the cognitive capacity of students in each region, each locality, each school, and each classroom is limited Students' mistakes and shortcomings will be opportunities for teachers to develop curriculum.

2.2.4 Opportunities to develop classroom curriculum in teaching Geometry from changesin Geometry content in the Middle School Mathematics curriculum after and before 2018in Vietnam

The Mathematics Curriculum in the general education curriculum (issued on December 26, 2018) also determined the content of the knowledge circuit "Geometry and