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HANOI NATIONAL UNIVERSITY OF EDUCATION

-DO DUC BINH

TEACHING GEOMETRY IN LOWER-SECONDARY SCHOOLS WITH

A FOCUS ON CURRICULUM DEVELOPMENT AT

THE CLASSROOM LEVEL

Major: Theory and Methods of Teaching Mathematics

Code: 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 the

University 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,

1 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 ofGeometry 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, especiallylacking research on “teaching Geometry in lower-secondary schools with a focus oncurriculum development at the classroom level”

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

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

2 Research objectives

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

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

schools

4 Scientific hypothesis

On the basis of theory and practice on the development of the Mathematicscurriculum at the classroom level, if teachers understand and implement classroomcurriculum development activities right in the process of preparing lesson plans, studyinglessons, in the process of teaching Geometry in lower-secondary schools, teaching resultswill be improved, and at the same time, practically contribute to the curriculumdevelopment 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 tothe 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 curriculumdevelopment at the classroom level in particular? What are the manifestations ofcurriculum 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 schoolswith 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 bothfeasible 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-secondaryschools with a focus on curriculum development at the classroom level

Chapter 4 Pedagogical experiment

Chapter 1 Theoretical basis 1.1 Overview of research related to the topic

1.1.1 In the world

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

a) On general matters

Research on general issues of curriculum development can include the work of KieranEgan, Robert Diamond and especially the work of Peter F Oliva In his work, Peter F Olivadiscussed quite carefully the concepts related to the curriculum (chapter 1), the principles ofcurriculum construction (chapter 2); curriculum planning – a multi-level, multidisciplinaryprocess (including classroom level, team and subject level, school level, local level, nationallevel, 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 thecurriculum building models, the curriculum's goals and objectives, the curriculumorganization and implementation, and the curriculum evaluation

Many other works can be mentioned such as the textbook “development of schoolcurriculum”, monograph of Floyd G Robinson, John A Ross, Floyd White, Colin J Marshand 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 curriculumdevelopment (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 strategicframeworks and thinking about curriculum development from the national to the classroomlevel 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 schoolcurriculum 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 thedevelopment of the junior high school geometry curriculum, only a few works related to thegeometry learning of junior high school students.

1.1.2 In Vietnam

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

A further study on the theory of curriculum development, including the works ofNguyen Huu Chau (2005), Tran Huu Hoan (2011) there have been a number of scientificconferences organized by the Ministry of Education and Training, focusing on innovation ofgeneral 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 on building general education curriculums after 2015 ", with 54 reports.

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

Meanwhile, there is an urgent immediate and long-term need for specific research tohelp 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 Thecurriculum is the totality of practical knowledge provided to students so that they can gainknowledge and skills in many places Curriculum can include syllabus (curriculum of eachcourse) 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 curriculum

is an overall blueprint for a training activity (which may last a few hours, a day, a week or years) That master design tells us all about the content to be trained, specifies what we can expect from the learners after the course; it outlines the process required to deliver the training content; It also tells us about the training methods and the methods of testing and evaluating the learning outcomes and all of that is arranged according to a tight timetable.”

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 toprincipals and teachers: Parents' unions, the business community, trade unions, politicalparties, 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 curriculumlevels 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: Classifyingaccording to the hierarchy in curriculum development, highly centralized curriculums ordecentralized curriculums (national, local, school level); or effective categorization andcurriculum implementation progress

a) Intended curriculum, implemented curriculum, attained curiculum

b) 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 theteacher's activities mainly take place within the classroom, with little connection to thecurriculum Related to the national curriculum, the local curriculum, the school curriculum.furthermore, the most important criterion for an educational curriculum is that thecurriculum 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 urgencyand 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 an individual teacher that is built on the basis of regulations of the national curriculum, local curriculum, 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 curriculumeach teacher can make different decisions about the curriculum, what to teach, and how toteach This is the stage where the training curriculum proposed in the plan turns into atraining curriculum that is implemented and tested The concept of the classroom curriculumabove is consistent with the "openness" and "autonomy" of the curriculum Teachers canpromote 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, therewere studies showing the role of teachers in curriculum development and affirming thatteachers are not just "workers " or “ technicians” execute curriculums from central or localregulatory documents Since 2000, there have been studies on the classroom curriculum Inthe world, people have different names for the concept of classroom curriculum: “classroomcurriculum”, “ curriculum in classroom”, “ curriculum for classrooms teaching”,… InAustralia, since 2012, the Ministry of Education Queensland has developed a set of teachingmaterials 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 teachingplans, 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 curriculumdevelopment as: SUPRA – international curriculums (for example, the Common EuropeanFramework 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 Inanother work, N T Hong Nhung (2016) introduced the concept of the classroomcurriculum: A classroom curriculum is a teacher's teaching plan that may includeone/several lessons, used to guide educational activities in class or out of class, in school oroutside 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 changesfrom 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 tocomplex, from incomplete to perfect object Development has objectivity, universality,richness, diversity and inheritance

We believe: Curriculum development is the process of changing the curriculum ormaking the curriculum more and more complete, more suitable for educational goals andwith 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 isincreasingly 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 aproduct 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 nationalcurriculum 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); anddetermine implementation methods that reflect characteristics and are consistent with schoolpractices, modern requirements and achievements (in educational science, technology, etc.);

to meet the requirements of developing learners' qualities and abilities, effectivelyimplementing 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's life would be extremely boring if they could not come up with a decision about the curriculum If teachers espouse the axiom of “change is inevitable and never ending” they will 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, selectcontent, teaching methods, learning resources, lesson plans, etc to meet all the differencesindividually in the classroom This work includes curriculum evaluation

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

The four characteristic signs of classroom curriculum development are described morespecifically 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 morecommon

- More suitable: more suitable for students' psychology and cognitive ability, theknowledge fits together and is more interconnected; Attract more students to participate inlearning activities, raise students' awareness level from low to high, help students solveproblems from easy to difficult

- More effective: has a result more than what is desired or expected, has greaterefficiency, 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 at the 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 developingstudents' abilities, giving students opportunities and the ability to self-discover, self-possessknowledge, 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 curriculummanagement institution, which is a major, revolutionary change in the design andmanagement of a curriculum, depending on the design and use objects Curriculum is ofteninterpreted at the following levels: National Curriculum, Local Curriculum, SchoolCurriculum and Classroom Curriculum This is also the model chosen in many countrieswith developed market economies in the years since the 1970s

As stated above, the term curriculum development has only been officially used inVietnam in the past ten years However, along with the development of the country, theeducation sector in general and curriculum in particular have also had changes related tocurriculum development, which are summarized in the form of educational experience Thiscan 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 theautonomy 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 beenstudied and interested by countries Up to now, general education curriculum developmenthas become a discipline, a subject Vietnam has been interested in this issue since the earlyyears of the twentieth century There have been many published works related to curriculumdevelopment

Teachers have an important role in the development of the curriculum, which isreflected 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 itclassroom-level curriculum development

Chapter 2 Practical 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 generaleducation 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 – changingtowards 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, termviii, in accordance with the subdivision orientation Revised the general educationcurriculum twice in 2002 and 2018

2.1.2 Curriculum development in Vietnam

Starting from the 2013-2014 school year, the development of the general schooleducation 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 in Vietnam

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

the policy of “a unified but flexible general education curriculum; the curriculum ensures a uniform orientation and core educational contents, which are compulsory for students nationwide, and at the same time empowers local authorities and schools with initiative and responsibility in selecting and supplementing a number of curriculums Educational content and implementation of educational plans suitable to the educational subjects and conditions

of the locality, of the educational institution, contributing to ensuring the connection of the school'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 classroom curriculum development

2.2.1 Opportunities to develop classroom curriculum in teaching Geometry from reviewing the content of Middle School Geometry knowledge in Vietnam and some countries around the world before 2018

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

2.2.2 Opportunities to develop classroom curriculum in teaching Geometry from issues

in building the content of Middle School Geometry in 2018 in Vietnam

How much knowledge and content to introduce and at what level to balance betweenVisual Geometry and Plane Geometry is an issue that needs to be perfected, throughexperience from practice

Innovating teaching methods for specific Geometry content is fertile ground thatcreates opportunities for teachers to constantly explore and discover during the teachingprocess 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 from approaches when building Geometry content in the Middle School Mathematics curriculum

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

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

2.2.4 Opportunities to develop classroom curriculum in teaching Geometry from changes

in Geometry content in the Middle School Mathematics curriculum after and before 2018

in Vietnam

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