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MINISTRY OF EDUCATION AND TRAINING

HANOI NATIONAL UNIVERSITY OF EDUCATION

NGUYEN THI THU TRANG

DESIGNING AND USING AUTHENTIC ASSESSMENT

IN TEACHING MATHEMATICS TOWARDS COMPETENCE DEVELOPMENT FOR PRIMARY SCHOOL STUDENTS

Specialization : Theory and methods of elementary school teaching

Code : 9.14.01.10

SUMMARY DOCTORAL THESIS IN EDUCATIONAL SCIENCE

HANOI - 2024

HANOI NATIONAL UNIVERSITY OF EDUCATION

Science instructors:

1 PhD Vu Dinh Phuong

2 Associate Professor Dr Tran Ngoc Lan

Opponent 1: Prof Dr Tran Trung

National Academy

Opponent 2: PhD Le Tuan Anh

Hanoi National University of Education

Opponent 3: Assoc Prof Tran Viet Cuong

Thai Nguyen University - University Of Education

The thesis will be defended in front of the School-level Thesis Examination

Committee at Hanoi National University of Education

at … hour … day … month… year…

The thesis can be referred to the following libraries:

- National Library of Vietnam

- Library of Hanoi National University of Education

OF THE AUTHOR RELATED TO THE THESIS

[1] Nguyen Thi Thu Trang, Vu Dinh Phuong (2021), Characteristics of authentic

assessment tasks in teaching Mathematics towards developing competency for elementary school students , Hanoi University of Pedagogy Magazine, April 2021 [2] Nguyen Thi Thu Trang (2022), Proposing an authentic assessment procedure

in teaching Mathematics in elementary schools according to STEM education orientation , Teachers Magazine, No 184 (August 2022), p 80 – 83, ISSN

1859 – 2902

[3] Nguyen Thi Thu Trang (2022), Awareness of primary school teachers on

authentic assessment's tasks in teaching Maths in the direction of competence development for primary school students – Case study in Binh Duong province of Vietnam , International Journal of Social Science and Human Research , Volume

06 Issue 01 January 2023, p 108 – 114, ISSN 2644-0695

[4] Nguyen Thi Thu Trang (2023), The process of designing authentic assessment in

teaching Mathematics towards developing competency for elementary school students Vietnam Journal of Educational Sciences, Volume 19, Number 4 (2023), ISSN 2615-8957

[5] Nguyen Thi Thu Trang, Vu Dinh Phuong (2023), Building authentic assessment

criteria in teaching Mathematics in the direction of competence development for primary students, Knowledge and Learning Magazine, Publishing House

Inderscience ( accepted for publication )

[6] Nguyen Thi Thu Trang (2022), Current status of determining authentic

assessment criteria in teaching Mathematics towards developing competency for elementary school students, Teachers Magazine, No 195 (July 2023), p 22 – 26,

ISSN 1859 – 2902

INTRODUCTION

1 Reason for choosing the topic

(1) Derived from the role and goals of Mathematics

Mathematics is considered one of the mandatory subjects in the 2018 general education program This program also states the requirements for the basic stage of

Mathematics, which is “helps students systematically understand the most necessary

mathematical concepts, principles, and rules for everyone, as a foundation for learning at the next learning levels or can be used used in everyday life" [1] Mathematics also focuses on developing specific abilities such as mathematical ability including the following core components: mathematical thinking and reasoning ability; mathematical modeling competency; mathematical problem solving ability; mathematical communication competency; ability to use tools and means to learn mathematics These are important skills that help students not only access mathematical knowledge and problem solving skills but also be able to solve situations in life

(2) Originating from the requirement to innovate assessment in high schools to meet the 2018 general curriculum

Resolution 29 of the 8th Central Conference, session XI in 2013 on Fundamental and

comprehensive innovation in education and training also sets out requirements for innovating

forms and methods of examination, testing and evaluating educational results according to direction for assessing learners' abilities; Combine regular assessment with periodic assessment

at the end of the semester or school year following the model of countries with developed education The change in assessment is also clearly affirmed in Circular 27/2020/TT-BGDDT, promulgating Regulations on assessment of elementary school students, emphasizing the assessment of the formation and development of students' qualities and abilities The information collected from assessment activities for elementary school students not only helps

students " determine the level of student completion of learning and training tasks according to

the requirements to be achieved and specific manifestations of the Competency components of each subject and educational activities are specified in the primary school general education program and the formation and development of student qualities and abilities [but also] timely adjustment of the process teaching, supporting, and promoting students' progress according to

primary education goals

(3) Derived from the practice of assessment activities in elementary schools in teaching towards developing competency for students

In practice, current primary school teachers have also changed their perception of assessment They not only focus on summative assessment (periodic assessment) but also pay attention to process assessment to provide more accurate comments about students However, elementary school teachers still encounter many difficulties and confusion when assessing learners' competency on the basis of identifying manifestations of competency in teaching content and in the implementation context When conducting assessments, most teachers only care mainly for the purpose of evaluating student learning outcomes compared

to program requirements

(4) Derived from the role of authentic assessment in teaching towards developing competency for students

Authentic assessment is one of the forms of assessment that receives attention to evaluate students' learning process Authentic assessment has been researched and used in a number of high school subjects around the world According to Mueller (2005) , authentic assessment directly measures students' knowledge and skills through practical learning tasks that students perform In their study , Fook and Sidhu believes that authentic assessment is welcomed by students and needs to become part of the teaching cycle In authentic assessment , students approach practical problems that need to be solved, and teachers will give feedback to help students evaluate their strengths and weaknesses, identify their current abilities as well as need to practice Focus on developing weak capabilities

The above analysis shows that assessment in learning in general and learning Mathematics in particular has many suitable points to evaluate the goals and requirements to

be achieved in terms of mathematical competency in Mathematics Curriculum 2018 Mathematics assessment has been noticed and applied to teaching a number of subjects at vocational schools, universities, and high schools in some countries around the world In Vietnam, assessment has also begun to be researched and applied, but mainly in teaching university students In elementary school, the use of assessment in general and assessment

in teaching Mathematicsto develop students' competency has not been paid attention

Based on some theoretical bases and current situations mentioned above , the

implementation of the research topic "Designing and using authentic assessment in

teaching Mathematics towards competence development for elementary school students ”

is truly necessary

2 Research purpose

Proposing a design process and some measures to use authentic assessment in teaching Mathematics towards competence development for elementary school students

3 Objects and subjects of research

 The objects of research: Assessment activities in teaching Mathematics in

elementary schools

 The subjects of research: Some theoretical foundation issues on authentic

assessment; The process of designing authentic assessments and some measures to use authentic assessments in teaching elementary mathematics contribute to improving results

study this subject

4 Scientific hypothesis

If we propose a design process and some measures to use authentic assessment in teaching Mathematics in the direction of developing competency for elementary school students and apply the process and some of the above measures in a flexible way, ensuring specific principles and conditions will contribute to improving learning outcomes in this subject

5 Research tasks

The thesis focuses on performing the following tasks:

 Research, compare, analyze, and synthesize theoretical perspectives and authentic assessment approaches in teaching in general, and teaching Mathematics in the direction of developing primary school students' competency in particular

 Propose a design process and some measures to use authentic assessment in teaching Mathematics in the direction of developing competency for elementary school students

 Organize experiments to test the feasibility and effectiveness of the process and some proposed measures

6 Scope of the topic

 Research on the issue of authentic assessment in teaching Mathematics in the direction of developing primary school students' competency to improve students' Mathematicslearning results

 The topic focuses on surveying the current situation in some primary schools in Binh Duong province

 The topic focuses on experiments on 3rd and 4th grade students in some primary schools in Binh Duong province; Organize assessment through a number of contents: Some statistical elements (grade 3), Measurement - Calculation and estimation with quantitative measurements (grade 4) of the 2018 MathematicsGeneral Education program

7 Research methodology and methods

The project will use the following research methods:

 Theoretical research methods

 Investigation methods using surveys, interviews, and observations

 Professional solution

 Experimental methods of pedagogy and mathematical statistics

8 Contributions of the thesis

- Developing a design process and propose some measures to use authentic assessment in accordance with the 2018 Mathematics Education Curriculum

- The research results in the thesis can be used for teachers as a reference in assessment activities when teaching Mathematics in the direction of developing competencies for elementary school students

9 Arguments presented in defense

 The use of assessment in teaching Mathematics in primary schools is necessary and consistent with the current trend of educational innovation

 Authentic assessment are consistent with the requirements for reforming assessment in teaching in the direction of developing students' abilities

 The feasibility and effectiveness of the design process and some measures to use authentic assessment in teaching Mathematics in the direction of developing competency for elementary school students contribute to improving learning outcomes in high school Mathematics elementary

10 Structure of the thesis

In addition to the Introduction, Conclusion, References and Appendices, the thesis includes 4 chapters:

Chapter 1 Theoretical basis for designing and using authentic assessment in teaching

towards competence development for elementary school students

Chapter 2 Current status of design and use of authentic assessment in teaching towards competence development for elementary school students

Chapter 3 Design process and measures to use authentic assessment in teaching Mathematics towards developing competency for elementary school students

Chapter 4 Pedagogical experiments

CHAPTER 1 THEORETICAL BASIS FOR DESIGN AND USE OF AUTHENTIC ASSESSMENT

IN TEACHING MATHEMATICS TOWARDS COMPETENCE DEVELOPMENT

FOR PRIMARY SCHOOL STUDENTS 1.1 Overview of the research issue

1.1.1 Some studies on assessment in teaching toward developing competency

1.1.1.1 Research on the origins of assessment in teaching toward developing competency

In 1984, Frith and Macintosh focused on researching how to guide teacher assessment in the classroom Besides, Shepard (2000) believes that constructivism has a positive impact on assessment change Assessment is one of the factors that support learning activities instead of just focusing on measuring the learning results that students achieve Assessment is important to the development of each individual and this is also the basis for teachers to evaluate learners' abilities Since the late 20th century, competency assessment has become the current assessment trend to meet the labor needs of society

1.1.1.2 Research methods and assessment tools in teaching toward developing competency

According to Paul Black, Dylan Wiliam (1998), researchers on assessment in education, said that: some researchers emphasize that in order for competency-based assessments to have the required quality, teachers must use Coordinate many assessment methods, forms, and tools Authors Baartman, Prins, Kirschner and van der Vleuten (2007) said that: testing and assessing student competency is an assessment activity that requires

students to demonstrate their ability by asking questions Respond in written/oral form, by participating in group activities or by self-expression, or by creating a specific product Robert Glaser (1981) deals with describing individual levels of performance after task completion with behavioral criteria; From there, infer students' abilities

1.1.1.3 Research on assessment in teaching toward developing student competency

There are many authors who have researched on assessment in teaching toward developing students' competency such as: Nguyen Cong Khanh (2017), Hoang Hoa Binh (2015), Nguyen Thu Ha (2014), Tran Ngoc Lan (2015); Chu Cam Tho and Vu Anh Tuan (2015); Nguyen Quang Thuan (2016), Nguyen Huu Hau, Pham Van Hien (2017), Le Thu Phuong (2018), Le Thai Hung , Nguyen Thi Phuong Vy (2020), Nguyen Dang Nhat (2020), Tran Hoai Phuong (2020), Le Thu Phuong (2020), Nguyen Cong Khanh and Tran Thi Ha (2020), Duong Thi Thu Huong (2021) This shows that assessment in teaching towards developing students' capacity is an issue that many scientists are paying attention to doing the research and applying in practice

1.1.2 Some studies on authentic assessment

1.1.2.1 Research on the origins of authentic assessments

In the research paper of Airasian & Russell (2007); Black & Wiliam (2009) and Boyle & Charles (2013), assessment activities are required to focus more on process assessment instead of just focusing on learning outcomes, and the implementation of tasks Assessment will support student learning Formative assessment should take place throughout the learning process, with the primary goal of providing information about the learner's progress On the other hand, assessment should be integrated into the learning process to support students' knowledge and skills The foundation for the above viewpoint is that social constructivist educators believe that learning is an active process (Tombari & Borich, 1999) Social constructivism also shares the same view with cognitive theory, emphasizing that learning is formed from practical situations (Brown , Collins and Duguid, 1989; Herrington and Oliver, 2000; Kim, 2011)

The term authentic assessment was mentioned by Archbald and Newmann in 1988 According to Wiggins (1990), assessment is an assessment activity in which students must use knowledge to demonstrate the solution of valuable situations in a timely manner effective and creative ways and incorporated into classroom assessment Later, Newman, Brandt, and Wiggins (1998) argued that assessment is called assessment when it measures meaningful products or performances that have value beyond school success At this time, Terwilliger (1998) expressed concern to Wiggins and others about the interpretation of the term, viewing assessment as a criticism of traditional assessment methods less authentic or not authentic [36] Cumming and Maxwell (1999) have shown the relationship between assessment and authentication results [37] In the next stage, many researchers proposed different terms and definitions of assessment, such as: Gulikers, Bastiaens, and Kirschner (2004); Jon Mueller (2005), Fook and Sidhu (2010)

Besides some researchers using the term “authentic assessment”, some authors use the phrase “performance assessment” instead of “authentic assessment” in their research, e.g Authors Darling-Hammond and Adamson (2010) However, some authors clearly distinguish

between “performance assessment” and “authentic assessment”, such as Meyer (1992), Palm (2008), Wiggins (1990)

1.1.2.2 Research on methods and tools of authentic assessment

In research on authentic assessment, some authors focus on research on assessment methods and tools Brown, Knight (1994), Kniveton (1996), Struyven, Dochy and Janssens (2005) mention a number of assessment methods such as: assessment methods through learning records, projects, conducted case studies, conduct research; write, revise and discuss articles; planning to carry out activities (Wiggins, 1990) Besides, some authors also pay attention to research on assessment tools in teaching, such as: Kerka (1995), Black & William (1998), Karge (1998), John Scott (2000), Prestidge and Williams Glaser (2000), Morris (2001) The authors have listed many tools used in assessment such as: role-playing and drama products; diagrams, maps; academic records; blueprints, data sheets, charts, timing diagrams,

1.1.2.3 Research and apply authentic assessment in practice

Darling-Hammond & Snyder (2000) ; Webb (2009); Koh (2011) ; Nguyen Thanh Nhan (2012); Doan Quang Trung (2019) Besides, assessment has been proven to have practical value when applied to assessment activities in high schools such as Baartman, Prins, Kirschner and van der Vleuten, 2007) ; Tonya R Moon, Catherine M Brighton, Carolyn M Callahan (2005) ; Azim & Khan (2012) ; Inayah, Komariah & Nasir (2019) Thomas Romberg and Linda Wilson (1995) ; Supinah (2021 )

With the meanings of assessment and the research trend on competency assessment of foreign researchers, it shows the novelty of the thesis topic and the urgency that it needs to be researched to contribute to the effective implementation of accurate assessment practice in teaching Mathematics in the direction of developing primary school students' abilities

1.2 Some theoretical issues about assessment in teaching toward developing competency

1.2.1 Some related concepts

1.2.1.1 The concept of "Assessment in education"

Inheriting the concepts of assessment in education from the authors, assessment in

education of this thesis is considered: the process of teachers collecting and processing

information through activities such as observation and monitoring , exchange, check and comment on the learning and training process of students Thanks to that, teachers can interpret qualitative or quantitative information about the results of learning, training, formation and development of some qualities and abilities of elementary school students and motivate, advise, Support students to adjust their learning

1.2.1.2 The concept of “Formative assessment”

Formative assessment in the thesis is considered an assessment activity carried out

during the teaching process to collect information about student learning Thanks to that, teachers can give accurate comments and feedback and students self-assess and peer-assess with the purpose of supporting students' learning activities, helping to improve students' learning outcomes

1.2.1.3 The concept of “Self-assessment”

Self-assessment means students self-evaluate and make judgments about the level of student achievement compared to the agreed assessment criteria From there, students identify their strengths and weaknesses and find ways to improve and enhance their learning results

1.2.1.4 The concept of “Peer Assessment”

Peer assessment is the process by which students receive information to evaluate their progress, the level of achievement of learning goals, and give comments and feedback

to their classmates Therefore, peer assessment helps students better understand their own weaknesses and strengths, reflect, and adjust their learning to achieve better learning results

1.2.3 The concept of assessment in teaching toward developing competency

Assessment in teaching towards competence development in elementary school is to assess the learning process of primary school students by requiring students to apply knowledge and skills to solve practical problems Thereby, teachers promptly comment and feedback to support students in learning activities, adjust teaching activities and students self-assess and peer-assess to improve learning Therefore, assessment in teaching towards competence development in elementary school contributes to improving learning outcomes for learners

1.2.4 The role of assessment in teaching toward developing student competency

Assessment helps teachers evaluate students' learning process based on behavioral manifestations, providing necessary feedback so students can adjust their learning; helps teachers monitor the development of students' abilities, thereby adjusting teaching and learning activities to suit students; helps students develop their potential competency, high-level thinking ability and the ability to apply knowledge and skills to solve practical problems

1.3 Some theoretical issues about authentic assessment

1.3.1 The concept of authentic assessment

In this thesis, assessment is considered as: a form of assessment used by teachers in

the process of teaching elementary school students to help teachers evaluate and students self-assess and peer-assess their ability to apply knowledge , students' Mathematicsskills through evidence collected from the process of students solving tasks associated with real- life contexts, or simulating from real-life contexts to create meaningful products or expressions means" Therefore, this form of assessment helps improve students' learning

outcomes

1.3.2 The position and role of authentic assessment

Assessment has played an important role in influencing educational innovation Assessment supports assessment activities in teaching in the direction of developing competency more effectively Applying assessment in the teaching cycle will change the way of looking at assessment, creating a positive step in innovating teaching methods, meeting the goal of forming and developing competency of the General Education program pine (2018)

1.3.3 Characteristics of authentic assessment

The task of authentic assessment must be linked to reality, requiring students to create products or expressions through the combination of knowledge and higher-level

thinking skills to solve problems; The context in assessment is often real or simulated reality; Students are the subjects of the task implementation process, requiring coordination and interaction between students and students, students and teachers Students can self-assess and monitor their personal progress or learning progress; It is necessary to use assessment criteria with indicators in assessment to provide feedback to learners Assessment criteria must be clear and built based on assessment criteria associated with practice Assessment criteria need to be disseminated in advance or students should be allowed to develop their own assessment criteria when starting to perform the assessment and assessment task

1.3.4 Authentic assessment task

The task of assessment must include issues raised in contexts related to reality; The assessment task requires students to use high-level thinking to analyze, synthesize, and apply existing knowledge and skills to solve posed problems and demonstrate creativity; Assessment tasks require students to respond by creating authentic products or quality representations; The task of authentic assessment guides the criteria for evaluating the process and results of implementation so that teachers can evaluate students and students can self-evaluate and peer-evaluate

1.3.5 Authentic assessment criteria

Authentic assessment criteria in this thesis can be understood as the concretization of assessment standards by performing authentic assessment tasks, with real contexts or simulating real contexts, and achieving results , real products, as a basis for assessing the degree to which students achieve the expected requirements of subjects, lessons, and groups of lessons

1.3.6 Several tools are used in authentication assessment

When using assessment in teaching Mathematics in elementary schools, a number of assessment tools will often be used such as: assessment tasks, assessment sheets, self-assessment sheets, rubric tables (built based on the criteria) authentic assessment criteria), data tables, charts, timelines, event sequences, design tables, management plans, research reports, study records, etc

1.3.7 Authentic assessment design process

Jon Mueller (2005) gave the steps to design assessment according to the following steps: Determine assessment standards; Designing authentic assessment tasks; Determine assessment criteria; Build assessment rubric; Grade or evaluate according to standards and adjust teaching style

Author Mohammad Syaifuddin (2020) mentioned the process teachers use when implementing assessment in teaching Mathematics for high school students including the following steps: Identify basic competencies from the program; Prepare learning indicators

of basic competencies; Developing indicators that test basic competencies; Choose an authentic assessment of knowledge, skills, and attitudes; Develop assessment rubrics

Authors Sally Brown And Kay Sambell (2022) provide steps to design assessment: Identify important learning outcomes that need to be assessed; Gradually transform learning outcomes into requirements for performing assessment tasks; Identify the impact objects of

requirements for performing assessment tasks ; Describe the subject or professional context; Identify the results and evidence collected during the assessment process

1.4 Characteristics of elementary school students

1.4.1 Psychological characteristics of elementary school students

Intentionality, mental work skills, and reflection are three psychological characteristics that create conditions for students to perform assessment tasks The driving force of the psychological development of primary school students is the resolution of the conflict between the psychological level they have achieved and the new requirements of school life (especially learning activities) placed before them Therefore, when implementing authentic assessment in the process of teaching primary school students, the authentic assessment task requirements are set before the students and are designed based on real-life contexts Some conflicts will appear during the resolution process problems, and create motivation for the psychological development of primary school students And this motivation is also the condition that stimulates children's desire to perform the tasks of authentic assessment

1.4.2 Cognitive characteristics of elementary school students

The imaginative characteristics of elementary students support the implementation of the task of authentic assessment in a more convenient way The real context can be the context students have experienced or the context they are experiencing for the first time Language is very important to pay attention to when developing assessment tasks and criteria so students can self-assess in assessment If you do not pay attention to the level of language development at each age level, it will lead to students not understanding the task, causing obstacles for them in performing the task and assessment criteria Involuntary attention in thriving children Therefore, teachers should provide clear learning tasks, associated with real-life problems, with appropriate time and suggestions and instructions that will encourage students to complete the tasks well This characteristic shows that the use of assessment in evaluating primary school students is reasonable, because assessment tasks associated with real-life problems will help students be interested and attracted to the process of performing the task

1.5 Authentic assessment in teaching Mathematicsto develop competency in elementary schools

1.5.1 The concept of authentic assessment in teaching Mathematics to develop competency for elementary school students

Assessment in teaching Mathematics in the direction of developing competency for

primary students is understood as: a form of assessment in which teachers organize for primary

students to apply existing Mathematicsknowledge and skills to solve an authentic task related to mathematics with a real-life context, or imitate from a real-life context and create a meaningful product or expression This form of assessment also requires students to self-assess based on the authentic assessment criteria agreed upon with the student before performing the authentic assessment task Therefore, this form of assessment not only evaluates mathematical ability but

also becomes more meaningful for the development of students' mathematical ability

1.5.2 Assessment requirements in teaching Mathematics to develop competency for

elementary school students

Teachers perform formative assessment (or regular assessment) in combination with parent assessment, self-assessment, and peer assessment Teachers carry out the assessment process to record the results achieved in the process of performing students' actions to demonstrate the assessment of general and mathematical abilities, including: thinking and mathematical abilities mathematical reasoning, mathematical modeling competency, mathematical communication competency, competency to use mathematical learning tools and means

1.5.2 Objectives and content of the 2018 General Education Mathematics program at the elementary level

1.5.2.1 Objectives of the 2018 General Education Mathematics program at the elementary level

In the 2018 General Education program, primary school mathematics subjects state the following teaching objectives:

a) Contribute to the formation and development of mathematical competency with required requirements

b) Have basic, essential mathematical knowledge and skills in: Numbers and calculations, Geometry and Measurement, Statistics and Probability

c) Along with other subjects and educational activities such as: Ethics, Nature and society, Experiential activities, contribute to helping students have initial understanding of some careers in society

1.5.2.2 Content of the 2018 General Education Mathematics program at the elementary level

The content of the 2018 General Education program at the elementary level includes three content streams: Numbers and calculations, Geometry and Measurement, Statistics

and probability

1.5.3 Ability to apply authentic assessment in teaching Mathematics towards developing competency for elementary school students

1.5.3.1 Some guiding documents

1.5.3.2 Mathematics and authentic assessment in teaching Mathematics towards developing competency for elementary school students

CHAPTER 2 CURRENT STATUS OF DESIGNING AND USING AUTHENTIC ASSESSMENT IN TEACHING MATHEMATICS IN ORDER TO DEVELOP COMPETENCY

FOR PRIMARY SCHOOL STUDENTS

2 1 Overview of the current situation survey

2.1.1 Purpose, subjects, survey time

* Survey purpose: to show the current state of teachers' awareness and the current

state of authentic assessment activities in teaching Mathematicsfor competence development for elementary school students in Binh Duong province