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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 THE THESIS WAS COMPLETED AT HANOI NATIONAL UNIVERSITY OF EDUCATION Science instructors: PhD Vu Dinh Phuong 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 LIST OF RESEARCH WORKS 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 (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 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 Research purpose Proposing a design process and some measures to use authentic assessment in teaching Mathematics towards competence development for elementary school students 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 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 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 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 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 Contributions of the thesis Theoretical value - Systematize and clarify a number of theoretical issues on assessment and authentic assessment - Contribute to affirming the meaning and role of authentic assessment in teaching in general and teaching Mathematics towards developing primary school students' competency in particular Practical value - Clarifying the current situation of assessment of subjects in primary schools, focusing on clarifying the current situation (Advantages and disadvantages) of assessment in teaching Mathematics in the direction of developing competency according to the requirements of the General Education Program 2018 - 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 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 chapters: Chapter Theoretical basis for designing and using authentic assessment in teaching towards competence development for elementary school students Chapter Current status of design and use of authentic assessment in teaching towards competence development for elementary school students Chapter Design process and measures to use authentic assessment in teaching Mathematics towards developing competency for elementary school students Chapter Pedagogical experiments CHAPTER 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 reallife 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 10 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 CURRENT STATUS OF DESIGNING AND USING AUTHENTIC ASSESSMENT IN TEACHING MATHEMATICS IN ORDER TO DEVELOP COMPETENCY FOR PRIMARY SCHOOL STUDENTS 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 11 * Survey subjects: Primary teachers directly participating in teaching Mathematics in primary schools; Heads and deputy heads of professional teams at primary schools * Survey time: from May 2021 to September 2021 2.1.2 Survey content : Find out the awareness and skills of teachers in assessing mathematical abilities of primary students in teaching Mathematics, the current status of teachers' activities in assessing mathematical abilities for primary students, the awareness and current status of using activities in assessing mathematical abilities of primary students in teaching Teaching Mathematics in the direction of developing competency for primary school students 2.1.3 Survey method 2.1.3.1 Survey method by questionnaire 2.1.3.2 Interview and conversation methods 2.1.3.3 Survey method through studying learning records in elementary schools 2.1.3.4 Statistical methods and survey data processing 2.2 Analyze the results of the current situation survey a) Advantages: Most teachers have been trained on assessment in teaching toward developing competency recently Teachers can somewhat distinguish between assessing abilities and assessing skills Most teachers have used a variety of assessment methods and tools quite often and have not encountered many difficulties during use Most teachers have learned about authentic assessment through training programs on assessment, colleagues, and documents Besides, teachers also show confidence in designing and using assessment in Mathematics teaching activities in the direction of developing students' competency in practice b) Difficulties: Teachers still have difficulties in choosing and designing assessment tasks in general and assessment tasks in particular to assess the achievement of teaching goals; determine assessment criteria and standards; not clearly understand the characteristics of the assessment task Most teachers are not equipped with the design process and the process of using assessment in teaching in the direction of developing students' competency CHAPTER PROPOSING DESIGN PROCESS AND MEASURES OF USING AUTHENTIC ASSESSMENT IN TEACHING MATHEMATICS TO DEVELOP COMPETENCY FOR PRIMARY SCHOOL STUDENTS 3.1 The process of designing authentic assessment in teaching mathematics to develop competency for elementary school students 3.1.1 Principles of designing authentic assessments in teaching Mathematics to develop competency for elementary school students 3.1.1.1 Ensuring the requirements to be met and the objective of assessing mathematical competency according to the requirements of the general education program (2018) 12 3.1.1.2 Ensure the specificity of authentic assessments 3.1.1.3 Ensure compatibility with elementary school students 3.1.2 The process of designing authentic assessment in teaching Mathematics to develop competency for elementary school students Prepare phase Implementation phase Feedback phase Step 1: Determine the object, goal, and time of assessment Step 6: Assign authentic assessment tasks Step 10: Organize self assessment, peer review Step 2: Determine assessment standards Step 7: Unify criteria for authentic assessment Step 11: Comment Step 3: Design authentic assessment tasks Step 8: Organize the implementation of authentic assessment task and collectevidence Step 12 : Organize reflection Step 4: Develop authentic assessment criteria Step 9: Organize reports on implementation results and collect evidence Step 5: Choose and design authentic assessment tools Diagram The process of designing authentic assessment in teaching Mathematics to develop primary school students' competency 3.1.3 Instructions for using the process of designing authentic assessment in teaching Mathematics to develop competence development for elementary school students 3.1.3.1 Preparation phase Step 1: Determine the object, goal, and time of assessment After determining the assessment object, teachers use the Mathematicscurriculum to select the appropriate knowledge unit for the assessment object In the Mathematics curriculum, the contents with the requirements to be achieved develop from low to high and in parallel 13 determine the expression of the mathematical competency element at each educational level Therefore, when designing assessment in teaching Mathematics in elementary schools, teachers also need to determine the elements of mathematical competency corresponding to the requirements to be achieved by the unit of knowledge in the general curriculum of Mathematics (2018) , primary Teachers rely on the requirements of the unit or topic to be met, helping authentic assessment to be linked to the Mathematics curriculum in elementary schools and have practical meaning To set authentic assessment for the right activities that need to be assessed, teachers consider the specific requirements to be met for each activity in the lesson corresponding to the requirements to be met that have been selected for assessment Step 2: Determine the standards to assess Once you have determined the mathematical competency that needs to be assessed in step 1, the teacher will rely on the component capacities that make up that mathematical competency to determine the standards that need to be assessed Step 3: Design the authentic assessment task Teachers list activities and behaviors that may appear in practice, meet practical needs and correspond to the assessment standards identified in step Besides, teachers need to pay attention to the context and the Real situations give rise to behaviors and activities to supplement the content of authentic assessment tasks The requirements for expressing the results of the assessment task are written based on the requirements of the situation selected above in a real-life context and based on the requirements for expressing the component competencies of the selected mathematical competencies for Evaluate Step : Develop authentic assessment criteria In order for teachers to be able to build and use competency assessment criteria, they need to complete a specific assessment criteria table, describe the corresponding student behaviors and closely match the requirements of the assessment task Criteria for authentic assessment, in addition to having to be based on the assessment standards in step 2, must also be based on the content of authentic assessment tasks developed in step Teachers can determine criteria for authentic assessment based on the following specific steps: Determine criteria for authentic assessment based on the following specific steps: Assessment criteria are based on the assessment standards determined in step Then, adjust and supplement the assessment criteria determined based on the authentic assessment task in construction in step Step : Select and design assessment tools When determining the goal of evaluating mathematical ability, teachers should choose tools to evaluate students' processes and products such as observation sheets of the implementation process, products, and product assessment forms such as tables tests, rubric tables, level scales, etc Then, based on the standards and criteria described based on the content of the assessment task, teachers design the content of the assessment sheets 3.1.3 Implementation phase Step - Assign authentic assessment tasks During this stage, teachers need to help students understand the context and requirements of the assessment task associated with practice Therefore, teachers also need to 14 use language that is easy to understand, suitable for students' ages, or simply and realistically realize the task so that students feel that the context and requirements of the task are close, interesting, and within their ability children's performance skills authentication assessment criteria In this step, teachers can provide a pre-built criteria table or ask some suggested questions surrounding the authentic assessment tasks and the standards of the assessment goals identified in the authentic assessment design section The teacher records the answers and agrees on a number of criteria focusing on the assessment standards and goals that the teacher has identified in the assessment design part Step – Organize the implementation of authentic assessment tasks and collect evidence Teachers organize students to perform authentic assessment tasks in groups or individually During that process, teachers observe and collect evidence and information based on behavioral manifestations according to plans and tools built to evaluate students' mathematical abilities Step – Organize a report on the results of implement the authentic assessment task and collect evidence After the specified time expires, the teacher organizes representatives of each group or a few students to present the products they have made and how to implement the products From there, teachers supplement or re-evaluate the information and evidence they have collected in the step of organizing students to perform the authentic assessment task 3.1.3.3 Feedback phase Step 10 – Organize self-assessment and peer assessment After students report the results of performing the assessment and assessment task, the teacher organizes for students to use the assessment form with the authentic assessment criteria agreed in step to conduct self-assessment and peer assessment Step 11 - Comments Teachers receive assessment products and tools that students have used to supplement evidence for assessment activities After that, the teacher gives feedback and comments to students after synthesizing and analyzing the information obtained from the process of observing students, the products of the assessment task and the assessment tool obtained in the previous step Step 12 - Organize reflection Teachers will use the results of student assessment to help teachers reflect on the effectiveness of teaching students' mathematical knowledge and skills according to the requirements to be achieved and the students' ability to apply knowledge and skills in situations 3.1.4 Some examples illustrate the process of designing assessment assessment in teaching Mathematicsto develop competency for elementary school students 3.1.5 Conditions for implementing regulations The design process evaluates accurately practice in teaching Mathematics in the direction of developing competency for elementary school students 3.1.6 Some content in the 2018 Mathematicscurriculum can be evaluated accuracy 15 3.2 Proposing some measures to use authentic assessment in teaching Mathematics towards developing competency for elementary school students 3.2.1 Strengthen the organization for students to approach situations in real or simulated contexts when organizing and carrying out assessment tasks 3.2.1.1 Goals and basis for proposed measure 3.2.1.2 Content and implementation Here are some ways to it: Method : Create conditions for students to experience space, real contexts or simulate real contexts Method : Use documentaries or real-life information Method : Organize students to role-play solving situations in the assessment task Method : Provide facilities, utensils, some working tools, in real life 3.2.2 Provide meaningful feedback on student learning when implementing authentic assessments 3.2.2.1 Goals and basis for proposed measure 3.2.2.2 Content and implementation Teachers need to identify detailed instructions or assessment scales for each assessment task During the implementation phase, teachers share, discuss and agree with students in front of the class on expected results and criteria expressed in assessment forms before organizing students to perform assessment tasks The assessment criteria in the selfassessment and peer-assessment sheets used by students, although different in the way of using and expressing appropriate language for students, must have the same content as the assessment criteria in the student assessment sheet One of the principles of feedback in assessment is to focus on behavior, not people This comment principle also needs to be agreed upon with students when conducting peer assessment During assessment, teachers also need to give timely comments and feedback to suggest students improve their learning results in the future, instead of criticizing what students have done 3.2.3 Use a combination of assessment tools when implementing authentic assessments 3.2.3.1 Goals and basis for proposed measure 3.2.3.2 Content and implementation Authentic assessment in teaching Mathematics in the direction of developing competencies is used in assessing the process of teaching Mathematics To collect information about mathematical competency components, one cannot use just one assessment tool Arranging the day's activities in chronological order will help children use their time more effectively Create your Saturday morning timetable by writing the activities you will do, arranging them in order and choosing the appropriate time for each activity Below are different time clocks You can choose the time clock suitable for each of your Saturday morning activities to attach to the timetable: 16 With the above task of authentic assessment, teachers need to use many assessment tools to collect evidence for assessing the specific assessment criteria below: Table 3.16 Select assessment tools Assessment criteria Assessment tools 1.1.1 Point out the facts and requirements of the Question, assessment task that needs to be performed Assessment form 1.1.2 Ask some questions about arranging a suitable Assessment form time for Saturday activities 1.2.1 List some activities on Saturday mornings in Question, the appropriate order Assessment form 1.2.2 Select the correct time on each watch suitable Product, for each activity mentioned Assessment form 1.3.1.Arrange activities corresponding to time in a Product, reasonable manner Assessment form 1.3.2 Present the entire process of arranging Product, activities with corresponding time according to the Assessment form requirements of the task 1.4.1 Evaluate whether the arrangement of Saturday Assessment form, morning activities at the corresponding time meets self-assessment, peer assessment the requirements of the task or not 1.4.2 Show experience in arranging daily activities Assessment form, with appropriate time self-assessment sheet From the above examples, it can be seen that in order to collect complete information corresponding to each assessment criterion as a basis for giving feedback on the expression of component abilities of mathematical abilities, teachers need to use a combination of many assessment tools This is the basis for teachers to give accurate feedback to students, support students in improving their Mathematicslearning, and at the same time self-evaluate their own teaching effectiveness Thanks to that, students' mathematicslearning results are improved CHAPTER PEDAGOGICAL EXPERIENCE 4.1 Experimental purpose Evaluate the feasibility and effectiveness of the design process and some measures to use assessment in teaching Mathematics in the direction of developing competencies for students' Mathematicslearning results 4.2 Location and time of experiment 4.2.1 Location: The experiment was conducted at a number of primary schools in Binh 17 Duong province 4.2.2 Experimental time 4.2.2.1 Experiment round 1: from January 2022 to May 2022 4.2.2.2 Experiment round 2: from March 2023 to May 2023 4.3 Experimental content 4.3.1 Experiment round : Designing a survey to evaluate authentic assessment designed according to the process and a questionnaire to survey opinions on a number of measures to use authentic assessment in teaching Mathematics towards developing competency for primary school students ; Discuss with some teachers about the design process and some measures to use assessment in teaching Mathematics in the direction of developing competency for elementary students ; Require teachers to design assessment in teaching Mathematics in the direction of developing competency for elementary students according to the process ; Organize testing of a number of teaching plans using assessment that teachers design and apply some proposed measures in some grades and of Binh Chuan and Hoa Phu primary schools to evaluate the feasibility of the method process and some proposed measures 4.3.2 Experiment round 2: Discuss with some teachers about the design process and some measures to use assessment in teaching Mathematics in the direction of developing competency for elementary students; Require teachers to design assessment in teaching Mathematics in the direction of developing competency for elementary students according to the process; Use the survey above to get the opinions of some experts on authentic assessment in teaching Mathematics in the direction of developing competency for elementary school students that teachers have designed; Organize students to take entrance tests; Organize testing of a number of teaching plans using assessment that teachers design in the process of teaching Mathematics in some grades and of primary schools representing regions (city, town, district) of Binh Duong province to evaluate the effectiveness of the process and some proposed measures; Collect data from observing the experimental process; Organize students to take exit tests; Analyze the collected data to evaluate the impact of the process of designing assessment assessment and some measures of using assessment assessment in teaching on mathematicslearning outcomes of students 4.4 Experimental object 4.4.1 Experiment round primary school teachers are teaching grades and at Hoa Phu primary school and Binh Thuan primary school (in Thu Dau Mot city and Di An city) in Binh Duong province These teachers all have university degrees majoring in Primary Education 176 students (including 87 grade students and 89 grade students), from Binh Chuan primary school and Hoa Phu primary school 4.4.2 Experiment round 2: primary school teachers are teaching grades and at some primary schools in Binh Duong province These teachers all have university degrees majoring in Primary Education