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MINISTRY OF EDUCATION AND TRAINING VINH UNIVERSITY PHAM THI KIM CHAU DESIGNNING AND USING LEARNING SITUATIONS TO SUPPORT THE ASSESSMMENT OF CALCULATION CAPACITY OF SENIOR PRIMARY SCHOOL GRADERS THROUGH EXPERIENTIAL ACTIVITIES Major: Theories and Methodologies in teaching Maths Code: 9.14.01.11 SUMMARY OF DOCTORAL DISSERTATION ON EDUCATIONAL SCIENCE NGHE AN - 2019 This dissertation was ompleted in: VINH UNIVERSITY Scientific supervisors: Prof PhD DAO TAM PhD PHAM XUAN CHUNG Reviewer 1: Assoc Prof PhD Nguyen Thi Kim Thoa Reviewer 2: Assoc Prof PhD Tran Ngọc Lan Reviewer 3: PhD Thai Huy Vinh The dissertation was successfully defended at the Boards of Examiners of Univeristy level, in Vinh University, No 182, Le Duan Street, Vinh city, Nghe An province at……., on……… 2019 This dissertation is available at: National Library of Vietnam The Information Center – Library of Nguyen Thuc Hao, Vinh University INTRODUCTION Motivation of the study Primary school is the foundation level, students inherit preschool calculation operations such as: Counting, measuring, estimating, surveying, predicting, Students' thinking which bears experience, perception often base on activities with visual objects or models Therefore, in teaching as well as in assessment, it is necessary to create opportunities for students to take part in and experience The 2018 general education program for Math emphasizes the need to create opportunities for students to experience Math with its outstanding advantages, create many opportunities to develop students’ calculation capacity Vietnam is implementing its process of education reform The formation and development of capacity as the ultimate goal of education Talking about capacity, we touch upon all elements of the teaching process, in which assessment should be considered as a teaching activity Circular 22/2016 / TT-BGDĐT states: The assessment must be for the student's progress or for students’ study improvement and for learning activities Assessment not only allows teachers to judge whether students meet the learning requirements, but also helps students form and develop their capacity; help students realize the mistakes from which they adjust their learning activities and teachers have a foundation to adjust teaching activities The general education program in Maths emphasizes that assessing students' ability must be done by evidence that demonstrates the results achieved in the process of students’ performing actions The directive points of view are the guideline for the study of approaches to disclosure of students' abilities in the process of calculation operations Currently, coordination between students’ performance assessment and classroom teaching activities through student behavioral demonstration is an urgent issue Furthermore, the problem of learning situation design has been interested by many scientists, but the design of learning situations supporting the assessment of calculation capacity of senior primary school graders through calculation activities has not been thoroughly studied For the above reasons, we choose the research topic of the thesis: “Designing and using learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities” * Literature review Regarding to calculation capacity, in the UK, the term "numeracy" is used According to Crowther Report (1959), numeracy means broad scientific knowledge By 1976, numeracy was understood as the ability to use skills with numbers and concepts in a practical context (Callaghan, 1987) Cockcroft (1982) defines numeracy as the necessary skills and arrangements of ordinary people in work and daily life These definitions focus on skills with numbers, measurement, data processing, applying math skills to solve problems in a specific context In the US, Mathematical literacy of PISA is nearly synonymous with numeracy, emphasizing mathematical connections in many situations Cambridge's 2017 elementary mathematics program attached great importance to developing students’ calculation skills in term of four aspects : listening-observing-dong and sharing and four supporting elements: Audio learning-Visual learning-Interactive learning-Shared learning facilities In Russia, V.A Kruchetxki considers that calculation capacity is the ability to perform fast and accurate calculations, usually mental arithmetic In Australia, in National Report on Schooling in Australia (1997), the authors stated: Numeracy is an effective use of mathematics to meet the general needs of daily life, in paid work, and in community life and citizens Numeracy in practice: Teaching, learning and using mathematics emphasized on the effective teaching skills such as interdisciplinary, integrated teaching, in which mathematics has a more proactive role than other subjects In Vietnam, calculation capacity used to be understood as human understanding and confidence when using numbers and calculations Pham Van Hoan (1981) concluded that the calculation capacity was the quick and accurate performance of calculation, even in mental arithmetic Recently, the Ministry of Education and Training listed calculation capacity as tool capacity in core capacity groups The 2018 General Education Program the calculation capacity is seen as the specific capacity of students of general education level, with mathematical ability being the most focused demonstration of calculation capacity In terms of capacity assessment, Wolf (2001) argues that competency assessment is based on the description of specific output products, so clearly that teachers, students and stakeholders can visualize relative relativity Relevant and accurate student achievement after the learning process The PISA international assessment program not only evaluates knowledge and skills in the General Education program, but also focuses on 04 areas (understanding math, reading comprehension, scientific understanding, problem solving) The issue of assessing the capacity of primary school students was also studied in TIMSS (2011) through a system of questions and ways to quantify the capacity of primary students In Vietnam, recognizing the importance of capacity assessment, the Ministry of Education and Training issued Circular 30 of 2014, Circular 22 of 2016 on assessing primary students which emphasizes "Assessing primary students through activities of observing, monitoring, exchanging, examining and commenting on the learning process of students", " through observing the students’ experiential activities", "assessment as a learning method " The capacity assessment has attracted many interested scientists such as: Nguyen Cong Khanh (2014) in Renewal of examination and assessment of students according to capacity approach Nguyen Duc Minh (2014) in Guide for teachers to assess the capacity of senior primary school graders Nguyen Khai Hoan (2015) in Assessment of students according to competency approach Nguyen Thi Lan Phuong (2016) in The capacity-led program and learners’ capacity assessment In general, the above studies only focus on students’ capacity assessment issues The problem of using learning situations to support assessing calculation capacity of senior primary school graders has not been studied in a comprehensive way, so the research topic “Designing and using learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities” is an urgent issue The purpose of the study The dissertation studies how to design learning situations and demonstrates that designed learning situations can support assessing the calculation capacity of senior primary school graders through experiential activities Accordingly, the dissertation proposes orientations to improve students' calculation capacity in the teaching process, contributing to improving the effectiveness of mathematics teaching in primary school The subject and scope of the study - Subject of the study: Learning situations support to the assessment of students’ calculation capacity through the demonstration of senior primary school graders during the experiential process - Scope of the study: maths in senior primary school classes, students’ experience on learning situation in class, assessment of the teaching process The task of the study - Studying relevant theoretical basis to propose concepts, components of calculation capacity of the elementary school students and corresponding expressions; Concepts, methods and tools for assessing the calculation capacity of senior primary school graders through experiential activities - Researching the current situation of designing and using learning situations to support the assessing the calculation capacity of senior primary school graders through experiential activities, students’ mistakes in calculation activities - Proposing the process of designing learning situations, the process of testing the designed learning situations, the process of using learning situations to support the assessment of calculation capacity, the orientations to improve senior primary school graders in the teaching process Methodologies of study - Theoretical research method: Studying documents and situation of domestic and international research on calculation capacity, designed learning situations, experiential activities and capacity assessment to form the theoretical rationale of the dissertation A priority analysis and prediction of students' calculation plans will be done based on mathematic knowledge and psychology - Case study: In chapter 1, we chose some 5th graders by random to examine the mistakes of the senior primary school graders in the calculation activity, selected some grade investigate the difficulties and mistakes in calculation by senior primaru school graders, 4-5 primary teachers to survey the current situation of designing and usinglearning situations in assessing the calculation capacity of senior primary school graders In chapter 2, we chose a few groups of students in grade (or grade 5) if the content of the learning situation is related to grade (or grade 5) to examine the students’ demonstration in performing the calculations during experience process Similarly, in chapter 3, for each learning situation, we chose students by ramdom to identify each student's calculation capacity The results of this survey are the basis for us to identify the situation, the feasibility of the learning situations and the calculation capacity of students - Observation - investigation: Use teacher survey forms to collect the situation of designing and using learning situations in assessing students' calculationg capacity Observe students' computational experiential activities in learning situations that combine the use of student surveys to collect their mistakes in the calculation That is an important practical basis in the thesis, in adjusting learning situations, in supporting the assessment of calculation capacity and in the orientation of improving the calculation capacity of students - Educational experiment: Organizing for students the calculation experience on the designed learning situation, combining post-analysis to determine whether the learning situation is appropriate and how to adjust fit, test modified learning situations and continue to adjust if not appropriate (in chapter 2) When the learning situation is feasible, we conduct experiments to evaluate students' computational competence (in chapter 3) Because our assessment objective is not to classify students but to improve students' computational capacity, we not stop at assessment results, for students who are not qualified to complete Study situation, we help children to successfully solve the learning situation The organization for students to experience in chapter just to collect evidence to determine the calculation capacity of the students to demonstrate the learning situation designed to support the assessment of the students' calculation capacity, support help improve students' calculaition capacity Scientific hyperthesis If determining the calculation capacity components of the elementary school students and their respective expressions, designing learning situations and appropriate assessment tools, it is possible to support the assessment of ability Student's calculation force Contribute to improving students' calculation capacity and improving the effectiveness of elementary mathematics teaching Contributions of the dissertation 7.1 Theorietical contributions - The system of theoretical bases of experience, calculation activities and capacity to calculate, evaluate and evaluate calculaiton capacity, learning situations Proposing concepts and components of calculation capacity of the primary school students and corresponding expressions, characteristics of the learning situation; Concepts, methods and tools for calculating calculation capacity of elementary school students through experiential activities 7.2 Practical contributions - Setting up the process of designing learning situations for students to experience calculations - Setting up the process of testing the designed learning situations - Setting up the process of using learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities - Proposing orientations to improve the calculation capacity of senior primary school graders in the teaching process Theorietical poits to be defended - Designed learning situations offer opportunities not only for senior primary school grdaers to reveal their calculation activities but also for teachers to investigate the students' calculation activities, thereby serving as supporting tools to the assessment of calculation capacity as well as measures to improve the calculation capacity of students - Learning situations create opportunities not only for senior primary school graders to experience calculation but also for teachers to test the feasibility of learning situations Organization of the dissertation In addition to the introduction, conclusions, references, appendices, the main content of the thesis consists of three chapters: Chapter 1: Theoretical and practical basis Chapter 2: Designing and experimenting learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities Chapter 3: Using learning situations to support the assessmnent of calculation capacity of senior primary school graders through experiential activities Chapter THEORETICAL AND PRACTICAL BASIS 1.1 Experiential activities of senior primary school graders 1.1.1 Conceptions on experiential activities of senior primary school graders There have been many kinds of perpectives and classification of experiential activities; however, the experiential activities of senior priamry school graders with two kinds in this dissertation - Experience for changing strange phenomenon to familiar ones to students: For unfamiliar situations, students can not immediately apply calculations, formulas, rules and procedures for calculations but it requires that the problem must be changed either under understandable of processed forms so that the calculated contents can be revealed, that is to turn the unfamiliarities to familiarities - Experience for connecting maths with the reality: Because the dissertation’s approaches are in connection with learning situations in class, it is necessary to connect mathematics with the reality by organizing such in-class activities as cake division, game participation, or to create realistic simulation through hypothetical situations 1.1.2 Learning by experience Students’ participation in experiential activities, meaning that they are directly involved in the activity, results in creating new experiences and abilities The level of experience shown on the participants’ self-improvement is reflected in the change from narrow knowledge to broad understandings, from unable application to successful application, from mechanical application to flexible application, from flexible application to creative application 1.2 Calculation activities of senior primary school graders 1.2.1 Conceptions on calculation activities of senior primary school graders The calculation activity of senior primary school graders can be understood as the activities the students to change the strange maths problems to familiar ones, thereby using the existing knowledge to solve the learning situation Thus, the calculation activities may include: using calculations, formulas, rules and processes; using math tools; using thinking manipulations; using math language and mathematical models 1.2.2 In class and out of class calculation activities of senior primary school graders Students’ experiential calulation activities are organized activities, initially implementing external (speaking, writing, doing, creating) forms through interaction and communication, then transforming into the internal forms (analysis, synthesis, generalization, ), which gradually turns into their capacities 1.2.3 Knowledge enhancing calculation activities of senior primary school graders Knowledge plays the role in orienting, adjusting students’ calculation activities Therefore, weak knowledge will lead to difficulties or easy occurence of errors in calculation 1.2.3.1 Knowledge regarding to calculation methods 1.2.3.2 Knowledge regarding to dialectical materialism in phylosophy 1.2.3.3 Knowledge regarding to the capacity of knowledge association and mobilization 1.3 Calculation capacity of senior primary school graders 1.3.1 Conceptions on calculation capacity of senior primary school graders Calculation capacity of senior primary school graders is their capacity to process information, the relationship of quantity in solving maths problems in primary schools 1.3.2 Components of calculation capacity of senior primary school graders 1.3.2.1 Foundations to propose components calculation capacity of senior primary school graders In order to propose the calculation capacity components of senior primary school graders, we rely on existing research on the components of calculation capacities, the objectives and tasks designed in textbooks for senior primary school graders, the contentos maths textbooks, the cognitive characteristics of senior primary school graders in math learning, the reality of calculation capacities of senior primary school graders, and their calculation activity 1.3.2.2 Proposing the components in the calculation capacity of senior primary school graders Basing on the aboved-mentioned backgrouns, we propose components in calculation capacity of senior primary school graders as follow: a) Capacity to use calculations, formulas, rules and processes: The capacity to use calculations, formulas, rules, processes in calculation activities in elementary schools can be defined as the ability to identify and recall these capacities correctly and apply them directly in calculations on a specific context b) Capacity to use maths tools: The capacty to use math tools in calculation activities in elementary schools can be defined as the capacity to connect the contents of the given maths problems with mathematical tools effectively in their direct calculation on a specific context c) Capacity to use thinking operations: The capacity to use thinking operations in calculation activities in elementary school can be defined as the capacity to perform thinking and thinking styles to mobilize knowledge effectively in calculation activities on a specific context 11 presentation or simulation of events, setting up learning activities to offer an unresolved problem, requiring students to experience calculation activities to solve it The learning situations are in two forms: - Pure mathematical situation: is a situation that solves mathematical problem and relates only to requirements related to mathematical knowledge The pure mathematical situation can be divided into two types: The situations needing no visual representation and the situations that need support of visual representation - Practical situation: A situation in which its subjects contains elements of practical contents, in which at least one question / request / task exists and requires students to experience calculation activities for solution The practical factors here are practical contexts, including: In interdisciplinary learning, personal or school life activities, entertainment activities or social participation in the society 1.4.2 The characteristics of learning situations to support the calculation capacity of senior primary school graders through experiential activites We know that not all calculation tasks can be fully simulated in a situation However, to encourage students to express the demontration of calculation capacity, the learning situation is required to ensure the following characteristics: The learning situation must contain requirements for students to experience; elements of calculation capacity, an existence of conflict, motivated activities, and finally the subjects of activity 1.4.3 The use of learning situations to support the assessment of calculation capacity of senior primary school graders in experiential activities Depending on the purpose of use, the learning situation has its own functions If the sheet is used order to collect students' demonstrations of calculation capacity, it is necessary to print out the contents of the study situation on A4 paper and give them to the students We call it a learning situation card and students write down their calculation on the blank space At that time, the learning situation sheet is considered as an assessment tool If the sheet is used to encourage students to demonstrate their calculation behavior, then the learning situations can be viewed as an opportunity for students to experience and reveal calculation capacity If it is used to improve students' caculation capacity, the learning situations can be considered a teaching solution The dissertation is concerned with the students’ experience on learning situations and emphasizes the teachers’ experience in designing and testing learning situations 12 1.4.4 Assistance sheets Each student's ability is different, so facing with the same problem, some may be creative independent in solving while others will need help Instead of instructions, we designed an assistance sheet to assist students in experiential calculation activities This is also the foundation for us to propose the orientation to improve students' calculation capacity in Chapter The content of the assistance sheet contains suggestions and orientations for students to calculations 1.5 Assessing calculation capacity of senior primary school graders through experiential activites 1.5.1 Conceptions on assessing the calculation capacity of senior primary school graders through experiential activities On inheriting the research on assessing students’ capacity, we believe that assessing the calculation capacity of senior primary school graders through experiential activities are the process of making judgments, drawing conclusions or judgments about the level of students’ calculation; explaining the progress of students' calculaiton capacity In particular, the judgments, conclusions and judgments are based on analyzing the information systematically collected in students’ behavioral expression in the process of experiential calculation activitiies in learning situations 1.5.2 Methods to assess the calculation capacity of senior primary school graders through experiential activities Calculation capacity is revealed through the students' behavorial expression during experiential activities while behavior, attitudes, are difficult to be quantified and quantitative assessment methods are difficult to access On the other hand, due to the characteristics of elementary students, which are often unplanned and unrestrained, observing and explaining student behavior is often easier and more accurate Therefore, we conduct qualitative assessment by observing and studying students’ learning products 1.5.3 Tools for assessing the calculation capacity of senior primary school graders through experiential activities Behavorial demonstrations are evidence to assess students' calculation capacity, which are accessed by many different tools The dissertation is concerned with scales (assessment of each component of calculation capacity, table determining calculating 13 capacity levels) and assessment tools (observation sheets, video clips / photos, learning situation sheet, assistance sheet) 1.5.3.1 The scale to assess the calculation capacity of senior primary school graders through experiential activities - Level 1: Students cannot recall mathematical objects, concepts, properties, models related to calculations in the current situation; or they can recall them but they not work in the current situation - Level (Remembrance, recreattion): Students can recall, apply objects, concepts, properties, mathematical models related to calculations in the current situation - Level (Connection, integration): Students can link information for calculation applicable in solving simple problems; create connections in different representations; read, explain math languages and their relationships The demonstration at this level are built on the level of calculation by bringing the calculation into a context that is not completely familiar but still has an almost familiar structure - Level (Reflection): Students can identify calculation content in situations; use math knowledge to solve situational problems; mathematical analyzing and reasoning These demonstrations relate to the ability to find calculation plans and perform calculations in unfamiliar situations It includes elements that reflect on processes needed or used to solve problems 1.5.3.2 Video clips and photos Students’s expression behavior is diverse, complicated, and it can be timely observed or it is not activated during the observation process Therefore, the observer needs to arrange video cameras / cameras to save the information, so as to test and evaluate it and review it when it is needed 1.6 The current situation of designing and using learning situations to support the assessment of calculation capacity of senior primary school students through experiential activities 1.6.1 The current situation of teachers’ awareness on the conceptions of calculation capacity by senior primary school students Many teachers have been vague not only of the pconceptions of calculation capacity by senior primary school graders but also determining the students’ calculation activities 14 1.6.2 The current situation of teachers’ awareness on the conceptions of calculation capacity by senior primary school graders Most of the teachers agree that the student’s demonstration on calculation capacity remained too low 1.6.3 The current situation of innovation in assessing the calculation capacity of senior primary school graders 1.6.4 The current situation of using methods and tools to assess the calculation capacity of senior primary school graders through learning situations 1.6.5 The reality of designing and using learning situations to support the assessment of calculation capacity by senior primary school graders through experiential activities Because teachers have never used learning situations to assist the assessment of students’ calculation capacity they didn’t give any suggestions on the process of designing, experimenting and using of learning situations to assist assessment 1.6.6 The current situation of calculation capacity of senior primary school graders in their calculation activities Many teachers admitted that students’ calculation capacity was not high enough 1.6.6.1 Some difficulties and mistakes in applying calculation operations, formulas, rules and processes 1.6.6.2 Some difficulties and mistakes in using calculation tools 1.6.6.3 Some difficulties and mistakes in thinking and speculating activities 1.6.6.4 Some difficulties and mistakes in using mathematical language 1.6.6.5 Some difficulties and mistakes in methematical modelling 1.6.6.6 Some other difficulties and mistakes 1.7 Conclusion for Chapter From the data analysis has revealed that there is not clear about the awareness of teachers on the demonstrations of calculation capacity Assessments in primary schools usually are based on test scores which are a little regard with the evaluation of students' experience in the learning situation Therefore, there is necessity approach for teachers to take not only change their perceptions but also in their implementation The performance of students’ calculation capacity needs to be described in details It is needed to establish a scale of calculation capacity along with appropriate criteria, set up an observation sheet of 15 students' calculation behavior on each element of computational competence to ensure consistency between observations of a student or between students On the other hand, students often encounter difficulties in making calculations These mistakes should be illustrated in the learning situations to determine the student's calculation capacity and improve the student's calculation capacity To respond to the requirement, chapter has set of views on experience activities, calculation capacity, and ability assessment, learning cases including analysis, and some comments Thus, the thesis proposes types of computing experience, concepts, and computational competence components and corresponding demonstrations of senior students at elementary school; concepts and characteristics of learning situations to support evaluating calculation capacity through experiential activities; calculation methods and evaluation tools The introduction of calculation competency is also the basis for designing the observation sheet of students' calculation behavior The introduction of specific learning situations to create opportunities for students to interact, experience, and disclose calculation activities; supporting helping sheet to encourage students to overcome mistakes and orientations for calculation; video clips to record the process of students 'calculating experience, as a demonstration of evaluating students' calculation capacity This issue will be further illustrated in chapter and chapter The results of the research of chapter which have published in articles in magazines and conferences: Hanoi University of Education Journal [ 2], Journal of Educational Science [1], Education Journal [4], Vietnam Journal of Education [5], International Workshop at Vinh University [3] Chapter DESIGNING AND EXPERIMENTING LEARNING SITUATIONS TO SUPPORT THE ASSESSMENT OF CALCULATION CAPACITY OF SENIOR PRIMARY SCHOOL GRADERS THROUGH EXPERIENTIAL ACTIVITIES In this chapter, we designed learning situations With each designed learning situation, based on the knowledge of mathematics and psychology, we analyze and analyze the students' calculation plans However, the designed products can be subjective, to ensure that learning situations encourage students to reveal calculation activities that we conduct through internal validation by nesting Students experience the learning situation and collect 16 evidence, analyze the posterity to determine the appropriate learning situation and adjust accordingly; continue testing modified learning situations on other student groups and the process is repeated until the learning situation is feasible Testing tools are learning situations and assistance sheet Test subjects are groups of students in grades and The observer is the author of the dissertation Some students helped with filming the process of students’ calculation experiential activities on learning situations 2.1 The process of designing learning situations to support the assessment of calculation capacity of senior praimary school graders through experiential activities 2.1.1 Proposal of process Inheriting the research on the process of designing learning situations, we consider the process of designing learning situations to assist the assessment of calculation capacity of senior primary school graders the following diagram: Identifying the objectives of assessment Identifying the contents of assessment Identifying the format of learning situations Identifying the context of experience in learning situation Identifying suitable information, facts Identifying questions/requireme nts to express the problem Designing learning situations Diagram 2.1: The process of designing learning situations a) Identifying the objectives of assessment: The problem questions :What is it to be assessed? which are the elements to be assessed? b) Identifying the contents of assessment: It is the behavoral demonstrations of students’ calculation capacity c) Identifying the format of learning situations: whether they are pure mathematical situations or visual representation situations or practical situations d) Identifying the context of experience in the learning situation: In primary school, the context of experience in learning situations includes internal mathematical context (mathematical rules, mathematical relationships, ) and real context (daily life, studying life or social life in the community) 17 e) Identifying suitable information and facts: A fact is necessary information containing relationships and calculation contents to solve in learning situations The facts can be expressed in words, tables, models, diagrams, pictures, f) Identifying the questions / request to express the problem: Learning situations to assess students’calculation capacity are required to have an open ending in the form of a question / request for students to experience calculation in different ways The contents of the assessment and the evidence identified will be the foundation for the reference assessor to design appropriate questions and requests g) Writing into a learning situation: Teachers sketch a structured learning situation: Introduction (description of the context of events), the content (describing the evolution of events), the questions / requests contain issues to be addressed In addition, teachers need to conduct learning situations to ensure mathematical accuracy 2.1.2 Designing learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities 2.1.2.1 Designing the learning situations on fraction model 2.1.2.2 Designing the learning situations on counting triangles 2.1.2.3 Designing the learning situations on the area of triagles 2.1.2.4 Designing the learning situations on cake division 2.1.2.5 Designing the learning situations on cloth selling 2.2 The process of experimenting learning situations to investigate the calculation capacity of senior primary school graders through experiential activities 2.2.1 Foundations to suggest the process In order to suggest the process of experienting the learning situations, we base on the existing research on assessment, model of lesson study, methods of internal validation 2.2.2 Proposal of the process Based on the above-mentioned foundation, we consider the process of learning situation experience to investigate the calculation activities of senior primary school graders through experiential ctivities in the following diagram: 18 Selecting the designed learning situations Conducting priori analysis Identifying evidence to be collected Organizing calculation activities for students on learning situations with the help of assistance sheet and collecting evidence Analyzing results after experiment Attaining evidence Unattaining evidence Adjusting learning situations/ assistance sheet Asserting the values of learning situations Diagram 2.2 The process of experimenting learning situations a) Choose a designed learning situation: Choose a designed learning situation for experiment b) A priori analysis: It is necessary to anticipate the calculation activities in solving learning situations, which help orient us in observation It is also necessary to anticipate the students 'mistakes related to the learning situation to propose assistance sheets to ensure students' progress and encourage students to expose their demonstrations to be investigated c) Identifying the evidence to be collected: Evidence in the scope of experience on the learning situation includes the students’ calculation behavior expressed in the discussion process, on the product of the learning situation card, assisting sheets, drafts through speaking, writing, calculation doing d) Organizing calculation activities on learning situations and assistance sheets for students to experience and collect evidence: We organize learning situations and assistance sheets for students to experience While the student experience their calculation activities we observe, record video clips, take photos as evidence and review them when it is needed When the given learning situations are completed, we collect the learning sheets and assistance sheets e) Post-analysis: Basing on students' demonstrations during the calculation experience on the learning situation, we consider whether each calculation activity in a priori analysis has revealed and has not yet revealed, students' difficulties and causes, thereby orienting ways to adjust learning situations or assisting sheets to encourage students to reveal their calculation demonstrations to be investigated 19 f) Affirming the learning situations: If the evidence ensures that the calculation of calculation activities such as a priori or a minimum ensures the disclosure of the required requirements of calculaiton capacity, the study situation is feasible Conversely, it is necessary to adjust to a more appropriate learning situation Requirements for calculation capacity: Requirements for calculation capacity at the end of primary school (most concentrated demonstration of calculation capacity) in mathematis programs in the 2018 General Education Program focus on familiar calculation activities; Student's calculation demonstration in simple, familiar or similar situations They correspond to level in the scale of calculation capacity We consider them as requirements that need to be met in calculation capacity of the senior primary school graders g) Adjusting learning situations / assistance sheet: If students the calculationseriously but still have not disclosed the requirements of calculation capacity, the learning situation is too difficult to encourage students to show off their demonstrations then we should reduce the difficulty of the learning situation or adjust the assistance sheets On the other hand, if most students reveal demonstrations showed in the priori analysis, it means that the learning situation is too easy, it is necessary to increase the difficulty of the learning situation If the expression of the learning situation and the assistance sheers have not showed thestudents unaware of the task of calculation, then it is necessary to adjust them for more appropriateness h) Organizing activities for student to experience in the learning situation and assistance sheets helped adjustment and collection of evidence: We tested the learning situation and adjusted assistance sheets on other different students and the process is repeated 2.2.3 Experimenting a number of specific learning situations to investigate the calculation activities of senior primary school graders through experiential activities 2.2.3.1 Experimenting the learning situation on the fraction models 2.2.3.2 Experimenting the learning situation of counting triangles 2.2.3.3 Experimenting the situaltion on the questions calculating the area of triangles 2.2.3.4 Experimenting the situation on cake division 2.2.3.5 Experimenting the learning situation of selling cloth 2.3 Conclusion on Chapter 20 Learning situations provide opportunities for students to interact, experience and disclose calculation behaviors The student's mathematical expressions are a practical basis for us to adjust the learning situation and helping sheets to ensure that students are exposed to expected calculation activities In chapter 2, we have proposed the process of designing and testing learning cases, learning situations and feasible helping sheets will be depicted The modified learning situations will be used to organize the students' calculation experience in supporting the calculation capacity in chapter 3, the modified helping sheets will be the basis for proposing orientations to develop students' calculation competence in the teaching process The research results of chapter which have published in articles in the Journal of Education [6], Journal of Science Vinh University [7], Journal of Hanoi University of Education [2], Journal of Educational Science [1] Chương USING LEARNING SITUATIONS TO SUPPORT THE ASSESSMENT OF CALCULATION CAPACITY OF SENIOR PRIMARY SCHOOL GRADERS THROUGH EXPERIENTIAL ACTIVITIES In this chapter, we conduct experiments using the learning situation designed in Chapter to assist in assessing students' calculation capacity through the proposed assessment toolkit For each learning situation, we illustrate on two students because we conduct case studies in qualitative assessment, based on the behavior of students' expression so that we analyze students’ difficulties and mistakes and capacity - If students were successfull in solving the learning situations, we measured their performance when students completed the learning situation, because the individual's ability is reflected in specific tasks We explained the progress of students' calculation capacity based on how students overcame difficulties and mistakes in the process of calculations on learning situations That is the foundation for us to propose orientations to improve students' calculation capacity in teacher’s designed learning situation activities - If the student were not qualified to complete the learning situations, we measured their calculation capacity when they asked for a assistance sheet The objective of evaluation in the thesis is not to classify but to support the progress of students, we not stop at the assessment results but help to relay students to complete learning situations We explained the progress of students' calculation capacity based on their ability to overcome difficulties and mistakes and accumulate experience The suggestions in the assistance sheet 21 supporting the progress of students 'calculation capacity, which is the foundation for us to propose an orientation to improve students' calculation capacity in teaching activities 3.1 The process of using learning situations to support the assessment of calculation capacity of senior primary school graders through experimential activities Identifying the objectives of assessment Identifying evidence to be collected Identifying the methods and tools of assessment Organizing learning situations for students to experience calculation activities and collecting evidence Identifying the level of calculation capacity of students Explaining the students’ headway in calculation capacity Diagram 3.1 : The process od using learning situations to support the assessment of calculation capacity senior primary school graders a) Identifying the assessment objectives: To identify the assesment objectives, it is necessary to answer the questions: What is the assessment for? Which element will be assessed? b) Identify the evidence to be collected: The evidence in the experience of learning situations of individual students include the calculation behavior shown on the product of learning situation cards, assistance sheet, drafts through writing, calculating, creating activities c) Identifying methods and assessment tools: Qualitative assessment is done by observing and studying students' learning products The assessment tools are the learning situation sheets, the assistance sheets, and the observation sheets d) Organizing the learning situation for students to experience calculation activites and collecting evidence: We delivered the learning situation sheets to students and instructed the students how to use them The process of students' experience on calculation on the learning situation were also the process that we collected evidence by observing, taking photos, recording video clips When students completed the learning situations, we 22 collected the students’ learning situation sheets, assistance sheets and considered them as students' calculation products e) Identifying the level of students’ calculation capacity: First we associated each evidence obtained with the students’ calculated behavior in the observation sheets to determine the level of achievement in each element of calculation capacity We then combined the results of each element in accordance with the level of students’ calculation capacit f) Explaining the progress of students’ calculation capacity: We explained the progress of students' calculation capacity primarily based on self-reference because we focused on the students’ values and expectations rather than external standards We based on the students’ performing tasks to identify their efforts to overcome the difficulties and mistakes made by students in the calculation process to successfully solve the learning situation 3.2 Using specific learning situations to support the assessment of calculation capacity of senior primary school graders 3.2.1 Using learning situations on fraction models 3.2.2 Using learning situations on counting triangles 3.2.3 Using learning situations on calculating the area of triangles 3.2.4 Using learning situations on cake division 3.2.5 Using learning situations on cloth selling 3.3 Orientating the improvement of the students’ calculation capacity of senior primary graders through experiential activities on learning situations 3.3.1 Orienting the improvement of the students’ calculation capacity of senior primary school graders through teacher’ designing activities on learning situations 3.3.1.1 Designing learning situations in accordance with the proposed process 3.3.1.2 Orientating calculation for students through teacher’ designing activities on learning situations a) For pure mathematical situations: Designing learning situations should be related to the students’ knowledge, calculation activities in accordance with generalization rules, visual representation elements, students’ mistakes b) For practical situations: To design practical situations, if derived from the practical context, teachers need to model their mathematics; If it comes from within math, teachers need to put them in a real situation by completing them Need to strengthen the design of hypothetical situations, problems with practical content attached to students' lives 23 3.3.2 Orientating the improvement of calculation capacity of senior primary school graders in teaching activities 3.3.2.1 Orientation 1: Helping students understand the meanings and nature of knowledge Learning activities should be organized for students to follow the path of discovery, exposing students in a situation where such knowledge arises It is required that guidance on calculations, formulas, rules and procedures should be carefully made It is necessary to train students in calculating and solving learning situations for the formation of skills The students’ difficulties and difficulties should be used for analysis, for solutions and experience accumulation 3.3.2.2 Orientation 2: Improving the students’ calculation capacity through calculation activities in accordance with generalization rules Students should practice preparing a table of facts in the learning situations The figures in the table will be a thinking fulcrum for students to predict the relationship between the elements that make up the rules 3.3.2.3 Orientation 3: Improving the students’ calculation capacity through calculation activities on practical learning situations It is necessary to create opportunities for students to experience calculation on a variety of practical situations so that students accumulate experience and avoid similar mistakes Students should be encouraged to create new situations by association, specialization, and generalization 3.3.2.4 Orientation 4: Create opportunities for students to practice regular calculation activities It is necessary to train students to become familiar with the various types of learning situations in the learning process, in discovering new knowledge and practicing practice In order to reinforce and expand knowledge for students, they have formed computational skills, contributing to improving their calculation capacity 3.4 Conclusion on Chapter Chapter has proposed the process of using a case of study to evaluate students' calculation capacity with illustrative examples The students’ calculation capacity will determine based on this procedure, experience the learning situation, and helping sheets improve the student's calculation capacity, the proposal evaluation toolkit is feasible 24 (measure of students' calculating ability) Concisely, the learning situation has been designed using for both to assist in assessing a student's calculation capacity and to assist in improving the student's calculation capacity It is necessary to apply the proposed orientations to adjust the teaching activities, prevent mistakes, and promote the progress of students' calculation capacity CONCLUSION The dissertation has reviewed the domestic and international research issues on calculation capacity and capacity assessment, analyzed some difficulties of teachers in assessing students' calculation capacity and some students’ wrong difficulties and mistakes in calculation activities Accordingly, we proposed elements of calculation capacity of senior primary school graders and corresponding expressions, proposed assessment tools and organizational tools for students to experience calculation The dissertation has outlined the characteristics of the learning situations, proposed the process of designing learning situations and illustrated examples, the process of testing the designed learning situations through the formalization method internally, the process of using a learning situation that supports the assessment of students' calculation capacity accordingly, we proposed some orientations to improve the calculation capacity of the senior primary school graders in the teaching process Pedagogical experiment has demonstrated that the process of testing learning situations, the process of using learning situations to support the assessment of students' calculaiton capacities, the orientations to improve the calculaiton capacity of the senior primary school graders through the experience of learning situations is feasible Assessessment on students’ experiential activities that is based on learning situations ensures the progress of students' calculation capacity In short, designed learning situations offered both an opportunity for students to interact in order to reveal calculation activities and a chance for teachers to examine the students' calculation activities, thereby supporting their calculation capacity; such learning situations are chances for students to experience calculation activities and for teachers to experiment the feasibility of learning situations The thesis provides a communication channel in approaching students' behavior when students experience learning situations In order to accurately assess the students’ calculation capacity, it is necessary to combine many other communication channels and occurence throughout the learning process THE DISSERTATION RELATED PUBLISHED SCIENTIFIC ARTICLES A Scientific articles Dao Tam, Pham Thi Kim Chau (2016), Using visual demonstrations to support the assessment of primary school students’ calculation capacity, Educational Science, Issue 128, dated 5/2016, p 9-11 Pham Xuan Chung, Pham Thi Kim Chau (2016), Using real learning situations to support the assessment of primary school students’ calculation capacity, Scientifi Journal – Hanoi University of Teacher education, Issue (2016), dated 12/2016, p 89-97 Pham Xuan Chung, Pham Thi Kim Chau (2017), Training students of Primary Eduction to design learning situations to support the assessment of calculation capacity of senior primary school graders, International workshop proceedings on “Training and fostering teachers, managers of general education and pedagogical teachers” Vinh Universiry, p 21 Dao Tam, Pham Thi Kim Chau (2018), Knowledge in its role of orienting and adjusting the calculation activities of primary school students, The Education, Issue 1, dated 4/2018, p 19-22 Dao Tam, Pham Thi Kim Chau (2018), Some characteristics of primary school students’ thinking in calculation activities, Vietnam Journal of Education, Vol 3, 2018, pp 38-42 Pham Thi Kim Chau (2019), Designing learning situations to assess calculation capacity of primary school students, The Education, Issue 1, dated 02/2019, p 33-38 Pham Thi Kim Chau (2019), Testing the feasibility of learning situations in assessing the calculation capacity of senior primary school graders, Scientific Journal – Vinh University, Volume 47, Issue 4B (2018), p 15-23 A Research project Pham Thi Kim Chau (2019), Designing learning situations to support the assessment of calculation capacity of grade students, Research project of unverity level, academic year 2018-2019, Dong Thap University, Code SPD2018.01.12 ... contributions - Setting up the process of designing learning situations for students to experience calculations - Setting up the process of testing the designed learning situations 6 - Setting up the... students' behavorial expression during experiential activities while behavior, attitudes, are difficult to be quantified and quantitative assessment methods are difficult to access On the other hand,... activities", "assessment as a learning method " The capacity assessment has attracted many interested scientists such as: Nguyen Cong Khanh (2014) in Renewal of examination and assessment of students according