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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 AC

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

Scientific supervisors:

1 Prof PhD DAO TAM

2 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:

1 National Library of Vietnam

2 The Information Center – Library of Nguyen Thuc Hao, Vinh University

INTRODUCTION

1 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”

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 8 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

2 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

3 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

4 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

5 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 4 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 4 (or grade 5) if the content of the learning situation is related to grade 4 (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 2 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 do 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 3 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

6 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

7 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

- 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

8 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

9 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 1 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 do 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

d) Capacity to use math language: The capacity to use math language in elementary

school math is reflected in the ability to understand, convert, express math language (speaking, writing) to effectively change the maths problem in calculation activities on a specific context

e) Math modeling capacity: The capacity to model mathematics in calculation

activities in elementary school is reflected in the ability to understand, establish, convert, explain and reflect mathematical models effectively in calculation activities

1.3.3.2 Proposing the demonstration of calculation capacity of senior primary school graders

Basing on the above-mentioned foundations, we propose the demonstrations of calculation capacity of senior primary school graders as follow:

a) Demonstrations of capacity to use calculations, formulas, rules, processes:

Implement four arithmetic operations smoothly; manipulate calculations, formulas, rules and processes in familiar situations, apply calculations, formulas, rules, processes in slightly different situations, apply calculations, formulas, rules and processes in unfamiliar situations

b) Demonstrations of capacity to use math tools: Use math tools as what has been

introduced and practice in familiar situations, use math tools in a slightly different situation, use math tools in unfamiliar situations

c) Demonstrations of capacity to use thinking manipulations: Present the correct

order of performing calculations in expressions, check the calculations, results and calculation process, use simple inferences, able to monitor and evaluate a series of available arguments, use existing knowledge to identify factors for calculation in the current situation adjust thinking process to another direction if the current calculation approach fails, develop

a series of arguments in the calculation process use thinking manipulations to find a calculation plan in an unfamiliar situation, predict, propose appropriate hypothesis for the calculation process transform the calculated contents to change the unfimiliarities to familiarities, summarize, reduce the calculation rules to put the cumbersome calculation on simple calculation, consider the problem in many respects; do not be content with a calculated way, reach for a fast, unique calculation, and breakthrough leap in reasoning, point out the evidence to justify the correctness of the problem, evaluate the calculation methods for the best option, generalize the results of calculations

d) Demonstrations of capacity to use math language: Say or write the names of

learned maths, interprete calculations and results, dentify familiar symbols and forms in known situations, explain familiar standard representations, switch between representations, explain the process and calculation results; withdrawn relationships or statements; mathematical expressions associate, coordinate between different representations for calculation (diagrams, tables, shapes, letters, symbols), understand and dealing with languages and forms of expression in unfamiliar situations, explain the process and calculation results in many ways; complex relationships or newly drawn statements switch between different types of performances to facilitate calculation and convert language easily from unfamiliariy to familiarity use performances to explain the correctness of the problem Combining representations to create ways of calculating problems, convert math language

to natural language to express the meaning of math knowledge in the reality

e) Demonstrations of capacity to perform mathematical modeling: Identify familiar

mathematical models in similar situations, knowing how to create mathematical modeling for slightly different situations or unfamiliar situations, convert, perform both forwarding and conversing interpretation for mathematical models and situations, demonstrate and evaluate the solution in a real context to consider the feasibility of the established model, change to model if the calculation is not appropriate

1.4 Learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities

1.4.1 Conceptions on learning situations to support the assessment of calculation capacity of senior primary school graders through experiential activities

Inheriting the conceptions of teaching situations, we consider learning situations that support the assesment of senior primary school graders in experiential activities as the

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