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NGUYEN DANG MINH PHUC INTEGRATING DYNAMIC MANIPULATIVE MODELS WITH ELECTRONIC MATHEMATICS TEACHING AND LEARNING ENVIRONMENT FOR ENHANCING THE STUDENTS’ ABILITY OF EXPLORING NEW... With t

NGUYEN DANG MINH PHUC

INTEGRATING DYNAMIC MANIPULATIVE MODELS WITH ELECTRONIC MATHEMATICS TEACHING AND LEARNING ENVIRONMENT FOR ENHANCING THE STUDENTS’ ABILITY OF EXPLORING NEW

The work was done at Vinh University

The supervisor: Assoc Prof Dr Tran Vui

Reviewer 1: Assoc Prof Dr Tran Kieu

Reviewer 2: Assoc Prof Dr Trinh Thanh Hai

Reviewer 3: Dr Tran Trung

The thesis will be defensed in front of the Board of University level in Vin University,

On hours date month year………

This thesis can be found at:

- National Library of Vietnam, 31 Trang Thi street, Hanoi

- Information Center – Library Nguyen Thuc Hao, Vinh University

INTRODUCTION

The mathematical objects shown on the blackboard or on paper are static, the characteristics and their relationship often described by the language or symbolic representations

However, in a dynamic geometry environment, the object will show the characteristic behavior and can become the raw material used to "experiment" The idea for students to perform experiments as an empirically they often do in the other sciences subjects of mathematics educators have become ever more viable in the dynamic geometry environments They can conduct the experiment for suggesting hypotheses, verifying results, detecting invariants, finding relationships to constructing new knowledge

With this study, we hope to survey the status of students learning mathematics that forms the foundation for using software in teaching, research the constructing of electronics teaching and learning environments, integrating the dynamic mathematics models to the environment to help improve students' ability to discover new knowledge

CHAPTER 1: INTRODUCTION STUDY BACKGROUND

1.1 Introduction

With the student center of the teaching process, the autonomy of students in discovering knowledge was impressed In a positive learning environment, they have many more conditions in the exchanges, study with classmates through learning group or through interaction The dynamic manipulative models designed on the software can help students to discover knowledge through operations on that model with initial guidance Students will reduce the dependency on teachers in the reception of new knowledge Instead, base on to the active and their initiative actions, students will discover new knowledge with teachers as mentors

The development of a positive learning environment depends on many factors such

as the lesson contents, the existing infrastructures, teachers’ capacity, the ability to adapt to the environment of the students Teachers actually are researchers based on reality to build a suitable environment, using appropriate teaching equipment and integrating process of equipment into that environment for meeting effective teaching and learning

1.2 Research needs

Dynamic geometry software, with its original strength, which can preserve the invariance of the geometrics images or keep the rational role relationships of objects

With the interaction between students and computer models, students can discover, explore new knowledge for themselves With learning environments that use teaching facilities in the application of information technology, students have more opportunities to explore mathematical knowledge The problem is the need of how to create learning environments, design and build dynamic mathematics models as well

as the integrating models into electronic learning environment to be effective in teaching and learning

1.3 The study

The study needs to find a way to integrate the dynamic mathematics models to this learning environment to build e-learning environments to enhance mathematical

thinking and experimentation We chose the research topic: "Integrating dynamic

manipulative models with electronic mathematics teaching and learning for enhancing the students’ ability to explore new knowledge"

1.4 Research purposes

The purpose of the thesis is to:

 Study the effectiveness of dynamic manipulative models in supporting to enhance the students’ ability to explore new knowledge

 Research and develop electronic teaching and learning in supporting to enhance the students’ ability to explore new knowledge

 Develope the students’ ability to explore new knowledge through abduction and induction when conducting the investigation on electronic dynamic manipulative models

 Research on the experiment mathematics on dynamic manipulative models in supporting students enhancing their ability of exploring new knowledge

1.5 Research question

With the goal of integrating the model with environmental manipulation in electronic teaching to enhance the ability to discover new knowledge of students, this study proposed scientific hypothesis as follows:

If the model integrated with environmental manipulation in electronic teaching a scientific basis will enhance the ability to discover new knowledge through experimentation students math

Research Question 1: performing math operations in the mathematical model of

the impact of electronic support improving the ability to discover new knowledge of how the students?

Research Question 2: Building the e-learning environment, such as how to

effectively support students in improving the ability to discover new mathematical knowledge?

Research Question 3: Develop the ability to discover new knowledge through the

student's reasoning and inductive extrapolation models on the electronic manipulation like?

Research Question 4: Empirical estimates of the impact model sports electronic

support students enhance explore how new knowledge?

1.6 The meaning of the study

The findings of the study will help teachers create e-learning environment at the high school level math, including the integration of mathematical models to support dynamic manipulations improve students' ability to care break new knowledge, thereby fostering self-exploration capabilities, learning, enhance creativity in problem solving and decision making

CHAPTER 2: LITERAL REVIEW 2.1 Background history

2.1.1 The development of the learning environment

In recent years, parallel to the traditional learning environment, have emerged and developed new learning environment First of all, there is the appearance of the teaching facilities of information technology applications such as overhead, projector, designed on the model of the software used mixed with auxiliary equipment such as tables, handout episode With the desire to help students more easily in the knowledge discovery, these new devices are developed and constantly upgraded Number of schools equipped with these devices and more A number of studies have been done with this new learning environment as research to create electronic teaching equipment, namely models on software design activities, to support student learning Math

2.1.2 The shift in mathematics education

In the 1970s, the interest in mathematics education mathematics Tan (New Mathematics), which emphasizes the development and introduction of new content as the algebraic structure, and transformation matrix In the 1980s, back to the basic theme (Back- to- Basic) to be concerned, at which math skills are taught as a core

content of school mathematics So the math content related to the development of skills for students to be included in many of the math textbook Deductive inference from that is emphasized in the classroom Students acquire the knowledge, methods, and forms to practice math skills to apply them in homework However, in the 1990s

it was realized the problem is that students need to learn and need to learn the most when tectonic theory commonly accepted in the computing educators worldwide

2.1.3 Dynamic Geometry soft wares and Applications

Dynamic geometry environments are becoming popular in schools There are many different arguments about the effectiveness of dynamic geometry software in mathematical reasoning of students However, the dynamic geometry software has proved useful in the development of their reasoning The learning environment needs

a new course teaching the theory underlying sense reasoning

2.1.4 The teaching theories that affect mathematics education reform

2.1.4.1 Activity theory

With a focus on operations, activity theory emphasizes the basics of teaching methods are "exploiting the potential of each activity content as the basis for the organization of the teaching process achieve targets set" Operational perspective in teaching methods, which can be expressed in the mainstream of thought: Give the students perform and practice the activity component is compatible with the content and teaching objectives, suggested activities base for learning activities; led students create new knowledge, especially knowledge as the means and methods of operating results, distribution levels and activity as a basis for teaching process control

2.1.4.2 Situations theory

The basic premise of the theory of situations of Brousseau's knowledge, or use the built-in situations are determined by the suppression of this situation Therefore, it is thought that by creating artificially suppressed, the teacher has the ability to stimulate students to build a certain type of math knowledge The interest in the meaning of knowledge on the subject has made theoretical situation more humane

2.1.4.3 Constructivism theory

Theory tectonic theory is somewhat similar to the situation because it is particularly interested in how people learn Basically, learning theory associated with the interaction of two factors: the diagram of learner knowledge and new knowledge

2.2 Theoretical Framework

2.2.1 Basic constructivism

The view is created for that, the development of mathematical ideas are explained through interactive culture of human society, in which special attention is devoted to examining how the performing multiple systems, symbols and tools provide an opportunity for the formation of meaning

2.2.2 Constructivism in education

Tectonic theory, as a theory in psychology, and cognitive talk about how people learn , it does not provide the specific model of teaching , and also suggest what should not be in programs Tectonic theory , here are the key ideas to help people grasp the significance of learning and thus more applicable to general education and mathematics education in particular has been formed

2.2.3 Constructivism perspective in Teaching and Learning mathematics

Tectonic theory focuses on the role of internal cognitive processes and "install data" in the first private individual students in their own learning math ¬ reachable collaborative learning organizations to create opportunities for students to exchange and discuss approaches to understand their problems

According to this view, there are many approaches to improving math education: finding different ways to attract individual student participation, develop information-rich environment to study math, preparing multiple threads accounting or related problems to help students to empirical evidence

2.2.4 Constructivism theory for e-learning

Tectonic theory is a theory of the superiority of teaching used in the current educational reform This theory encourages students to construct their own knowledge based on personal experiments and directly applicable to their environment The learning of each individual student at the center of the learning process

Theory tectonic theory is considered ideal for electronic learning (e -learning ) for the following reasons:

 tectonic theory views the student is the center of the learning process

 tectonic theory that knowledge is built and applied consistent with the empirical personal

 tectonic theory views the student as entities rather than passive activities to fill information

CHAPTER 3: METHODOLOGY AND RESEARCH PROCESS

3.1 Design the research process

To answer the research questions outlined in Chapter 1, the study was conducted according to the following steps:

 Research results and researchers have done studies to determine the strengths and the support of mathematical models sporting impact in improving the ability to discover new mathematical knowledge

 Research studies , articles , results from previous studies had to examine the current learning environment through the investigation process and from which

to build the mathematics learning environment that integrates active manipulation of the mathematical model , which defines the roles of teachers , students , the teaching model support , assessment methods and related issues

 Research Design and integration of mathematical models sporting impact on the mathematics learning environment , especially e-learning environment used

to build mathematical models on the dynamic geometry software in order to develop the ability to discover new knowledge by students

 Research the available research results about reasoning , especially reasoning and inductive extrapolation from which mathematical models designed to manipulate support students in developing reasoning to extrapolate , extrapolation of the with inductive as well as conclusions on the role of software in the creation of a supportive environment for students to create extrapolation

 Research the available research results, models designed to manipulate the ability to perform research experiments mathematics through manipulation of the model in improving the ability to explore is new students

on inductive inference and extrapolation , we experimentally on students from three classes 11A2 , 11B1 and 11B2 of the Hai Ba Trung Street , Hue The experimental

results by the empirical estimates will be conducted in two classes of schools Phan Boi Chau , Nghe An

3.3 Research tool

Research tools include the mathematical models designed on The Geometer 's Sketchpad software , tools, survey data analysis , lesson plan , handout

3.4 Methods of data collection

To answer the research questions outlined in Chapter 1, we carried out the data collection methods for the following topics:

 Collect data from the available studies on the ability to perform math and show the performances of dynamic geometry software as well as information collected through the experimental teaching in order to capture the effect of integration models to manipulate the environment in order to improve mathematics teaching ability to discover new knowledge by students

 Collect data from sources such as books, newspapers , yearbooks , articles , materials science download via the internet on mathematics learning environment positive ; gather information about the teaching environment is locally through the survey as well as the existing research on positive teaching environment

 Collect data from studies in extrapolating inferences as well as abroad At the time of the research data on deductive reasoning, inductive were also collected

to assess suitable for the discovery of new knowledge through extrapolation on the dynamic model manipulation The data obtained through experimentation will be collected for analysis and evaluation

 Collect data from the empirical study of mathematics in the development of mathematics, especially experimental studies using mathematical software

3.5 Method of data analysis

 From the data gathered through the study of mathematics performances , we can now perform the operations on dynamic geometry software designed by the positive model From there we analyze mathematical models in supported operations enhance the discovery of new knowledge of students

 From the data obtained through the research findings have , we evaluated the role of integrating the perspectives of students in teaching mathematics With the data collected through the survey process for students , we conducted statistical data to evaluate existing learning environment , the student's

perspective , the ability to perform survey work on manipulation of the model Since then, we evaluate the ability to integrate the operations model for building dynamic e-learning environment

 From the data collected through the research had to deduce inferences , inductive and extrapolation , we analyze the differences between the types of inference , focusing on extrapolation inference , especially extrapolate the impact on sport models The mathematical model has to be positive we analyze the possibility of developing applications for the extrapolation inference for students as well as design new models The data from the experiments will be analyzed to look for quantitative extrapolation of students doing surveys on dynamic models

 From the data collected by the empirical study of mathematics , we analyze the empirical estimates of the historical development of mathematics as well as

through experimental computer algebra software such as Maple , Mathematica

 From these data we suggest that the empirical math students through the design

pattern on dynamic geometry software

3.6 Scope of the study

 The content of the experimental lesson: Some search problems to develop rules inductive reasoning and deductive problem developed extrapolation

 Students participated in the experimental lesson: There are 174 students in relation to empirical thesis Including 110 students in the class 11A2, 11B1 and 11B2 of High School Hai Ba Trung Street, Hue City, 64 students in the class 11A1 and 11A2 specialized school of Phan Boi Chau, Nghe An

 Objects Survey: Students at schools in the city of Hue, Hai Ba Trung High School (83 children), Dang Tran Con (73 children); students in neighboring districts: Ha Trung high school (52 children), To Huu (63 children)

CHAPTER 4: INTERGRATING DYNAMIC MANIPULATIVE MODEL WITH ELECTRONIC TEACHING AND LEARNING MATHEMATICS ENVIRONMENT

4.1 The study results

4.1.1 The results for the research question 1

4.1.1.1 Mathematical representation

There are many different definitions about performances in mathematics education Most mathematics education researchers to distinguish between internal and external

representation, in which performers apart is the expression of ideas or concepts such

as charts, tables, graphs, diagrams, language and is represented in the model of perception that a person is in their minds Performances can be divided into 3 categories according to the developmental stage are Realistic Representation 

Iconic Representation  Symbolic Representation

4.1.1.2 Visual representation

Visualization is the ability to process and product of creativity, interpretation, and use reflection based on drawings, photographs, diagrams in our heads, on paper or on the scientific tools technology, with the aim of describing and communicating information, thoughts and ideas developed previously unknown to come to an understanding

4.1.1.3 Dynamic visual representation

To understand the concept of "dynamic manipulative" in mathematics education,

we consider the following examples are designed on GSP dynamic geometry software

Example Constructing graph of function 2

the value of the derivative f '(x A)changes sign from negative to positive; while

through x = 2 , the derivative changes sign from positive to negative and from negative to positive when x = 3

Furthermore, when going through the points with x-coordinate x = 1 and x = 3, the change of sign of f’(x) will occur more abruptly when the point has x-coordinate x =

2 Focus on surveying by dragging points A raging around the points x = 1 and x = 3,

you will see that the derivative changes sign as suddenly as leapfrogging derivative value from -2 to 2

4.1.1.4 Multiple representation and dynamic multiple representation

Multiple representation is the outward expression of ideas and mathematical concepts in order to provide the same information in different forms Dynamic multiple representation is shown performing on multiple computers via dynamic geometry software, which allows users to perform impact on performance

The use of multiple representation with and without information technology is one

of the main topics of mathematics education in recent years Multiple representation

offer an environment for students to effectively recognize and understand the math concepts learned

4.1.1.5 Evaluate some results through empirical teaching lessons

The task of teaching mathematics in empirical software designed on GSP will perform multiple shows The children have the opportunity to choose to perform actions: dragging parameter sliders, change the location of the point, the object Standing before a system can perform close relationship with each other, the I have the survey performed at all to find new relationships and focus operations on a certain performances The selection and implementation of actions on their performances are also discussed, although initially they conducted primarily by the method of trial and error

With the cost of surveying tasks limited number sequences ( 1)

n n

u n



 , students have many different expressions when performing language use (interspersed with performances sign) to describe what they observed For example, the larger the value

of n, the comments I have "u n as gradually to 0" , or "absolute value of the smaller u n" There are a few groups also provide additional comments on behalf characteristics

change as "u n values constantly change sign" , "u n receive a positive value and

negative when n even and when n odd respectively

4.1.2 The results for research question 2

4.1.2.1 Integrating students attitudes on teaching and learning mathematics

Information technology and communication has been applied in teaching mathematics in an effort to innovate teaching methods in recent years In applying the strengths of the software animated geometry to teach math, we participated in

compiling the book "Discovering Algebra and Calculus 11 with The Geometer's

Sketchpad" , "Exploring Calculus 12 with The Geometer 's Sketchpad" and has

received positive feedback from teachers high school math The model of the electronic manipulation has been used not only in the details, but also expand their teaching in the teaching hours daily by our mobility and ease of use In addition, the model also can be integrated into the learning environment on the Internet through the Java -style animation frames running directly on the Web browser in the online learning system

4.1.2.2 Surveying the learning environment

We analysed the survey results for the 271 students have used computers from two high schools in the city centre of Hue (group A, including 156 children) and two schools in neighbouring districts (group B, 115 children ) on May 03, 2009

4.1.2.3 The feedback for the development of e-teaching and learning environment

We conducted the survey through questionnaires for students of four secondary schools in four schools of Thua Thien Hue provice and feedback of students following deserve attention

• Number of students exposed to computer

• How often you use basic computer programs

• The level of proficiency in perform basic operations on the computer

• Level students / teachers of students using computers, projectors, lights in school

4.1.2.4 Some survey results

Survey results showed that the average student in group A had time to use the computer almost reached 3 to 5 years , group B to cross the threshold from 1 to 3 years The standard deviation of the two groups were similar and low

Survey how often they use basic computer programs showed average both groups

A and B level between 3 and 4 in Group A despite frequent communication with the computer more The standard deviation of the two groups are almost the same and are quite high because there are many more activities surveyed and a 5 rating

Survey proficiency in implementing basic operations on the computer showed that

in group A had an average of between levels 1 and 2 Overall, the children in this group can perform good actions either alone or have the help of others The students

in group B average remains close to 2, the more you need the support of others than group A Comparison of standard deviations in the two groups was found in Group A have a more uniform level

4.1.2.5 Electronic teaching and learning mathematics

The role of students and teachers in the teaching environment is described electronically as follows:

 Students are actively promoting their abilities

 The teacher acts as a mediator to guide their ideas to achieve the purpose of the

lesson