Teaching advanced mathematics to students in universities of industry towards teaching associated with occupation

+ Although there are some researches into Maths teaching in practice, there is no research into Teaching Advanced Mathematics to Students in Universities of Industry towards teaching as

INTRODUCTION

1 REASONS FOR CHOOSING THE TOPIC

+ For undergraduate education, the education and training sector is renovating towards focusing on capacity development of learners in order to train human resource of Vietnam For Universities of industry, this is shown by enhancing the quality of vocational training

+ In fact, Advanced Mathematics Teaching in Universities of industry still remains a lot of shortcomings, in both teaching and learning, especially the application of Maths to vocational training This is a hot topic and should be researched to establish solutions in order to requirements of enhancing the application of Maths to occupation

+ Although there are some researches into Maths teaching in practice,

there is no research into Teaching Advanced Mathematics to Students in

Universities of Industry towards teaching associated with the vocational training practice

For all above reasons, We chose the topic: Teaching Advanced

Mathematics to Students in Universities of Industry towards teaching associated with Occupation for the doctoral dissertation

2 OBJECTIVES AND SCOPE OF THE RESEARCH

2.1 Objectives of the research

To develop a method of teaching advanced Maths associated with the training vocational training practice to students in Universities of industry

2.2 Tasks of the research

+ To research into theoretical and practical bases

+ To develop a method of teaching advanced Maths associated with the training vocational training practice to students in Universities of industry

+ To apply teaching methods to teaching advanced Maths, in order to enable the students to apply the knowledge to the vocational learning practice

4 RESEARCH METHODS

During the research, we selected and used the following research methods:

theoretical research; Observation; Teaching experiment and Mathematical Statistics

5 THE OBJECT AND SCOPE OF RESEARCH

The object of study is the process of Advanced Mathematics teaching to

students in University of Industry The research was carried out on students in two groups of mechanical and electrical industries in the industrial universities

in Viet Nam

6 NEW CONTRIBUTIONS OF THE THESIS

- In the theory: clarify the conception of teaching advanced mathematics to students in University of Industry towards associated with occupation and the meaning of it

- In the practice: proposing some advanced mathematics teaching measures to students in the industrial universities (mechanical and electrical industries) towards associated with occupation These measures are feasible and effective

7 THE ISSUES RAISED IN THE RESEARCH

- The conception of teaching advanced mathematics towards associated with occupation in the industrial universities

- Objectives, contents and teaching methods in Advanced mathematics towards associated with occupation in Universities of industry

- The pedagogical measures in teaching advanced mathematics associated with occupation in industrial universities students

8 STRUCTURE OF THE THESIS

The dissertation is divided into three chapters:

- Chapter 1: Theoretical and practical bases

- Chapter 2: Methods of Teaching Advanced Maths associated with vocational training practice to students in Universities of industry

- Chapter 3: Teaching experiment

CHAPTER 1 – THEORETICAL AND PRACTICAL BASES

1.1 DOMESTIC AND FOREIGN RESEARCH SITUATION

For the purposes of theoretical research into association of Maths teaching with the practice, in this section, we will focus on research into theoretical matters in Vietnam and in the world in relation to teaching and learning Maths associated with application to the practice, particularly:

1.1.1 Research situation in the world

1.1.2 Research situation in Vietnam

Findings show that:

In the world and in Vietnam, Maths education (even from high school level, to undergraduate and vocational training) associated with the practice has been research for the final purposes of forming and enhancing the ability of learners to apply Maths to the practice

1.2 MATHS TEACHING ASSOCIATED WITH THE PRACTICE

For the purpose of developing teaching methods, in this section, we will research theories of Maths teaching associated with the practice, particularly,

we will focus on clarifying two points: Relationship of Maths and the practice and Maths teaching associated with the application of Maths to the practice

1.2.1 Relationship of Maths and the practice

1.2.2 Maths teaching associated with the application of Maths to the practice

1.2.2.1 Some concepts

1.2.2.2 The necessity to strengthen the practicality of teaching Mathematics 1.2.1.1 Mathematics is derived from the practice, reflects to and serves the practice

1.2.1.2 Roles of mathematical tools in the practice

Thereby, we can find that: Maths is derived from the practice, and always aims to serve the needs of practical life Therefore, Mathematics teaching and learning should be associated with application of Maths to the diversified practice

1.3 TEACHING ADVANCED MATHS IN UNIVERSITIES OF INDUSTRY

In order to obtain practical bases for solutions, in this section, we will research into situation of Advanced Maths teaching and learning in Universities of Industry via:

1.3.1 Objectives and contents of training electricity and mechanics in Universities of Industry

1.3.2 Contents of Advanced Maths in Universities of Industry

1.3.3 Advanced Maths teaching associated with electricity and mechanics training objectives and practice in Universities of Industry

1.3.4 Current status of Advanced Maths teaching in Universities of Industry 1.3.5 Analyzing the causes and assessment

Of which, we propose the concept of Advanced Maths teaching associated

with electricity and mechanics training objectives and practice in Universities

of Industry as following:

 The occupational field herein only have vocational training of students in

electricity and mechanics in Universities of Industry (according to the above

specific training objectives and programs);

 Advanced Maths teaching associated with electricity and mechanics

training means:

During Advanced Maths teaching, teachers make students be aware of and have habits of occupational orientation through enhancing knowledge and skills (first step) to apply Mathematical knowledge and methods to resolve some practical situations during learning electricity and mechanics in Universities of Industry, in order to form professional qualification (section 1.3.1)

In order to achieve the above requirement, those who teach Maths should

exploit practical and disciplinary-related situations to let students get familiar, and participate in activities during discovering Mathematical knowledge and methods, then apply them to resolve practical Mathematical questions during maths learning, and apply them to practise electricity and mechanics

 Professional capability for students of each electricity, mechanics are required to the extent as set forth in the Section 1.3.1 (According to the decision

No 1251/QĐ-ĐHCN, dated 31/7/2014 of Hanoi University of Industry)

 Learning and applying Advanced Maths to the practice of students in

Universities of Industries are within the scope of learning the prescribed

Advanced Maths contents of the programs ad vocational trainingand professional practice in the universities Therefore, students study in relatively

stable, unified, favorable evironment through mostly assumed practical situations during theory and practice lessons in the universities

 Teaching methods based on implementing integration and interdisciplines: In order to students are able to apply Maths to the further

professional practice, it is required to actively train the activities during learning in the universities of industry, through the combination of Advanced Maths and other basic subjects (Physics, Chemistry, Informatics), and special subjects (Mechanics, Theory of Electrical Circuits, etc), in combination with practice for electricity and mechanics

On the other hand, by survey of current status of Advanced Maths teaching and learning in universities of industry, we draw the followign comments (section 1.3.4):

 The majority of Maths teacher in the Universities of Industry only consider teaching as complete implementation of the training program, they are not aware of exploiting its practical applications, on other words, Advanced Maths teaching in the Universities of Industries leans towards imparting Maths as a pure scientific subject, therefore the teaching methods are academic, lack clarification of functions, tools and applications to Maths to the practice

 On the other hand, in order to meet the above requirements (as stated in the questionnaire 01), they are also run into difficult in understanding knowledge and teaching methods of other subjects (Physics, Engineering, etc); even understanding, consulting their workmates who are teaching related subjects, Maths teachers still cannot clearly understand of physics, engineering, etc, especially the relation and functions of Mathematical tools in the students’ occupational practice On the other hand, Maths teachers also rarely use the Mathematical tools to explain or answer practical problems of some majors in universities of industry

 Because Advanced Mathematics including relative much knowledge is only taught during 90 periods, Maths teachers mainly spend time teaching theories and practising via exercises, hardly or rarely using Mathematical knowledge and methods, including guiding students to make practical situations, then to develop mathematical models, and to use mathematical knowledge for solving

 For teachers who take interest in Maths teaching associated with application

to the vocational training practice, they are met with difficulty in enhancing their related knowledge, in searching reference materials, in order to establish exercises whose contents are in consistent with Maths knowledge, etc

 Currently, contents and methods of academic result assessment for Advanced Maths in the universities of industry mainly inclue pure assessing Mathematical knowledge and skills, excluding requiring to apply Advanced Maths to the living practice in general and to the vocational training in particular, etc Thus, students’ learning is mainly to cope with the requirements and assessment methods, and they do not have passion in researching to apply Advanced Matahs to their training majors

 The survey results reflect the shortcomings of Advanced Maths teaching and learning situation in the Universities of industry, especially in the aspects of

application of Maths to the vocational training practice

 Among all reasons, we can see that selection of contents, teaching methods and testing – assessing of Advanced Maths of teachers have an significant impact on the above current status On the other hand, the current status shows that: a lot of Advanced Maths teachers do not fully take interest in requirements

of Advanced Maths teaching associated with the students’ occupational practice,

or have a shortage of necessary relevant knowledge and have a lack of skills of Advanced Maths application to practical exercise solving

1.4 SUB-CONCLUSION OF CHAPTER 1

The research into every specific problems in relation to Maths teaching associated with the practice shows that:

For Advanced Maths teaching in the Universities of Industry, increasingly exploitation of mathematical tools associated with vocational training practice is an essential factor during engineer training The research results in the chapter 1 clarify scientific bases and practical requirements of Advanced Maths teaching in the Universities of Industry towards associated with the vocational training practice Those are also bases for us to develop Advanced Maths teaching solutions (see chapter 2), in order to associate Maths with the objective to develop professional knowledge of students in the Universities of Industry

CHAPTER 2: ADVANCED MATHS TEACHING ASSOCIATED WITH

VOCATIONAL TRAINING PRACTICE TO STUDENTS IN

2.1.1 Orientation of Advanced Maths teaching associated with vocational training in Universities of industry

2.1.2 Requirements of Advanced Maths teaching associated with vocational training

in Universities of industry

On that basis, we propose and develop 6 methods of Advanced Maths teaching in order to enhance application of Maths to the training practice in Universities of Industries For each method, we analyze scientific bases, significance, functions; present how to implement and illustrate through teaching specific contents of Advanced Maths in Universities of Industry

2.2 METHODS OF ADVANCED MATHS TEACHING ASSOCIATED WITH VOCATIONAL TRAINING IN UNIVERSITIES OF INDUSTRY 2.2.1 Method 1

Holding seminars on Maths and seminars on interdisciplines in order to improve Maths teachers’ knowledge and skills of applying Advanced Maths to solve some exercises of basic and major subjects in the majors of Electricity and Mechanics

2.2.2 Method 2

Developing and using examples and exercises during Advanced Maths teaching associated with training practice in the majors of Electricity and

Mechanics, in order to train students’ skills of applying Advanced Maths to

their occupational practice

2.2.3 Method 3

Combining teaching methods and using assistance tools in order to associate Advanced Maths teaching with the vocational training practice 2.2.4 Method 4

Renovating contents and methods of testing – assessing academic results towards application of Advanced Maths to the occupational practice

2.2.5 Method 5

Enhancing to guide students in the Universities of Industry to self-study towards application of Advanced Maths to the occupational practice

2.2.6 Method 6

Letting students perform the process of application of Advanced Maths

to the occupational practice through Scientific Research Council

Analyzing solutions of the dissertation:

In the universities of industry, with the aim of teaching Advanced Maths associated with occupational practice, we develop teaching methods in order to exploit the practicality of Maths towards both above directions Especially, we

guide students to use mathematical tools to solve practical mathematical exercises

in relation to occupation which is trained in the Universities of industry

Methods ofAdvanced Maths teaching associated with the training practice are to:

 Associate with vocational training in the universities of industry, especially meet requirements of training renovation towards capacity development of trainees

Which are shown in the teaching methods in the dissertation

 Impact on factors and steps of training process, by various ways to organize

Which are shown in the Method 2 (impact on contents of Advanced Maths teaching); the Method 3 (Impact on teaching method, using assistance tools during Advanced Maths teaching); the Method 4 (Impact on testing – assessing academic results)

 Impact on teaching theories and Advanced Maths excerises solving, practising the skills of applying Advanced Maths to solving practical mathematical exercises in relation to the occupational practice

Which are shown in the Methods 1, 2, 3, 5

 Impact on the link among subjects in relation to training objectives of the universities of industry, ensure a close link among subjects during vocational training; Help students to strengthen their knowledge of related subjects, be fully aware of the interdisciplinary spirit, and then better understand the roles

of mathematical tools

Which are shown in the Method 1 (Enhancing teachers’ capacities,

interdisciplinary seminars); the Method 6 (Maths teachers participate in guiding students to perform scientific research in company with teachers of majors);

 Enhance study activities of students, and give priority to practice activities and improving the skills of applying Maths to the diversified practical situations

Which are shown in the Methods 2, 6

 First of all, in this dissertation, the solutions are developed for students in majors: Electricity and Mechanics in the Universities of industry, because such solutions in the training program and practice are relatively clear and familiar with students in the universities of industry

 Method system:

From the approach and orientation as stated above, we didided the teaching methods into 3 groups based on the bases and assessment of their impact, as following:

Group of method 1

Enhancing capacity for advanced mathematics teachers, including

method 1 and method 2

Group of method 2

Renovating methods facilities in teaching advanced mathematics and assessment methods with requirements apply to professional practices This group of method include method 3 and method 4

Group of method 3

Developing self-learning and self-study ability in industrial universities students towards applying advanced mathematics to solve professional

practices problems, including method 5 and method 6

For each method, at first, we clarify the necessity and theoretical bases, in order to ensure the scientific methods; identify purposes, build contends and how to implement the methods Finally, we give examples of using the methods during Advanced Maths teaching in the unviersities of industry The teaching methods has been completely presented in the dissertation, and because of the limited space of the dissertation summary, we only present some examples of the above methods

Examples of the Method 2

According to te 6-credit program, by reserching into textbooks, materials, teaching outlines of some universities of industry ([7], [8], [9], [23], [36], [42], [50], [51]), we count the Advanced Maths exercises which are using at present:

Hanoi university of industry – 125 exercises; Quang Ninh university of industry - 117 exercises; Viet Tri university of industry - 121 exercises; Viet

Hung university of industry - 107 exercises; Nam Dinh university of industry -

113 exercises The concern is that all these exercises are in the form of pure mathematical exercises, meeting requirements of Maths, but not associate with the vocational training practice in the universities of industry

On the basis of research into the number of exercises, it is required to have knowledge of Advanced Maths and specific contents of every exercise,

we develop a system of exercises (including 110 ones) which have been classified as following:

 At first, we collect and select 70 Advanced Maths exercises which are purely about Maths, in order to equip students with basic knowledge for strong foundation of mathematical knowledge and skills, students are not required to apply Maths to the practice

 Then we continue to collect and build 20 exercises with content, forms

related to diversified life practice or assumed practice which can be solved by using applications of Advanced Maths knowledge

 Finally, we collect and build 20 exercises with content, forms and approach

to solve based on: requirements of applying to the practice for students who are majoring in Electricity and Mechanics in the universities of industry

However, it should be that: deep knowledge of occupation or of special subjects (Principles of mechanics, design and manufacture of machines, electrical circuit theory, .) is very complicated Thus, during developing, collecting and designing the practical occupational exercises, we converted some situations in relation to occupation practice to life practice, omit complex factors , in order to help students easily apply to solving problems

It should also be added that, the addition of a number of practical problems in relation to occupation to Advanced Maths teaching contents for students in Electricity and mechanics in the Universities of Industry does not

mean that we “perform tasks” of teachers of special subjects With the general

objectives of the universities of industry – vocational training, this is extremely important: through practical problems in relation to occupation, we assist teachers of special subjects in equipping the students with mathematical tools for solving practical problems in relation to occupation

After fact-finding, we find that solution of almost of the practical problems in relation to occupation in textbooks of electric circuit theory and mechanics which are beeing used in the universities of industry need relatively difficult knowledge and methods of Advanced maths, meanwhile is briefly presented, is not identified

how to use mathematical tools This make the students very difficult, especially during solving similar problems in the study practice and occupational practice

Meanwhile, thanks to the initiative bringing such problems into Advanced Maths, we help the students understand theoretical bases and how to apply knowledge and methods of Advanced Maths to the occupational practice, help them easily understand, easily remember and know how to apply the knowledge and methods of Advanced Maths

The examples, exercises with contents related to occupational practice that we presented in this dissertation are referred from textbook of special subjects However, their solutions are presented and explained in detailed and carefully so that the student will easily understand, but accuracy, science, simple are ensured, also they are close to the knowledge of Advanced Maths, are suitable to cognitive ability, knowledge and skills of the students

Bringing practical problems into the contents of Advanced maths teaching for students in Electricity and Mechanics in the universities of industry will achieve two objectives:

+Students are interested in and master knowledge of Advanced Maths;

+ Habit and ability to apply the knowledge of Advanced Maths will be formed,

in order to solve practical problems of the special subjects, meet vocational training objectives of the universities of industry

This is one of the practical contribution of the disseration to the quality, efficiency of Advanced Maths teaching to students in Electricity and Mechanics in the Universities of industry

 40 problems are presented in the Appendix 3 of the dissertation, here, we only

give some problems:

Exercise 7: Applying system of linear equations to solve problems in relation

to electric circuits

Based on the below electric circuit

Find out electric circuits i i1 , 2 , ,i i i i3 4 , , 5 6

Exercise 8: Applying differential equations in electric circuit research

Based on the below electric circuit,

Power E= 4 cos10

25 t, R=40, L=1 H,

16 10 F  Calculate voltage of Capacitor C

and electric current of the circuit at the moment

t, the voltage of Capacitor C at the initial

electric current is 0

Exercise 9: Applying differential equations

in solving dynamic problems

A train is moving on a horizontal line at constant velocity V0 then is braked Value of total resistance force ((brake force, friction…) impacting on the train

is equivalent to 1

10 its weight P Identify its movement during the braking and its distance from the braking to stop

Examples in relation to the Method 3

Example 1: Considering an ellipse structure in mechanical as shown

AB slider has a length of 10 meters Vertex A slides in Oy, vertex B slides in

Ox Assuming vertex B is slipping away origin O with 1m/s speed How speed of vertex A of slider is sliding on the origin O when B sliding to point far away from origin O about 6 meters

Step 1: Establishing Mathematical model of problem

Called x ,y respectively distance from Bto O and from A to O (x, y is a function of t)

The mathematical problem inform '

When x 6, take the place of  1 we havey 8 Replace x 6, y 8, ,

y t   ( negative, because A is sliding down)

This means that the distance from vertex slider A versus origin O is declining at the rate of 3 /

4 m s Step 3: Conversion results into answer practical questions format

Vertex B slip away origin O with 1m/s speed When reach to position far away from origin O is 6 meters, vertex A of AB slider slip to origin O along Oy

with 3 /

4 m s speed

Example 3: On the surveillance camera, or in the endoscopic medical devices,

or in the robot factory, etc, there is very important part so-called magical eye

In order to fabricate such part, it is required to pay attention to its rotation speed, from this fact, we consider the below problem

A patrolman goes along the rail (straight line) at the speed of 1,2 m/s A searchlight on the ground is far 6.1m from the rail, and always lights towards such person Calculate rotational speed of the searchlight if the patrolman is

far 4.57m from the searchlight

Step 1: To develop a mathematical

model of the problem

Assign the distance from the man to

the closest point to the road surface to x,

assign the angle between the length

of the light beam emitted from the

searchlight

to the man and the straight line

perpendicular to the road surface to 

Assume x t'( )= 1,22 m/s

We should calculate '

( )t

 when x = 4,57m

Step 2: To process the mathematical model

- Based on the figure, the equation including x and  is x 6,1 tan 

- Derivate both sides including t, we have: 2

Step 3: To Convert the result into an answer to the practical question

At the moment that the man is far 4,57m from the closest point to the road surface, rotational speed of the searchligh is 0,128 rad/s

m 4,57 m