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

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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
in Universities of industry.

+ To perform teaching experiment to test the feasibility and effectiveness
of the solutions.
3. SCIENTIFIC HYPOTHESIS
If appropriate methods of Advanced Maths teaching associated with the
vocational training practice in Universities of industry are developed, the students
will be able to apply Mathematics tools to their study and vocational practice.


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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


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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);

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 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.


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 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:


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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
UNIVERSITIES OF INDUSTRY
In this chapter, we develop an Advanced Maths teaching method in
universities of industry, particularly:
2.1. ORIENTATION AND REQUIREMENTS OF ADVANCED MATHS
TEACHING ASSOCIATED WITH VOCATIONAL TRAINING IN
UNIVERSITIES OF INDUSTRY
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.


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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,


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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


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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


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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


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Find out electric circuits i1 , i2 , i3 , i4 , i5 , i6 .
Exercise 8: Applying differential equations in electric circuit research
Based on the below electric circuit,
Power
E= 4 cos10t ,
R=40  ,
L=1
H,
25

4

C= 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 its weight P. Identify its movement during the braking and
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its distance from the braking to stop.
Examples in relation to the Method 3
Example 1: Considering an ellipse structure in mechanical as shown
y

y
A

A

Slider
Slider

y'(t)=?

y

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O

B

x

O

B
x'(t)=1

x

x

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 B to O and from A to O (x, y is a function of t)
The mathematical problem inform x' (t )  1 m / s . The requirement set out is
find y , (t ) when x  6 meters. In this mathematical problem, the relation between x and
y : x2  y 2  100 1
Step 2: Handling mathematical model
We have: 2 x.x, (t )  2 y. y, (t )  0  y ' (t )   x x, (t )  2  .
y


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When

x 6,

we have

take the place of 1 we have y  8 . Replace

y ' (t )  

3
4

x  6 , y  8 , x, (t )  1

in  2 

( 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 m / s .
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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 m / s speed.
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6,1 m

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
4,57 m
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: dx  6,1. 12 d  d  1 cos2  dx
dt

It means

 ' (t ) 

1
cos2  . x ' (t ) .
6,1

Because

x ' (t ) =

cos  dt

1, 22

dt 6,1
1,22
  ' (t ) 
cos2  .
6,1

dt

- If x = 4,57 (m), according to Pitago, length of the light beam is 7,2m, then
cos  0,8   ' (t )  0,128.
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.


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Examples in relation to the Method 5
Assign tasks and guide students self-study by applying Advanced maths
to the practice of Mechanics via the problem:
If a piece or a piece of wire is homogeneous, then its linear density is
even, and is identified by weight per one unit of length    m l  and is
calculated by kilogam per meter (kg/m). However, it is assumed that a metal
bar is not homogeneous, then its weight as measured from the left end to the x
point is m  f ( x) as shown in the figure.

- Weight of a metal bar from point
m  f ( x2 )  f ( x1 ) ,

x  x1

x  x2 is measured
density  m  f ( x2 )  f ( x1 )
x
x2  x1

to the point

thus its average density is: Average

by

- If x  0 , it means that x2  x1 , we can calculate average density in the
increasingly smaller distances. Linear density  in the point x1 is the limit of
values of average density when x  0 , it means that Linear density is variable
speed of respective weight according to its length. Then, we have:
m dm

x 0 x
dx

  lim

- Therefore, linear density of the metal bar will be the derivative of the
respective weight according to its length.

- For example, if m  f ( x)  x , in which x is calculated in meter (m) and m is
calculated in kilogam (kg), average density of the metal bar, provided that
1  x  1, 2 , will be measured as following:

m f (1, 2)  f (1)
1, 2  1


 0, 48 kg m
x
1, 2  1
0, 2

- In which the density at the right side at


x 1

will be measured as following:

dm
1

 0,50 kg m .
dx x  1 2 x x  1

Examples in relation to the Method 6
Example 3:
Guide students who are performing scientific research by assigning tasks
to the students so that the students will practise and apply the 8-step process,

apply Advanced maths to solve problems in relation to electricity and
mechanics.
Exercise 1
Step 1: Calculate the magnitude of the magnetic field B generated from the
electric current I (its contact side with the circle of radius r is within the plane
perpendicular to the wire, its center is the wire axis).


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Step 2: According to Knowledge and methods of Physics, a stable electric
current I in a long wire will generate a magnetic field B whose contact side
with the circle is within the plane perpendicular to the wire, its center is the

wire axis (See the figure).
The madnetic field at the point M is far a distance of r from the center
O of the wire, the direction of the electric current is from P to Q.
I is electric currents flowing through the surface bounded by a closed
curve C and μo is constant (magnetic permeability of the environment). Then,
Ampere law in relation to impact of electric current on magnetic field states
that:  Bdr  0 I
C

Step 3:
Here C is a circle, its radius is r. Hypothetically, B has its contact side
with the circles in the plane perpendicular to the wire, thus:
B=|B|T in which T is tangent line in a unit of the circle C, and |B| is the
magnitude of the magnetic field at the point on C (far a distance of r from the
center of the wire).
Step 4: Here, in order to calculate B, we rely on 2 formulas:

- Ampere law formula (in Physics).  Bdr  0 I
C

- Formula to calculate the integral of curve (in Maths)
- Compare two results and find the magnitude of the magnetic field B.
Step 5:
Assign: x  r cos , y  r sin  . Then: B  B   sin  ,cos  .
2

B   sin  , cos   r sin  , r cos   d

Have:  Bdr  
C

0
2



 



B r sin 2  , r cos 2  d 

0

2



B rd  2 r B

0

On the other hand, according to the Ampere Law, we have:  Bdr  0 I .
C

Then: |B| =

0 I
2 r

.


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Step 6: Teachers let students self-check the whole process of problem solving,
including steps: Understanding the task and collect knowledge; Mathematical
modeling; solving problem; converting results and answering the question.
Step 7: Students convert the results into question to the initial practical situation.
An electric current I, under the condition of environmental magnetic
permeability μo, whose contact side with the circle C of radius r is on the plane
perpendicular to the wire and the circle’s center is the wire axis, will generate a
magnetic field B (At the point C – far a distance of r from the center of the
wire), the magnitude of B is |B| = 0 I .
2 r

Step 8: After solving the practical problems (1-2-3-4), the students discuss and

agree the way to present their assignment, tasks.
Problem 2
A rocket burning fuel is moving in the space at the
speed of v(t), its weight m(t) at the moment t. If we
only consider its thrust force ve impacting on the rocket,
then it can be derived from Newton Law 2 on
movement of as following: m dv  dm ve
a) Prove that

dt
m(0)
v(t )  v(0)  ln
ve
m(t )

dt

b) In order to increase speed of the rocket twice as
impulse of thrust force, how many is rate of weight of
burned fuel and the initial weight.
Solution
a) Based on the Newton Law 2, we have:

m

dv dm
dv 1 dm

ve 


ve
dt dt
dt m dt

Integrating the two sides, we get:
t
 m(t ) 
dv
1 dm
dm
0 du du  ve 0 m du du  v(0) dv  ve m(0) m  v(t )  v(0)  ln  m(0)  ve
v (t )

t

 m(0) 
 v(t )  v(0)  ln 
 ve
 m(t ) 

b) According to the assignment:

m(t )

(q.e.d.)
v(t )  2 ve , v(0)  0 .

 m(0) 
 m(0) 
 m(0) 

2 ve   ln 
 ve  2 ve  ln 
 ve  ln 
2
 m(t ) 
 m(t ) 
 m(t ) 


Note that: m(0)>m(t) thus ln  m(0)   0 . Deduced
 m(t ) 

:

According the a, we get:

m(t )  e2 m(0) .

Thus, the weight of burned fuel and the initial weight is:
m(0)  e2 m(0)
 1  e2
m(0)


16

2.3. SUB-CONCLUSION OF THE CHAPTER 2
Associating Maths teaching with vocational training is a requirements and
a inevitable trend in universities in general, and in universities of industry in
particular. In chapter 2, we propose a method of Advanced Maths teaching,

which is shown in:
Identifying the direction and principles as a basis for building a system
consisting of three groups with 6 methods is to teach the students Advanced
Maths in Electricity and mechanics in universities of industry, and is illustrated
by a number of specific examples, in order to associate Maths with the
vocational training practice in “Mechanics’ and “Electric Engineering”, to
contribute to undergraduate education and training reformation towards
concentrating on the development of professional capacity.
CHAPTER 3 – TEACHING EXPERIMENT
This chapter presents the process of teaching experiment in order to assess
efficiency and the ability to implement the solution outlined in Chapter 2,
including:
3.1. PURPOSES, OBJECTS AND SCOPE OF TEACHING EXPERIMENT
3.1.1. Purposes
To verify feasibility and effectiveness of the proposed methods in the
dissertation, which focuses on understanding and assessing effectiveness of 6
methods of Advanced maths teaching as developed in the Chapter 2.
3.1.2. Contents
Within the framework of the dissertation, we have selected some main
contents in advanced mathematics to express the solutions. For the students in
two core major of universities of industry, Electricity and Mechanics, the
knowledge of Maths which is the most widely used includes integral calculus and
differential equations. Therefore, we select 5 lessons in this topic including total
length of 20 periods, in order to perform teaching experiment and test, assess, of
which 16 periods of theory and 4 periods of test, particularly:
 Unit 1: Derivative and differential of one-variable derivative – Applications
(2 periods)
 Unit 2: Integral -Application (3 periods)
 Unit 3: level-1 Differential Equations, leve-2 Differential Equations (6
periods);

 Unit 4: Derivative - differential of two-variable functions (2 periods);


17

 Unit 5: Two, three-layer Integral (3 periods) .
 Test: Derivative – Integral -Application (2 periods)
 Test: Two-variable Derivative - Differential Equations (2 periods)
3.1.3. Objects
Phase 1: The experiment conducted was conducted in Hanoi University of
Industry
- Time: From 15 / 9 /2013 to 20 / 6 / 2014
- Participants are students of classes: Electricity 1 and electricity 2 – Course 8;
Mechanics 6 and Mechanics 7 – Course 8. In which, the first group of
experiment and the first group of control are Electricity 1 and electricity 2,
respectively; the second group of experiment and the second group of control
are Mechanics 6 and Mechanics 7, respectively.
- Teachers: Nguyen Van Truong (teaching group of experiment), and Tran Thi
Hong Trang (teaching group of control).
Phase 2: The experiment conducted was conducted in Viet Hung University
of Industry
- Time: From 18/08/2014 to 24/06/2015
- Participants are students of classes: Power supply 1 – Course 38, Power
supply 2 – Course 38, Machinery manufacturing 1– Course 38, Machinery
manufacturing 2– Course 38. In which, the first group of experiment and the
first group of control are Power supply 1 – Course 38, Power supply 2 –
Course 38, respectively; and the second group of experiment and the second
group of control are Machinery manufacturing 1– Course 38, Machinery
manufacturing 2– Course 38, respectively
- Teacher teaching group of experiment: Ha Dang Toan; Teacher teaching

group of control: Do Phuong Long.
Students of the groups of control and the groups of experiment of each
university had the similar awareness and qualification to each others (based on
results of enhance Maths exam). However, enhance quality of students in Hanoi
University of industry was higher than that of Viet Hung University of industry.
All teachers in the teaching experiment in the groups of control and the
groups of experiment have good professional qualification and skills.
3.2. EVALUATING RESULTS OF THE TEACHING EXPERIMENT
3.2.1. Qualitative evaluation
Classroom atmosphere of the groups of experiment was ebullient,
students were partially aware of significance and application of Maths in the
life and in the occupation; thus they were more interested in and more active to


18

participate in study activities than the groups of control. In the event of
difficulty in applying Advanced Maths to practical problems, students in the
groups of experiment actively raised questions to teachers and answered
questions of teachers, initially formed the ability to use knowledge and
methods of Maths for problem solving. On the other hand, by discussing with
teachers who taught the groups of experiment and the teachers who obsered
lessons after every period, we obtained a lot of their ideas, but all of them
agreed that: in general, the proposed teaching methods were feasible, and if
they were comprehensively deployed, quality and effectiveness of Advanced
Maths learning of students in university of industry would be improved.
All above things will be important bases for us to give qualitative
evaluation of the effectiveness of teaching experiment, as following:
The developed contents and methods of Advanced maths teaching
partially met requirements of increasingly associating with occupational

practice, in consistent with awareness of students, and also with current
demand of Advanced Maths teaching and learning. The students were initially
aware of familiar with applying the knowledge of Advanced Maths to problem
solving in the occupational practice. In addition, thereby, the students mastered
the nature and significance of the knowledge of Advanced maths.
3.2.2. Quantitative evaluation
Quantitative evaluation is mainly relied on results of 2 tests (according to
training regimes of each Advanced Maths module), those tests were used for both
groups of experiment and groups of control. Each test includes 2 parts, the rate of
requirements of Maths and requirements of practical application is 60 – 40.
+ The first part (60%) includes pure knowledge of Maths, aims at assessing the
understanding of Advanced of the students
+ The second part (40%) includes problems related to knowledge of special
subjects, aims at assessing the application of Advanced maths to the
occupational practice of the students.
TEST 1 (Length: 90 minutes – Only for students majoring in Electricity)
Question 1. (2 points)
a. Based on the function
b. Calculate:

x

( x  1)e , khi x  0
f ( x)   2

 x  ax  1, khi x  0

x

L  lim  2  

x a
a


tan

x
2a

Find

a

so as to

f ' (0) .


19

Question 2. (2 points)
Write Taylor expansion of the function
vicinity of

x  2.

Then calculate the integral

f ( x)  x4  8x3  24 x2  50 x  90

I 

in the

x 4  8 x3  24 x 2  50 x  90
dx
( x  2)2

Question 3. (2 points)
Calculate the area of the plane figure delimited by Cacdinoid r  a(1  cos ) , a  0 .
Question 4. (4 points)
a. Based on an electric circuit as below figure.
K

i(t)

E(t)

C

Have C  1 F .At the moment t  0 , the lock K ( UC (0)  0 ) is closed and we obtain
the graph of electric current in the circuit i(t ) over time as follows.
i(t)
1
4
0

1

Calculate voltage U C (t ) .

b. Based on an electric
circuit as the figure.

1

t

2

-1
i(t)
R
E(t)

C
L

What equotion does express Kirchhoff 2 Law?
( A)

(C )

1
di(t )
i(t )dt  L
 E (t )

C
dt
1

di(t )
R.i(t )   i(t )dt  C
 E (t )
L
dt

R.i(t ) 

Some statistical results

;

( B)

;

( D)

di(t )
 E (t )
dt
1
1 di(t )
R.i(t )   i (t )dt 
 E (t )
C
L dt

R.i(t )  C  i (t )dt  L

20

Chart 3.7. Marks of the test 2 of students majoring in Electricity
(The first group of experiment)
25
20
15
TN

10

ĐC
5
0
1

2

3

4

5

6

7

8

9

10

Chart 3.8. Marks of the test 2 of students majoring in Mechanics
(The second group of experiment)
25
20
15
TN

10

ĐC

5
0
1

2

3

4

5

6

7

8

9

10

The statistical results show that:
Marks of the tests show that the acquiring basic knowledge of both Groups
of experiment and Groups of control are similar to each other. Particularly, the
students of both groups of experiment and Groups of control, basically, can
solve almost knowledge of pure Maths in the tests. However, the part requiring
application of Advanced Maths to practical problems related to occupation,
there is a clear differentiation. For the groups of control, teaching is still
tradiational, teachers only focus on transmitting knowledge of Maths, guiding
students to apply and exploit knowledge of Advanced Maths to occpational
practice is rarely, or hardly; thus, the students cannot solve the practical
problems related to occupation. Meanwhile, for the groups of experiment, after


21

observating the way to present the test of students, we find that their
presentation and argument are relatively clear and deep, the students are
initially able to develop mathematical model of practical problems related to
occupation and able to solve academic problems and convert its results into
practical results. Therefore, average mark X of the students in the groups of
experiment is higer than that of the groups of control, and an important thing is
that students in the groups of experiment have less under-7 marks and have more

7-9 marks than the students in the groups of control do.
3.2.3. Statistical hypothesis verification
We mention statistical hypothesis H 0 : “The difference in the rate of
excellent and good marks is just random, teaching methods do not impact on
such rate (It means that apply teaching methods to enable students to have
ability to solve practical problems related to occulation by mathematical
models in the groups of experiment, but the ability to solve the problems of the
students in the groups of experiment is not different to that of students in the
groups of control). If the selected samples are representative, for statistical
hypothesis testing H 0 , we use the following formula:
- Calculate indicators:
+) nTN , nDC (Total number of students in the groups of experiment and in the
groups of control)
+) mTN , mDC (Total number of students whose marks are at least 7 points in the
groups of experiment and in the groups of control)
+)

pTN 

mTN
m
, pDC  DC
nTN
nDC

(The frequency of at least 7 point in the groups of

experiment and in the groups of control)
+)

p

+)

K

mTN  mDC
nTN  nDC

 pTN  pDC 



p 1 p

;

n

nTN .nDC
nTN  nDC

n



- Select the assumption: H0 : pTN  pDC , assumption H : pTN  pDC
- Conclude: By  , Look up table to calculate u12 .If K  u12 , reject H 0 , accept
H.
Apply the above formula to the groups of experiment and in the groups of

control in Electricity in Hanoi university of industry, we have:
nTN  100 , nDC  100 ; mTN  68 , mDC  9 ; pTN 

68
9
, pDC 
; p  77 ; n  50 .
100
100
200


The, we can calculate:

K

 pTN  pDC 



p 1 p



22
n
 8, 26.

By

  0,05 ,

Look up table, we

have u12  u12.(0,05)  u0,9  1,645 . We have K  8, 26  1,645 .
Thus, assumption is rejected and it can be concluded: The difference in the
rate of over-7 marks between the groups of experiment and the groups of
control is statistical.
3.3. SUB-CONCLUSION OF THE CHAPTER 3
Through the experiment and the obtained results, we can conclude as
following:
 The proposed methods in the dissertation can be performed during
Advanced maths teaching in the universities of industry
 Implementing of the above methods contributes to:
+ Ensure that the increasingly application of Advanced Maths to the
vocational training practice in Mechanics and Electricity is performed more
feasibly, more efficiently, especially develop the students’ ability to apply
mathematical tools to the practice (although only in the initial extent, formig
habit and ability to apply maths to some practical problems at many levels);
+ Help teachers know the necessity of advanced maths teaching associted
with vocational training practice, be aware of enhancing their own awareness and
skills of application of Advanced Maths to the practice.
 Results of the teaching experiment shows that the scientific hypothesis of
research has been tested, the feasibility and effectiveness of the proposed
solutions are initially confirmed.


23

CONCLUSION

Teaching Advanced Mathematics to student in Universities of Industry
towards associated with occupation is very necessary to research. The thesis
includes research into theoretical bases regarding Maths teaching associated
with the practice and finds the current status of this matter in the Advanced
Maths teaching and learning in the universities of industry, then propose
specific six measures to teaching advanced math associated with occupation
training practice to students in mechanical and electrical industries of industrial
universities..
The proposed measures represent different aspects of teaching advanced
maths period and impact positively on three aspects:
+ Impact on teaching competencies of teachers.
+ Impact on teaching methods and assessment methods.
+ Impact on self-learning and self-study methods of students.
Each measures are illustrated by specific examples. The exercises
selected in the thesis are evident pedagogical intent. It will help students realize
clearly the relationship between Advanced mathematics content in industrial
universities with general practice, it also help students improve capacity
associated with knowledge and skills of advanced math sassociated with the
practical situations of the students in the future.
The author has performed the teaching experiment in 4 classes of Hanoi
university of industry and 4 classes of Viet Hung university of industry,
initially affirmed the feasibility of the methods, and the correctness of the
scientific hypothesis as stated above.
The theoretical point of thesis given are based on theoretical studies,
actual situation of advanced maths teaching associated with occupation training
practice to students in Industry of Universities, so that ensure the scientific.


24

RECOMMENDATIONS
Contents of Advanced maths used in the universities of industry should be
reformed in consistent with the education objectives towards developing
capacity of trainees. Especially, it is necessary to reduce academic knowledge,
and to increase practise to apply Maths.
In addition, teaching should be reformed in contents, forms and means of
implementation, in order to obtain the objectives – developing the students’
ability to apply maths.
Moreover, it is required to further research into integration and
interdisciplines of the Advanced Maths teaching programs to both students and
teachers in the universities, to ensure the effective exploitation of combination
of subjects for the objective – vocational training towards characteristics of the
universities of industry.
Finally, it is required to research into “link” of vocational training
programs in the universities of industry and basic subjects (Advanced Maths,
physics, chemistry, informatics, etc), in order to teach students, to create
consistency; the universities should design and develop new programs towards
developing professional capacity of trainees.