The aim of the article is to propound a simplest and exact definition of mathematics in a single sentence. It is observed that all mathematical and non-mathematical subjects whether science, arts, language or commerce, follow the same steps and roots to develop, they all consist of three parts: assumptions, properties and applications. These three terms make the exact definition of Mathematics, which can be applied to all subjects also. Therefore all subjects can be brought under the same umbrella of definition consisting of these three terms. Following this mathematics has been defined as the study of assumptions, its properties and applications. Then different branches of mathematics have been discussed. A short paragraph has been devoted to technical teachers and students on engineering mathematics. In last how should we teach mathematics has been emphasized? A special focus on the type of assignment has been mentioned. This article will be useful for mathematics teachers and its learners, if it is discussed in the first few lectures of undergraduate and post graduate level as well as will be more fruitful for technical students as they can understand and apply it better than non-technical students.

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EXACT DEFINITION OF MATHEMATICS

Dharmendra Kumar Yadav

Assistant Professor, Department of Mathematics

Shivaji College, University of Delhi, Raja Garden, Delhi-27

ABSTRACT

The aim of the article is to propound a simplest and exact definition of mathematics in a single

sentence. It is observed that all mathematical and non-mathematical subjects whether science,

arts, language or commerce, follow the same steps and roots to develop, they all consist of three

parts: assumptions, properties and applications. These three terms make the exact definition of

Mathematics, which can be applied to all subjects also. Therefore all subjects can be brought

under the same umbrella of definition consisting of these three terms. Following this

mathematics has been defined as the study of assumptions, its properties and applications. Then

different branches of mathematics have been discussed. A short paragraph has been devoted to

technical teachers and students on engineering mathematics. In last how should we teach

mathematics has been emphasized? A special focus on the type of assignment has been

mentioned. This article will be useful for mathematics teachers and its learners, if it is discussed

in the first few lectures of undergraduate and post graduate level as well as will be more fruitful

for technical students as they can understand and apply it better than non-technical students.

Key Words: Axiom, Theorem, Properties, Conjecture.

AMS Subject Classification: 97D30, 00A05, 00A06, 03E65, 01A80, 97D20

Introduction

Carl Friedrich Gauss referred mathematics as the queen of science but unfortunately students

fear from this queen, although the subject is very essential to the growth of many other

disciplines. The science of mathematics depends on the mental ability. It is the means to develop

the thinking power and reasoning intelligence, which sharps the mind and makes it creative. The

development of human beings and their culture depend on the development of mathematics. This

is why, it is known as the base of human civilization. It is also the language of all material

science and the centre of all engineering branches which revolve around it. Therefore it is the

past, present and future of all sciences. Narlikar has focused on the importance of mathematics

by mentioning that in 1957 when the Soviet Union launched the first satellite Sputnik, the United

States realized that to match it, the teaching of mathematics had to receive boost. After that many

major steps have been taken to improve the quality education of mathematics not only in USA

but in the world too.

International Research Journal of Mathematics, Engineering and IT

Vol. 4, Issue 1, January 2017 Impact Factor- 5.489

ISSN: (2349-0322)

© Associated Asia Research Foundation (AARF)

Website: www.aarf.asia Email : editor@aarf.asia , editoraarf@gmail.com

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Previous Attempt to Define Mathematics

Although the research in mathematics has covered a milestone, a major drawback has been seen

in the literature of mathematics that it could not be defined properly, so that all mathematical

subjects can be combined in short and in a single sentence. No consensus on the definition of

mathematics prevails, even among professionals. According to Wikipedia, mathematics has no

generally accepted definition and there is not even consensus on whether mathematics is an art

or science. Gunter M. Ziegler mentions that in German Wikipedia the definition is interesting in

a different way: it stresses that there is no definition of mathematics, or at least no commonly

accepted one. Even the famous book by Richard Courant and Herbert Robbins entitled "What

is Mathematics?" (and subtitled "An Elementary Approach to Ideas and Methods") does not give

a satisfactory answer. He claims that it is impossible to give a good definition in a sentence or

two. A great many professional mathematicians take no interest in a definition of mathematics, or

consider it undefinable.

Traditionally it is defined as the scientific study of quantities, including their relationship,

operations and measurements expressed by numbers and symbols. In mathematics dictionary by

James & James it has been defined as the science of logical study of numbers, shape,

arrangement, quantity, measure and many related concepts. Today it is usually described as a

science that investigates abstract structures that it created itself for their properties and patterns".

According to Wikipedia, „ Mathematics is the study of quantity, structure, space. Mathematics

seeks out patterns and uses them to formulate new conjectures. Aristotle has defined

mathematics as „The science of quantity?‟. Benjamin Pierce defined it as „Mathematics is the

science that draws necessary conclusions‟. Haskell Curry defined mathematics simply as "the

science of formal systems". Albert Einstein stated that " as far as the laws of mathematics refer to

reality, they are not certain; and as far as they are certain, they do not refer to reality". More

recently, Marcus du Sautoy has called mathematics "the Queen of Science …… the main

driving force behind scientific discovery". Thus although all most all great mathematicians stated

something for it, no generally accepted definition could be produced. A little attempt has been

done in this article to define mathematics in a single sentence and exact form, which will be

accepted for centuries without any counter example.

Basic Terms of Mathematics

In every mathematical subject we find some general terms like axioms, properties, theorem, etc.

These are the basics of the subjects whose meanings are given as follows:

Axioms: James & James stated that the axioms of a subject are the basic propositions from

which all other propositions can be derived. They are accepted as the starting points and are

accepted true without any proof. With the help of axioms we decide whether a given

mathematical statement is true or false. It is also known as assumptions or hypothesis or

postulates or propositions.

Therefore mathematics can be regarded as a set and study of assumptions, because it starts with

axiom. But it ends with reality. Here the statement „end with reality‟ means although we start

with assumptions, but after its application and in the final result, we reach at the real destination.

Example: One right angle is equal to 900 is an assumption. It has no proof. Although now there

are many properties from which it can be proved, but the property from which it will be proved,

will also be an assumption.

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Property: Any mathematical statement derived using axioms is known as a property. A straight

angle is equal to 1800 is a property, which is proved as the sum of two right angles. It can be

further divided in two parts: Theorem and Conjecture.

Theorem: A general conclusion which can be proved by the help of axioms is called a theorem.

In general it is proved logically using assumptions as true.

Example: The sum of the three angles of a triangle is 1800 is a theorem.

Conjecture: A mathematical statement which has many examples but cannot be proved or yet to

be proved is known as conjecture. A well known conjecture is Goldbach's Conjecture which

states that „Every even integer greater than 4 can be written as sum of two odd primes‟. So far

either a proof or a counter example has not been found.

Applications: If we apply the assumptions and its properties to solve real life problems, we say

that such type of assumptions have applications.

Example: The sum of the three angles of a triangle is 1800 is an application of the assumption

that one right angle is 900 and a straight angle is 1800 .

Thus we see that in mathematical subject we have three main terms: assumptions, properties and

applications. So we can say that every mathematical subject is composed of three terms:

assumptions, properties and applications. Thus we can define ' Mathematics is the study of

assumptions, its related properties and applications‟ . In fact every subject is the set of

assumptions, its properties and applications as has been explained in the analysis below:

Analysis of Some Properties

Analysis 1: We remember that the sum of the three angles of a triangle is 1800 as shown in fig.-

1. Fig.-5 shows that one right angle is equal to 900. Fig.-3 and Fig.-4 show that two right angles

make one straight angle which is equal to 1800. Fig.-2 shows that the sum of three angles of a

triangle is equal to 1800, which is generally derived from the fact that when three angles <A, <B

and <C are placed on a straight line with their vertices coinciding at one point, makes a straight

angle which is equal to 1800.

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We know that in geometry angles are measured in terms of right angle. In British System, a

right angle is divided into 90 equal parts called Degrees, so a right angle makes 900. In French

System, a right angle is divided into 100 equal parts called Grades, so a right angle makes 100g .

Whereas in Circular Measure, a right angle is equal to

. Thus the sum of the three angles of

a triangle is 1800 in British system, 200 g in French system and 𝜋 radian in Circular measure

system.

Therefore we first supposed that a right angle is equal to 900. Then we developed the definition

of a linear pair of angles, for it the sum of two angles is 1800 and then developed a property that

a straight angle is equal to 1800. By the help of this property, we proved that the sum of the three

angles of a triangle is 1800. What we followed here is that, first we assumed, then developed a

property and finally applied it.

Analysis 2: A spherical balloon is pumped at the rate of 10 cubic inches per minute, find the rate

of increase of its radius when its radius is 15 inches.

Let y be the volume and x the radius of the balloon at any time t. Then

cubic inches per

minute and we have to find

when x=15 inches. Since the balloon is spherical,

.

90

1

15 410

4 10

4

4222

2xx

dt

dy

dt

dx

dt

dx

x

dt

dy

Hence rate of increase of the radius when radius is 15 inches is

inch/minute. For the

function y=f(x), the differential coefficient of y with respect to x has been denoted and defined

by

xxfxxf

x

dx

dy

)()(

0

lim

provided that the limit exists. It has been called the measurement of rate of change in y with

respect to x. After that the derivative of

is

, was found with many other

elementary functions. Then it was applied in many such problems as discussed above. So it also

followed the three main steps: assumption, properties and applications. Similarly many more

examples in mathematics can be analyzed.

Analysis 3: Let us consider the shadow formation on a screen by a point source of light. A

source of light at S falls on the opaque body AB and makes a shadow A‟B‟ on the screen.

Let us consider the following:

dsh : diameter of the shadow;

db : diameter of the body

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S: source of light;

AB: Opaque Body;

A‟B‟: shadow of the body on screen

lb : distance between source & opaque body;

lsh : distance between opaque body & screen.

The distances between different objects have been indicated in the following figure:

Opaque Body Screen

A' A'

A

d

Source S C' dsh d

l b B B'

B'

lsh

Now since triangles SAB and SA‟B‟ are similar, we have

sh

b

sh b

bd

d

ll l

BA

AB

SC

SC

'''

From this we conclude that the size of the shadow is always greater than the size of the opaque

body or object. It will be equal to the size of the object if the screen is in contact with the opaque

body. As the screen is moved away from the opaque body the shadow size increases. To find the

size of the shadow we used the concepts of similar triangles, which is itself an assumption and its

properties.

Analysis 4: In language we first learn its alphabets, then words formed using alphabets and

finally we make sentences using many words. For example, in English language, we first study

from A to Z. Then we study words like Ram, Eat, Apple, etc having special meanings followed

by grammar as properties. Finally we make sentence Ram eats an apple. So every language

follows the three steps of development: assumption, properties and application. In English 26

alphabets are assumption, words and grammar are both assumptions and properties, where as a

complete sentence is the application.

The same procedures follow in other languages like Hindi, Urdu, Sanskrit, etc. Similarly in

Commerce, we assume the definitions of GDP, NDP, Income, Development, Growth, etc. and

then apply it to study about the status of the society or nations.

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From above examples, analysis and the basic terms of mathematical subjects, we can define

mathematics in the shortest and compact form as „Mathematics is the study of assumptions, its

properties and applications‟ , which can be taken as the exact definition of mathematics. In fact

„all mathematical and non-mathematical subjects are the set and study of assumptions, its

properties and applications‟, whether it is science, arts, commerce, literature, etc.

Branches of Mathematics

As far as the branch of mathematics is concerned, it is divided into four fields: Arithmetic,

Algebra, Analysis and Geometry. In arithmetic we learn about numbers and basic arithmetical

operations. When we apply arithmetic in solving real life problems, we get equations and thus

lead to Algebra. When the basic properties of arithmetic and algebra fail, we need analysis. In

analysis we generally study about limits, continuity, etc.

In Geometry we study about shapes and size of the figures. It is divided into two parts: Plane (or

Euclidean) Geometry and Spherical (or Non-Euclidean) Geometry. Spherical geometry is

further divided into two parts: Elliptical (or Riemann) Geometry and Non-elliptical (or

Hyperbolic) Geometry.

The basic difference among the above is that, in plane geometry, the sum of the three angles of a

triangle if 1800 where as in spherical geometry it is not equal to 1800, but either greater than or

less than of it. In elliptical geometry it is more than 1800 but in hyperbolic geometry it is less

than 1800.

The shapes of a triangle in above three geometries are as follows:

Similarly other properties and figures can be studied in three geometries.

Pure and Applied Mathematics

For the sake of simplicity, mathematics is divided into two branches: Pure and Applied

Mathematics.

Pure Mathematics is concerned with increasing knowledge of the subject rather than using

knowledge in practical ways, i.e. its study is theoretical. For example, trigonometry, geometry,

set theory, vector, etc. It is concerned with concepts and ideas that do not necessarily have any

immediate practical application. Its importance can be better understood by the well known

statement "A pure mathematician makes dreams even beyond the imagination of human

beings, and it is the scientists and technologists to apply them."

Applied Mathematics is concerned with using knowledge of pure mathematics. It is not

theoretical but practical. In it we use the theories and concepts of pure mathematics. For

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example, mechanics, dynamics, statics, physics, etc. It is concerned with the use of mathematical

theories and principles as tools to solve problems in any field, whether it is research or problems

in actuarial science, economics, financial analysis, market research analysis, meteorology,

oceanography, aviation, aerodynamics, robotics, population studies, commercial surveys,

physics, chemistry, biology, social sciences, earth sciences, industrial research and development.

The study of problems in applied mathematics leads to new developments in pure mathematics

and theories developed in pure mathematics often find applications later. Work in applied

mathematics requires a theoretical background, which enables the mathematician to understand

the physical dimensions and technicalities of the problem. The study of pure and applied

mathematics is interdependent. Applied mathematics is like a flowing river having pure

mathematics on its two banks playing like domain on the boundaries. The two branches are so

interrelated and mixed that no sharp (or dividing) line can be drawn between them.

Engineering Mathematics

It is a part of applied mathematics. Kreyszig has mentioned that for the sake of deciding the

depth of studying mathematics, while teaching mathematics to the engineering students, we

should limit our knowledge of mathematics to the extent as far as the applications of the subject

are concerned. Technical students need solid knowledge of basic principles, methods, and

results, and a clear perception of what engineering mathematics is all about, in all three phases of

solving problems related to real and physical world: Modeling, Solving and Interpreting.

How To Teach Mathematics?

Ronning has pointed out that mathematics is becoming more and more important in study. More

and more decisions are made and actions are being taken on the basis of mathematical models.

So the problem arises that, what should we emphasize when we teach mathematics? What kind

of understanding do we want the students to develop? What kind of mathematics, and how much,

do all students need to know?

A simple answer of the question is that every chapter must be divided into three parts:

assumptions, properties and applications. When we start teaching, we must mention that what are

the basic assumptions in the chapter keeping in view that definition of a term is itself an

assumption. What can we obtain from the assumptions and in last how and where can we apply

these concepts? Even students may be allowed to remember the definition as their own

assumptions and then try to find out some properties related to them and the previous

mathematical or non-mathematical knowledge they have. In this way the learner will enjoy the

subject and they will improve their ability of mathematical power.

As far as the engineering mathematics is concerned, Kreyszig states that it would make no sense

to overload students with all kinds of little things that might be of occasional use. Instead it is

important that students become familiar with ways to think mathematically, recognize the need

for applying mathematical methods to engineering problems, realize that mathematics is a

systematic science built on relatively few basic concepts and involving powerful unifying

principles, and get a firm grasp for the interrelation between theory, computing and experiment.

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What should be the Format of Assignment?

Assignments play an important role in learning. In general it has been found that the teacher

gives some examples as assignments to solve. In this manner students generally do not care

about basic assumptions. They apply formula blindly and miss the basic concepts. They miss the

game of enjoyment that how properties are developed using assumptions, which finally fails our

aim of increasing mathematical ability in students. In fact the proper format of assignments must

follow the three main terms of the subject: assumption, properties and applications.

In other words, students must be directed to do assignment in three steps: first they must define

the basic terms of the chapter followed by the properties with proof. They must make a table of

the formulae and then solve at least five examples on each formulae or properties. In this way

students learn the definition, formulae and understand the basic structure of the chapter, which

makes them perfect in application. Thus our motives become more and more successful in

increasing the interest of mathematics among students.

Conclusion:

Finally we conclude the exact definition of mathematics as the study of assumptions, its

properties and applications. In teaching we must maintain the order of assumptions, properties,

and applications. This order must be maintained in assignments to get the desired aim of teaching

mathematics. Similarly all non-mathematical subjects can be defined as the set of assumptions,

its properties and applications.

Acknowledgement

Author acknowledges that the example on the size of the shadow has been taken from a lecture

delivered by Late Dr. P. Singh, Professor of Physics, BIT, Patna and the figure of triangles in

three geometries has been copied from Google. Some of the definitions have also been taken

directly from the sources mentioned in references.

References

Boaler J., The elephant in the Classroom: Helping Children Learn & Love Maths,

Chapter-1, Souvenir Press, 2008

Burton D. M., Elementary Number Theory, 7th Indian Edition, McGraw Hill Education

(India) Pvt Ltd, New Delhi, 2012, pp. 50-53

Courant R., Robbins H., What is Mathematics? An elementary approach to Ideas and

Methods, 2nd Edition, Oxford University Press, New York, 1996

Gakkhad S. C., Teaching of Mathematic, N. M. Prakashan, Chandigarh, 1991

James & James, Mathematics Dictionary, 4th Edition, CBS Publishers & Distributors,

India, 2001, pp.23, 169-170, 239, 387

Kennedy L. M. & Tipps S., Guiding Children‟s Learning of Mathematics, 8 th Edition,

Wadsworth Publishing Company An International Thomson Publishing Company, 1997

Kreyszig E., Advanced Engineering Mathematics, 8th Edition, John Wiley & Sons, 2005

Loney S. L., Plane Trigonometry, Part-I, Metric Edition, A. K. Publications, Agra, 1990,

pp. 1-17

Narlikar J. V., Mathematics: The Queen of Sciences, Education Article, Manorama Year

Book 2013, pp. 480-484

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International Research Journal of Mathematics, Engineering and IT (IRJMEIT)

42 | P a g e

Nelson D., The Penguin Dictionary of Mathematics, Penguin Books, 3rd Edition, 2003,

pp. 21, 78, 147, 185-186, 271, 399

Ronning F., Developing Knowledge in Mathematics by Generalising and Abstracting,

Mathematics Newsletter, Ramanujan Mathematical Society, Vol.17 (4), March 2008,

pp.109-118

Schleicher D. & Lackmann M., An Invitation to Mathematics From Competition to

Research (Preface: What is Mathematics? by Gunter M. Ziegler), Springer, XIV, pp.220,

2011

Sinha K. C., A Text Book of Calculus, Students‟ Friends, Patna, 1994, pp. 236-237

Vygodsky M., Mathematical Handbook: Elementary Mathematics, MIR Publishers,

Moscow, 1987

Ziegler G. M. & Loos A., Teaching and Learning "What is Mathematics",

www.google.com

https://en.wikipedia.org/wiki/Hyperbolic_geometry

https://en.wikipedia.org/wiki/Elliptic_geometry

https://en.wikipedia.org/wiki/Definitions_of_mathematics

... Mathematics has an abstract object of study, mathematics bases itself based on agreements show that mathematics fully uses a deductive mindset, and mathematics is imbued with the truth of consistency [5]. James & James define it as the science of logical study on numbers, shapes, arrangements, quantities, measures and others related concepts [6]. The conclusion from various opinions stated by those experts reveals that mathematics is a science containing structured and organized symbols with deductive evidence ranging from undefined elements to the deifned ones, to the axiom or postulate and finally to the argument. ...

... Mathematics is a science discipline about abstract structures (Jankvist, 2015;Yadav, 2017). However, the cognitive development of students is still on the concrete operational stage where they can solve problems that are related to concrete action or events (Ghazi & Ullah, 2015;Ojose, 2008). ...

  • Farida Puput

Students' critical thinking ability requires improvement from schools as an educational institution. Besides, it is important to maximally integrate character education into mathematics learning. One of the attempts was implementing mathematics comic that contains Pancasila values as teaching material through contextual teaching and learning. Therefore, this study aims to analyze the effectiveness of mathematics comic teaching material with Pancasila values in improving students' critical thinking and character. This is a quasi-experimental study that involves non-equivalent control group design. The population was fourth-grade students of elementary schools in Gajahmungkur District, and data were collected using a critical thinking test and questionnaire. The results showed that using mathematics comic teaching material with Pancasila values was (1) effective in improving students' critical thinking ability; (2) effective in developing character, especially discipline and hard work trait. In the beginning, both character traits were categorized as good, and after treatment, there was an increase in the very good category. Therefore, it can be concluded that the use of mathematics comic teaching material with Pancasila values is effective in improving critical thinking ability and character traits.

... The teacher added to the opinion that mathematics was more suitable as supporting material rather than became a focus on STEAM learning. This was certainly supported by the theory which stated that mathematics is the queen of science (Yadav, 2017). Mathematics as a basic science that must be learned in learning other disciplines, so that if mathematics became the focus of the material it would be very difficult to develop. ...

Science, technology, engineering, arts, and mathematics (STEAM) have been applied in various countries because they have been able to answer the challenges of the globalization era. The implementation of STEAM at school has demanded that teachers have a role in making a relationship between disciplines in science contained in STEAM. The purpose of this research was to describe the perceptions of experienced teachers about math-focused STEAM learning. The research was a descriptive study on 14 vocational high school mathematics teachers in Malang, Indonesia. They had 20-30 years of teaching experience. Data were collected using essay questionnaires. The result showed that their perceptions of STEAM learning were positive. However, they also said that there were several obstacles to math-focused STEAM learning. The first obstacle was the unavailability of supporting literature. The second obstacle was that there were teachers who have no received training. The third obstacle was only a limited number of mathematics material that can be applied in STEAM learning. Additionally, the teacher stated that mathematics was more suitable as supporting contain in STEAM learning than as the primary focus.

  • Osama Khadour Osama Khadour

The study aimed to know the reality of mathematics education in schools in the Syrian Arab Republic, and to develop it using educational technology based on the experience of The National Center for Distinguished and the experiences of developed countries, through: 1) Diagnosing the reality of mathematics education in the schools of the Syrian Arab Republic. 2) Diagnosis of the extent of the Syrian mathematics teacher's knowledge of mathematics teaching technology and the extent to which he has used it. 3) Diagnosing the reality of the infrastructure for mathematics education technology in Syrian public schools. 4) Identification the Obstacles to implementing mathematics education technology in Syrian public schools. 5) Identification the prospects for developing mathematics education in Syrian public schools. The researcher visited the center and met with mathematics teachers, and learned about the mechanism of teaching mathematics and the advantages of using educational technology in it, in addition to studying the experiences of some Arab and foreign countries in this field, with the aim of formulating proposals for development prospects. Then the researcher distributed the research questionnaire electronically in social media groups. And that in the period from 3/24/2020 to 7/13/2020. The sample of the study was two hundred and nineteen teachers of mathematics from different governorates in the Syrian Arab Republic. The most prominent results of the study: 1. Mathematics teachers at the National Center for Distinguished have high skills in using modern software in teaching mathematics: Geogebra, math type, Latex, Microsoft office, Moodle and other drawing software, and they acquired it through self-learning. 2. Mathematics teachers at the National Center for Distinguished use modern equipment to teach mathematics: desktop and laptop computers, interactive whiteboards, and projectors. 3. There are statistically significant differences between teachers 'answers about the extent of their knowledge of mathematics teaching technology and the extent of their use of it, based on the scientific qualification variable at a significance level (0.05), in favor of postgraduate degree holders. 4. There are statistically significant differences between teachers 'answers about the extent of their knowledge of mathematics education technology and the extent of their use of it, based on the course variable at a significance level (0.05), in favor of a group of online self-education courses. 5. There were statistically significant differences between teachers 'answers about the extent of their use and knowledge of mathematics teaching technology based on the gender variable at a significance level (0.05), in favor of males. 6. The weak level of technology integration courses in education in the field of modern mathematics software. 7. The study showed the impact of the Syrian war on the education process in addition to the Coronavirus crisis, and the emergence of the student's financial conditions problem. As he is no longer able to obtain private lessons as the highest percentage (91.8%), in addition to his poor level, his lack of interest in the subject and his fear of it, then the educational problems of the subject of mathematics related to traditional teaching methods, the failure to use modern methods and techniques in teaching, the weak salaries of teachers and the absence of their training courses, the poor performance of the first episode teacher, And problems related to the huge curriculum, and the large number of students in the classroom. The free and compulsory education in Syria had a positive impact on the process of mathematics education, in addition to the strength of the mathematics curriculum applied in Syria, and its ability to develop students' skills in mathematics. 8. The study showed that most of the modern educational equipment is not available. 9. The emergence of the problem of power cuts as the most prominent obstacles, the weakness of teachers in the English language, the high cost of equipment, in addition to the teachers not being well qualified for this technology. 10. The study showed that the most important thing that contributes to the development of mathematics education is the necessity to follow professional development courses before and during service, reduce the number of students in the classroom, raise teachers 'salaries, reduce the density of the material and accredit specialized mathematics teachers from the primary stage, and include the university degree with educational needs or combine it with a diploma in educational qualification, in addition to using technology in education. The study presented a set of proposals, the most important of which are: 1) The Ministry of Education's development of distance education platforms and the possibility of these platforms including qualifying courses for teachers. 2) The Ministry of Education develops teacher training courses and technology integration courses in education, making them special in all subjects and in mathematics in particular. 3) Developing a long-term strategy by the Ministry of Education to develop mathematics education, including the use of mathematics education technology. 4) Accrediting mathematics teachers who hold a diploma in educational qualification in the first grades. 5) Adding some subjects dealing with methods of teaching mathematics as basic subjects in the College of Science. 6) Increasing teachers 'salaries and reducing the number of students inside the classroom. Key words: Mathematics Education Technology, The National Center for Distinguished. Self-learning Online Courses.