CC BY
13UDC 510.24
THE SCIENTIFIC APPROACH TO TEACHING MATHEMATICS
Khikmatova Rano Artikovna Taslikent State Transport University Senior Lecturer, +998(98)-123-07-57, rano.liikmatova@bk.ru
Islamov Yorkin Abduxakimovich Taslikent State Transport University Senior Lecturer, +998(98)-123-07-57, rano.liikmatova@bk.ru
Annotation: The article describes science in various segments of math teaching starting with the nature of math to mathematical tasks as an important method in shaping the system of basic mathematical knowledge, abilities and habits in students. In the end, some drawbacks in math teaching are mentioned which occur due to the inappropriate treatment of science in the teaching process.
Аннотация: В статье описывается наука в различных разделах преподавания математики, начиная с природы математики и заканчивая математическими задачами как важный метод формирования у учащихся системы базовых математических знаний, умений и навыков. В конце упоминаются некоторые недостатки в преподавании математики, возникающие из-за неправильного обращения с наукой в учебном процессе.
Annotatsiya: Maqolada matematikani o'qitishning turli bo'limlari bo'yicha matematika tabiatidan boshlab, matematik masalalar bilan yakunlangan fan talabalarda asosiy matematik bilim, ko'nikma va malakalar tizimini shakllantirishning muhim usuli sifatida tavsiflanadi. Maqola nihoyasida matematika fanini о qitishda о quv jarayonida fanga notogri munosabatda bo lishdan kelib chiqadigan ayrim kamchiliklar to g risida to xtalib otildi.
Key words: math, teaching math, scientific approach, the science principle, mathematical concept, theorem, problem - task.
Ключевые слова: преподавание математики, научный подход, принцип науки, математическое понятие, теорема, проблема-задача.
Kalit so'zlar: matematikani o'qitish, ilmiy yondashuv, fan prinsipi, matematik tushuncha, teorema, masala-topshiriq.
"Live as if you were to die tomorrow.
Learn as if you were to live forever "
- -Gandhi
Introduction. The Decree of the President of the Republic of Uzbekistan dated April 29, 2019 "On approval of the Concept for the development of public education in the Republic of Uzbekistan until 2030" PF-5712 sets the goal to enter the top 30 countries in the world by 2030 PISA. It can be achieved by improving the quality and efficiency of educational institutions through the introduction of international standards for assessing the quality of education and training [1]. That is why quality and effective education creates a basis for new opportunities and innovations in the development of our country.
Modern mathematics teaching methodology offers various possibilities for solving the problem of involving students in independent and research work, it develops their problem solving skills and develops their creative thinking processes and skills. One of those possibilities is in the area of scientific framework. The foundation of a scientific framework is the principle of science and scientific research methods.
Teaching mathematics today primarily takes place within a professional framework. However, teaching math is a complex and demanding process. Even though being professional is
a condition for its success, it is not sufficient. The complexity is successfully resolved by relating math to other sciences. That way we get a process which has to take place harmoniously within several frameworks. The main frameworks are language frameworks, professional frameworks, methodology frameworks, scientific frameworks, pedagogical frameworks and psychological frameworks.
As it is not easy to achieve harmony, occasional slips and weaknesses occur in math teaching which significantly influence the quality of math education. That reflects negatively on the aims of modern math teaching which emphasizes involvement of students in independent and research work, developing skills for problem solving and the development of creative thinking and creative skills.
Modern mathematics teaching methodology offers various possibilities for solving the above-mentioned problem. A teacher can find many possibilities within the scientific frameworks. The foundation of scientific frameworks is the science principle and scientific research methods. These concepts often cause a dilemma. What does a scientific approach mean in math teaching? The aim of this article is to describe that meaning and to give a few postulates and issues which arise in scientific frameworks of math teaching. N.B. a math teacher does not have to be a scientist in order to appropriately, correctly apply the science principle, and research methods in math teaching.
The science principle. Didactic principles are the founding ideas and guidelines based on which teaching takes place. The basic characteristic of each principle is contained in the name of the principle itself which math teachers mostly understand. The same applies for the science principle. Nevertheless, the principle should be described in detail.
The science principle in math teaching consists of the appropriate harmony of teaching content and teaching methods on the one hand and the demands and regularities of math as a science on the other hand. That means that a math teacher should introduce students to those facts and form in their thought processes those mathematical occurrences, which are scientifically founded today. Math teaching has to be such to enable further broadening and enrichment of content and a natural continuation of math education at a higher level.
It is evident that from the description the principle of science makes a connection between math as a teaching subject and math as a science [2, 3].
Teaching mathematics. From the comparison mentioned, we can easily conclude that scientific methods are important for modern math teaching. That is why they are the subject of research in modern math teaching methodology. Through the selection of appr opriate problems and through the application of that method a creative teacher can prepare students for work, which is very similar to research work, work of a scientist. Plenty of math teaching content can undergo such applications on thus meeting the science principle in its extent.
What does our teaching practice show in that respect? During the lesson, the math teacher often says: "the analysis shows", "let's have a look at some concrete examples", "analogous it is proven", "this set of facts induce the conclusion", "the result of these observations is a generalization", "through specialization we get the formula", "mathematical concepts are abstract" etc. Do the students understand these words? How do we check their understanding? Knowledge of the procedures mentioned is often implied and therefore lack an explanation. That is not good.
Students should gradually and appropriately be taught how to analyze, synthesize, abstract, induce, deduce, generalize, specialize, observe analogies, regardless of whether they will be seriously involved in math at a later stage. As opposed to the usual acquisition of content, this is a higher level of mathematical education. Mathematical way of thinking is a valu able gain of mathematical education, applicable in many other activities. The words gradual and
appropriate are emphasized. If scientific procedures are appropriately and correctly applied, with a necessary feeling for the difficulty of math content and mathematical way of thinking, taking into consideration mathematical abilities of each student, it can be expected that math teaching will be successful. On the contrary, students will have significant difficulties in acquiring the teaching content and with time they can get the wrong impression that math is a more difficult subject than it actually is. Sadly, math books, and consequently the teaching process do not pay sufficient attention to the regularities of the application of scientific procedures. In teaching some math content, it can be established that they are wrong from that point of view. The science principle is therefore neglected.
Students' failures in math and the inadequate knowledge which is displays upon the completion of their education are for the majority part a consequence of the fact that teaching is mostly done at a lower level, where acquisition of content is overemphasized, while the higher level is neglected. The reason for this neglect lies in the fact that for high er level math teaching one needs more demanding scientific methods based on teaching which is heuristic and problem solving. On the other hand, the need for (appropriate) use of scientific methods in math teaching can be explained with the following facts:
Developing math is a concrete and inductive science, and math itself is an abstract and deductive science.
What is teaching math in that respect? Teaching math in primary school is also mostly concrete and inductive. Math teachers arrive at abstract postulations, generalizations by observing concrete objects and concrete examples and through inductive conclusions. This method is familiar and appropriate for students of that age. The inductive procedure is made up of a chain of inductive steps which lead to the understanding of the general. We begin with concrete objects and special cases, inductive conclusions are sequenced by analogy, and the observed facts are generalized. We observe a tight link between induction with concretization, specialization, analogy and generalization. The advantage of applying induction: implementation of the easier to more difficult principle, simpler to complex, studying new abstract concepts and phrases through observation and assessment, guiding students to new concepts, expression of new theorems, etc. The inductive approach is important in the development of a student's thought process which on the other hand is necessary for acquiring a lot of content in school math. Among such content are various rules, regularities, formulas, theorems, especially if they are not strictly derived or proven.
The opposite of induction is deduction. The deductive process of thinking and proving, takes place after induction, at a higher level of math teaching and math education.
An illustration of an appropriate methodological way of teaching mathematical content and the application of scientific methods is finding the sum Kn of all inner angles of a n angle with n sides.
In teaching this teaching unit, one should start from facts acquired in the previous grade. The first of those facts is a statement about the sum of all inner angles of a triangle: K3 =180°. The second fact is the statement about the sum of all inner angles of a square: K = 360° = 2 -180°.
Furthermore, for the sum of all inner angles of a pentagonal a formula should be derived K = 540° = 3-180°, for the sum of all inner angles of a hexagon a formula should be derived
K = 720° = 4 -180°, students should be encouraged to conclude that the formula for a heptagon
is K7 = 5-1800, for the octagonal K8 = 6-1800 etc. Comparison of formulas should follow.
Only after completing, all of those steps should be able to cognitively be ready for giving the following general statements:
The sum Kn of all inner angles of a polygon with n sides is given with the
formula Kn = (n - 2) -180°.
Questions such as: what is the sum K2008 = ? follow.
Let us analyze the described procedure. Analysis points to the special part of this topic (triangle, square) which is taught in the previous grade. The first two concrete steps are therefore students' background knowledge and initial inductive conclusions. The third and fourth steps are two new inductive statements. The fifth and sixth steps are conclusions arrived at by analogy, and in the end there is the observation of regularities, abstraction of concrete cases and stating the generalization. In making a statement proof can easily be observed, which synthesis is in this case. Upon proving the formula, considerations related to their application have a deductive character and are in a tight relation with specialization [3, 4].
In the example described, all 9 basic scientific methods are applied!
It is not difficult to recognize some important scientific procedures in the described process: analysis, synthesis, abstraction and generalization. That means that any concept, including mathematical concepts, after careful analysis develop through abstracting characteristics of objects which exist in nature and through generalization. In that way mathematical concepts, although abstract concepts, reflect some characteristics of the real world and in that way contribute to their awareness.
Conclusion. We have already mentioned that a math teacher need not be a scientist in order to appropriately and adequately apply the science principle and scientific methods in teaching. This occurs in math teaching without much interference. Solving a math problem implies some research and development. That is why the teacher has to create the spirit of curiosity in his students, the inclination for independent mental work and to show them ways to new discoveries. A creative math teacher using creative teaching methods has great chances to develop in his students creative characteristics.
REFERENCES
1. Decree "On the Strategy of actions for further development of the Republic of Uzbekistan". February 7, 2017, No. PF-4947.
2. M.K. Akinsola, F.B. Olowojaiye, Teacher instructional methods and student attitudes towards mathematics International Electronic Journal of Mathematics Education, 3 (1) (2008).
3. Moenikia, M. & Zahed-Babelan, A. A study of simple and multiple relations between mathematics attitude, academic motivation and intelligence quotient with mathematics achievement. Procedia Social and Behavioural Sciences, 2, (2010).
4. M. McVay, How to Be a Successful Distance Learning Student: Learning on the Internet, Pearson Custom Publishing, New York, USA, 2001.
