Correlation of Mathematics with other School subjects:

Relation of Mathematics with other School subjects:

   Mathematics in Economics

The level of mathematical literacy required for personal and social activities is continually increasing.  Mastery of the fundamental processes is necessary for clear thinking.  The social sciences are also beginning to draw heavily upon mathematics.

Mathematical language and methods are used frequently in describing economic phenomena. According to Marshall – “The direct application of mathematical reasoning to the discovery of economic truths has recently rendered great services in the hand of master mathematicians.” Statistical methods are used in economic forecast different issues of economics can be represented statistically such as ‘Trade Cycles’, Volume trade, trend of exports and imports, population trends, industrial trends, thrift, expenditure of public money etc.,

In economic theory and econometrics, a great deal of mathematical work is being done all over the world. In econometrics, tools of matrices, probability and statistics are used. A great deal of mathematical thinking goes in the task of national economic planning, and a number of mathematical models for planning have been developed. 

  Mathematics in Political Science

In Mathematical Political Science, we analyze past election results to see changes in voting patterns and the influence of various factors on voting behavior, on switching of votes among political parties and mathematical models for Conflict Resolution. Here we make use of Game Theory. 

Mathematics in Geography

            Geography is nothing but a scientific and mathematical description of our earth in its universe.  The dimension and magnitude of earth, its situation and position in the universe the formation of days and nights, lunar and solar eclipses, latitude and longitude, maximum and minimum rainfall, etc are some of the numerous learning areas of geography which need the application of mathematics.  The surveying instruments in geography have to be mathematically accurate.  There are changes in the fertility of the soil, changes in the distribution of forests, changes in ecology etc., which have to be mathematically determined, in order to exercise desirable control over them.

Mathematics in History:

Ø  To know the time period

Ø  To know the birth and death of historical persons

Mathematics helps in Calculation of Dates like duration of Britishers ruled in India? When Gandhi ji was born? Celebrate National Days and festivals, Cost in building of Taj-Mahal. Tenure of President in India. This gives us new information of the historical world. When the First and second world wars were fought? On account of economic considerations industrial revolution in Europe.

MATHEMATICS AND LANGUAGE:

• Math and Reading:- Students read about the discoveries or work of great mathematicians, and they can make poem on numbers.
• Math and Writing (numbers are converted into writing):- A student makes the pie chart and interprets in his own words.

e.g. Counting of alphabet, vowel, Read About The Life History of Mathematicians. Student can draw make a bar graph of time spent in school and home the whole week and can interpret. (Interpretation of Non-Verbal Data)

Nature & characteristic of Science

                                                        Nature & characteristic of science

Science is a systematic method of continuing investigation that uses observation, hypothesis, testing, measurement, experimentation, logical argument and theory building to lead to more adequate explanation of natural phenomena.  

Ø Methodological activity, discipline, or study. An activity that appears to require study and method.

Ø Knowledge, especially that gained through experience.

Ø Is the ongoing process of exploring and discovering the way nature works.  We may never know everything there is to know about life and the universe, but we can continue to expand our understanding by making observations, asking questions, & seeking answers.

Science is our attempt to understand the objects and events we experience in nature and the means by which we do so.  People develop understanding about things they experience by asking question and finding answers.  What is life?  Why does my heartbeat?  Why does it pump blood?  What causes diseases such as Herpes, Diabetes, or AIDS?  Why won’t my car start?  In attempting to find answers to questions such as these, one is actually doing science.  In biology most of the questions involve living things.  Finding answers to them involves you in doing biology… the science of life.

Steps to make Theory:

Observation → Analysis the questions → Hypothesis → Prediction → Testing Hypothesis / Experimentation if it is success then becomes Theory if not the again, we have to make new Hypothesis.

Nature of Science

1.     Science is a particular way  of looking  at nature

2.     Science is  an accumulated and systematized body of knowledge

3.     Science is an interdisciplinary area of learning.

Characteristics of Science: 

1.  It is guided by natural law

–   The pursuit of scientific knowledge must be guided by the physical and chemical laws that govern the universe (state of existence).

2.  It has to be explained by referencing these natural laws.

–   Scientific knowledge must explain what is observed by reference in nature.  We cannot invoke the explanations based on supernatural deities (ghosts, angels, gremlins, fairies, etc.) miracles, or magic.

–   Science must only rely on observable, testable evidence which must either support or not support hypotheses.  Extraordinary claims require extraordinary evidence.

3.  Science is testable against the observable world. 

–   We must be able to make observations in the real world, directly or indirectly, ask questions, or form and test hypotheses = a tentative, causal explanation/answer for an observation or phenomenon.

_   We use observations and/or tests to answer questions about the natural world.

–   Science relies on observable, testable evidence, which must either support or not support hypotheses.

4.  Its conclusions are tentative, that is, are not necessarily the final word.

_   If we draw a conclusion based on some observation or test on some event, we must be ready always to discard or to modify our conclusion, if further observations falsify it.

_   Can’t be scientific if you start with a conclusion and refuse to change it regardless of the evidence developed during the course of the investigation.

5.  It is falsifiable.

-       You must be able to disprove any statement.  If there is no possibility that the statement cannot be correct, then it isn’t science.  What this means is that science will seek out errors and correct them.  Unlike other philosophies, it’s a self-correcting system.  We add to and take away information on a daily basis depending on new discoveries and new evidence. 

6.  It relies on evidence that is testable (from observations and experimentations).  If we cannot make repeated observations or experiments to gather information, then it is outside the realm of science (e.g. UFO’s, haunted houses, etc.). 

7.     Science is logical & rational

8.     Science makes well-defined claims

9.     Scientific experiments are repeatable

10.   Science insists that extraordinary claims require extraordinary evidence

Audio-Visual Aids in teaching mathematics

Audio-Visual Aids in teaching mathematics

“Beauty attract to the person”

Popular saying on Audio- visual Aids:

The thing which I hear, I may forgot

          The thing which I see, I may remembered

      The thing which I do, I cannot  forget

 The use of Audio-Visual aids in teaching is not a fashion but is a matter belief and actual practice. That to say of ordinary visual aids e.g. charts. Graphs, map, models, etc. they are using films film-strips, epidiascope, tape-recorder, radio and television to make education valuable and worthwhile.

 Audio-Visual Aids an Fit Well in:

 a) Traditional system (from primary stage to higher secondary)

 b) Basic system of education

c) Project method kindergarten Montessori etc.

Features of Audio-Visual Aids:

 (i) Arouses interest,  (ii) Modifies attitude,  (iii) Claries concepts,  (iv) Stimulates thinking,  (v) Summarizes contents,  (vi) Demonstrates knowledge and  (vii) Concretizes knowledge.

 We  should  use to  Audio-visual packages to teach abstract and difficult oriented mathematical concepts, to enhance easy retention and high academic performance of our students. It will be  effective and efficient in the  classroom teaching-learning process.

Kothari Commission i.e The Education Commission (1964-66)

The Education Commission (1964-66)

Drawing on Nehru’s Mission and articulating most of his key themes, the Kothari

Commission (1964-66) was set up under the Chairmanship of Dr. D. S. Kothari

to formulate a coherent education policy for India. The Commission was most

comprehensive in nature, it reviewed almost all aspects of the education system

without limiting itself to any one particular aspect, unlike the Commissions that

came before and after it.

Two of the unique features of the Report are:

i) Its comprehensive approach to educational reconstruction; and

ii) Its attempt to project a blueprint of a national system of education for India.

According to the Commission, education was intended to increase productivity,

develop social and national unity, consolidate democracy, modernise the country

and develop social, moral and spiritual values. The crucial role of education in

national development appears in all its vividness throughout in the report,

appropriately titled “Education and National Development”.

The Commission identified the three important facets that would bring about the

desired educational resolution, they are:

· internal transformation so as to relate it to the life needs and aspirations of

the Nation;

· qualitative improvement so that the standards achieved are adequate and

become internationally comparable; and

· expansion of educational facilities broadly on the basis of manpower needs

with emphasis on equalisation of education opportunities.

It suggested the restructuring of education into a uniform pattern of 10+2+3. It

adopted a “manpower approach” to the enrolment issue and declared that the

principal purpose of higher education was to cater to the needs of industrial and

other sectors, even as it acknowledged its role in promoting social transformation.

The Commission sought to reorient educational system to the masses to help

people come into their own. It sought to end the dichotomy between work and

education to make the products good workers as well as educated individuals.

It recommended a minimum of 10 years of common curriculum for building

citizenship in a democracy and for linking the “work of knowledge” with the

“world of work”. In this concept, diversifies courses would be introduced only at

the +2 stage.

Major recommendations of the Commission included emphasis on Science and

Mathematics, introduction of work experience as an integral part of school

curriculum, introduction of common school system, educational structure with 12

years of schooling, free text-books at primary stage, provision of mid-day-meals,

promotion of education of handicapped and special measures for ensuring equality

of educational opportunities (regional, tribal and gender imbalances to be

addressed), establishment of school complexes, neighborhood school, three

language formula etc.

The Commission emphasized the need of alternative channels of education to

eradicate illiteracy and provide adult education. By laying more focus on

Mathematics and Science rather than Social Science or Arts, the Commission

reinforced the notion that India’s development needs are better met by scientists

than social scientists.

For improving the quality of education, the Commission focused on institutional

planning for improving standards nationwide, promotion of new work ethic,

improved teaching and learning materials and methods of teaching and evaluation,

and selective development of schools.

Teacher Status

The Commission emphasized that the most urgent need was to upgrade the

remuneration of teachers substantially, particularly at the school stages. It

recommended that the government should lay down minimum scales of pay for

teachers and assist States and Union territories to adopt equivalent or higher

scales.

Teacher Education

The Commission urged that professional preparation of teachers was the key for

qualitative improvement of education and recommended measures like:

· qualitative improvement in teacher education programmes;

· introduction of new courses for headmasters/teacher educators and

educational administrators; and

· expansion of teacher education institutions and recommendations of the training

facilities.