Vulnerable Subjects Research

Aim: To throw light on the state of vulnerable subjects in Clinical Research.
Objective: To understand current provisions and legislations available to protect the rights of vulnerable subjects with special emphasis on plight of sex workers enrolled in anti-HIV trials.
Individuals who are comparatively or entirely inept of defending their own wellbeing are termed as vulnerable research participants. When study includes such subjects additional care has to be taken to protect their rights. It is the investigator and his research team’s responsibility to ensure that these subjects are not exploited in the name of research. The study design team, sponsor, investigator must be aware of the special requirements needed for vulnerable subjects and they should develop the study protocol, informed consent form and the confidentiality agreement keeping the vulnerable subjects’ needs in mind.
The different types of vulnerable subjects included in clinical trials are classified on basis of their vulnerability. Some examples are as follows:
1. Cognitive and Communicative vulnerability:

This includes children and adolescents.

Patient’s suffering from mental retardation, dementia and other kinds of mental illness.

Enrollment of people with educational deficits and unfamiliarity with language.

Stressful emergency: conditions that do not permit otherwise capable adults to implement their capabilities efficiently.

2. Juridical or institutional vulnerability:

Person who is under the official authority of others (egs. Parents, guardians, warders, officers and judges) who may have their own benefits in whether the individual agrees to enroll in the study.

3. Deferential vulnerability:

Influence of other people in subjects life, determine their decision to enter the trial. Existence of an informal hierarchy (egs. Relatives, friends, masters, physician)

4. Medical vulnerability:

Prospective patients who have a severe medical condition, for which there are no existing efficient or satisfactory regular cure (examples: very aggressive and malignant forms of cancer, last stage AIDS and some uncommon ailments)

owing to their unusual medically tricky state, misuse of these patients throughout their hope for remission or improvement is not unusual.

5. Economic vulnerability:

Prospective subjects with low economic background may join trial with hope of getting income, housing and healthcare facilities.

Payment for participation or free access to healthcare services might constitute unfair inducements to enroll through exploitation of these subjects.

6. Infrastructural vulnerability:

Patient is tempted to enroll in trials, as they pre-suppose the availability to them of resources or facilities (egs. a rapid communication system, a reliable dietary intake, skilled healthcare professionals)

7. Social vulnerability:

Refers to individuals belonging to undervalued social groups or communities.(sex workers)[R. Colombo, The Most Vulnerable Subjects Of Biomedical Research IX General Assembly PAV – publications]

Exploitation was rampant in the absence of regulations, laws, guidelines and codes. Escalating physician to god-like position with immense faith in them and failure to recognize vulnerable subjects has resulted in horrific incidents in history of research. These major mishaps have convinced the medical fraternity the need for developing ethical guidelines and code for research specifically for the vulnerable populations.
The Nuremberg trial

The 20th century will always be remembered due to the shocking and upsetting experimentation performed by Nazi doctors. During the World War II, the Nazi physicians took advantage of the prisoners of war; they carried out experiments unparalleled in their range and the level of anguish and harm. Appalling studies such as injecting the poor prisoners with gasoline and live viruses, immersing people in ice water, and forcing them to ingest poisons have gone down in the history books as the most inhuman experiments.

The physicians in order to satisfy their scientific curiosity have performed these experiments which were of no use to the participants. These experiments usually resulted in the death of the participants.

After the war ended, there was a huge public outburst against these experiments and 23 physicians were indicted at Nuremberg for their willing participation in these experiments.

Sixteen were found guilty and sentenced while seven were hanged to death. This resulted in the origin of the Nuremberg Code, which made informed consent mandatory.

The Willowbrook study

The Nuremberg Code unfortunately did not put to end unethical research as not every researcher honored the Code. The three year long Willowbrook study is another example where vulnerable patients were exploited.

Willowbrook State School, an institution for mentally defective children were intentionally infect with the hepatitis virus, by being fed stools from infected persons or later by being injecting with purified virus preparations, to observe the natural history of this disease and then to test the effects o gamma globulin in preventing the disease.

Researchers defended the deliberate infection of these children by stating that the bulk of them acquired the infection in any case while at Willowbrook, and possibly it would be better for them to be infected under restricted research settings.

What was worse was that during the course of these studies, new inmates were admitted only if they agreed to participate in the hepatitis program!

There was obviously no full disclosure ad clearly coercion and undue pressure was used to enroll vulnerable subjects like children and mentally challenged.

Jewish Chronic Disease Hospital Study

At the other end of life’s spectrum, came the Jewish Chronic Disease Hospital Study where live cancer cells were infused into continually ailing and incapacitated patients.

These patients had been told that they were getting a skin examination. The patients were provided oral information about the test but no consent was documented.

Syphilis study

The most notorious example of prolonged infringement of human rights of a vulnerable faction of research participants was the long-term study of black males performed at Tuskegee by the United States Public Health Service.

Initiated in the 1930s to examine the natural history of untreated syphilis, continuing until 1972, this study recruited more than 400 black men suffering from syphilis.

These participants were recruited without informed consent and were mislead that a few of the measures taken in the interest of research were essentially “special complimentary treatment”.

Although along the way antibiotics become available, these were not given to the patients and the study resulted in 28 deaths, 100 cases of disability, and 19 cases of congenital syphilis.

The Belmont report published by the National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research on April 18, 1979 was one of the outcomes of the public outcry that resulted when the story of the Tuskegee study broke.[Urmila Thatte, Etical issues in clinical Research chapter 4, of Basic principles of clinical research and methodology by S K Gupta]

Guidelines for ethical conduct of research in human subjects that have came into picture:

Declaration of Helsinki, 1964

International Ethical Guidelines for Biomedical Research Involving Human Subjects, 1982, 1993, 2002

The Ethics of Research related to Healthcare in Developing Countries, Nuffield council, 2002

Indian council for Medical Research Ethical Guidelines for Biomedical Research on Human subjects

Regulations that protect children, so as to prevent their exploitation are:

Special Considerations for Children are:

Research that involves no more than minimal risk can be approved with adequate provisions for obtaining the assent of the child and permission from their parents/guardians. 45 CFR 46.404

The combination of assent by the minor subject and permission (consent) from the parents is deemed appropriate to enroll the child subject in the trial.

In case of life threatening events only consent from parents would suffice, as there is expectation of direct benefit. However the child must be given full explanation of the trial.

If the research presents an opening to comprehend, avoid or lessen a grave predicament affecting the health or welfare of children, but does NOT provide direct benefit to the subject or societal (indirect) benefit, than the research cannot be approved by the IRB unless HHS Secretary Approval is granted. 45 CFR 46.407 . Extremely rare- both Parent consent + child assent.

When parents of the child are deceased, unknown or incompetent then the legal guardian must give is consent.

Step parents, Grandparents, Adult siblings, adult Aunts or Uncles may not consent a child to research.

Regulations that protect women, so as to prevent their exploitation are:

Research studies involving pregnant women and fetuses must satisfy the following requirements to obtain IRB approval:

Preclinical studies have been conducted, including studies on pregnant animals; clinical studies, that include non-pregnant women and provide data for assessing potential risks to pregnant women and fetuses 46.204(a)

Risk to fetus is caused solely by interventions or procedures that hold prospect of direct benefit for the woman or the fetus or, 46.204(b)

If no benefit, risk to the fetus is not greater than minimal and the research develops important biomedical knowledge not obtainable by any other means. 46.204(b)


The voluntary choice of the prisoners must not influenced by any potential advantages entailed to them due to the study, which outweighs the risks. For example, Parole decisions must not be affected for prisoners participating in the trial.

The study is ethical, when the risk of participation is acceptable even to a non prisoner subject.

Selections of subjects are carried out in a fair manner. When spoilt for choice, randomization techniques must be used.

If necessary, adequate follow-up care must be provided to the volunteers.


A combination of assent from the subject and permission from the concerned legal authorities constitute for the informed consent.

The risk of participation would be agreeable to general volunteers too.

Selection is fair and unbiased

Adequate follow up is provided


Enrolling Sex workers in HIV vaccine trials that are ethical, valid and are not exploitative is a challenge that must be faced. Due to their nature of work, they require additional support.

Sex workers are generally from the downtrodden community, they are illiterate and understanding the language in the informed consent is a major issue for them. Hence the informed consent must be in the local language and should be easily understood.

The informed-consent must be prepared in such a way that it is in consultation with the community advisory and counsel board to ensure social sensitivity.

Confidentiality is an important issue. These women may face physical abuse and abandonment from their clients, if they enter these trials.

Supportive counseling should be provided before, during and after the test.

Sex workers must not only be given male condoms but along with that they should be provided with female condoms. Proper guidance on safe sex must be dispensed.

Clinical trial study team should increase awareness among the sex workers about AIDS. They should provide proper guidance to them, for prevention.

Sex workers should be treated equally as general women would have been treated in a clinical trials. Study team should be sensitive towards them and not discriminate and look down upon them.

Health Minister, Urbain Olangnena Awono of the Cameroon government has decided that they may have to put a stop to the Tenofovir trials taking place in the port city of Douala due to various allegations by AIDS activists. The health minister had scheduled an audit for the same.
The Tenofovir trial began in September 2004, Tenofovir is a established drug used for treatment of AIDS, manufactured by Gilead pharmaceuticals U.S. This trial was to determine whether Tenofovir can work as a prophylactic to prevent AIDS. The study recruited 400 sex workers free of infection. Half the women took a Tenofovir pill daily and the other half took a placebo. The study is conducted by Family Health and Insurance (FHI) with the support of U.S $ 6.5 million dollars from Bill and Melinda Gates Foundation.

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AIDS activists have demanded that this study be completely suspended on ethical grounds. They have said that the volunteers are vulnerable subjects and their rights have been exploited. Activists claim that the subjects have received inadequate counseling and healthcare. They have brought to notice that the sex workers are not fully informed about the risks involved in the trial. They also argue that the Study team has not promised to guarantee free healthcare if the workers become infected, which ideally every volunteer must receive.
The FHI have counter attacked and cleared their stand by assuring that free medical checkups and tests have been carried out. Various tests like gynecological, medical care, HIV, pregnancy have been carried out for free. However various Activists have disregarded this claim and said that these are all false promises and haven’t been materialized.
Another important issue that has been brought to notice was that, most of these sex workers were illiterate didn’t understand English and very little French, in spite of that the informed consent form were in English. However later it seen that the ICF shown to PlusNews was in French.
The study team had provided 96 male condoms to sex workers. However imparting knowledge to prevent the infection of disease would be like a conflict of interest for the researchers. As the trial would be a success only if the women were exposed, become infected. The sex workers are misinformed and they feel that by taking this pill they are now vaccinated against the disease.
In order to get their point across, so that the concerned authority would wake up to this injustice, AIDS activists in Paris staged a demonstration in front of the Cameroonian embassy in Paris. This demonstration got full coverage on the French T.V. This resulted in a public outcry against the trials.
The Tenofovir trial case study is an excellent example highlighting the profound impact media can have on the progress of the trial. The complete discontinuations of the trials prove that activists and non- governmental organizations with the help of the media can bring about change. These same activists are also involved in promoting research to combat the disease, but they can hinder the progress too. Hence researchers must be more aware about the ethical issues surrounding enrollment of sex workers.
Engaging in discussion and consulting with the participant’s community before the trial begins can avoid such media spectacle. The case study rightly brings to one’s notice that lack of consultation with the support groups and community network was the biggest error on the part of the research team. Extensive discussion with community networks and a good flow of communication would bridge the gap and increase the trust of sex workers in the trials.
The activists have rightly questioned why no subjects from general population have been enrolled to test safety of the drug. They have expressed concern and raised another important issue that the same trial would have provided women from Europe and U.S better benefits and adequate healthcare.
The burning issue against this trial has been that since the primary outcome is HIV infection, researchers will provide inadequatecounseling to prevent infection. Since there exits a conflict of interest, sex workers will not be encouraged to have safe sex.
Another important drawback of the trial has been its failure to provide sex workers with female condoms. They were provided with male condoms but negotiating for the same with their clients does not go down well with their trade. It is shocking that the sex workers were completely ignorant about the drug. They were misguided that the drug is a vaccine for AIDS, which made them more careless and prone to the disease.
On the other hand, Tenofovir trials aimed at providing a prophylactic for AIDS, which would be a major breakthrough in combating this deadly disease and would definitely be of great benefit to the sex workers. Such uncontrolled and extreme protest has led to the complete discontinuation of the trial which in turn is bad news for the sex workers. The sponsor company had also promised to market this drug in Cameroon for much reduced prices.
The validity of the media reports is doubtful as all the allegations made against the research team have been without any evidence. Activists instead of creating media backlash against the trial should have engaged in constructive dialogue with the research team stating their demands.
Clinical research has given millions of patients’ worldwide assurity that the medicine they purchase and consume, has been completely validated for its safety and efficacy. It ensures that these patients worldwide are getting the best medicine with utmost safety parameters.
Investigators along with their research team bear the ultimate responsibility for their work with human subjects. They have the privilege of using human subject to advance scientific research, in turn society expects that investigators will show respect for their research subjects. Unfortunately as history has shown some scientists still continue to value their quest for knowledge and potential for personal fame and financial gain more highly then respect for basic human rights. Hence, various guidelines, regulations, codes and law have come into picture to protect the human subject.
Special care and provisions must be made for subjects who are shunned from society. Sex workers live on the fringe of society and can rarely ask for their rights or support from public. In the interest of general health, to conduct trials for AIDS, this section of society must not be used as mere guinea pigs.
Particular guidelines and ethical code of conduct for researchers must be drawn in order to protect these oppressed subjects. Providing them information on AIDS is not enough, they must be given free health care and female condoms. They need compassion and justice from us.

Deanna Kerrigan et al, Environmental structural factors significantly associated with consistent condom use among female sex workers in the Dominican Republic, AIDS 2003 17:415-423 , Lippincott Williams and Wilkins.

Arnaud L Fontanet et al, Protection against sexually transmitted diseases by granting sex workers in Thailand the choice of using the male or female condom: results from a randomized controlled trial, AIDS 1998, 12: 1851-1859, Lippincott Williams and Wilkins.

Edward Mills et al, Media reporting of Tenofovir trials in Cambodia and Cameroon, 24 August 2005, BMC International Health and Human Rights.

Edward J Mills and Sonal Singh, Health, human rights and the conduct of clinical research within oppressed populations, Globalization and health 2007, 3:10, BioMed Central Ltd.

Peter H. Kilmarx et al, Protection of Human Subjects’ Rights HIV- preventive clinical trials in Africa and Asia: Experiences and Recommendations, AIDS 2001, 15 (suppl 5) : S73-S79, Lippincott Williams and Wilkins

Geeta Yadav et al, Associations of sexual risk taking among Kenyan female sex workers after enrollment in an HIV – 1 prevention trial, J Acquir Immune Defic Syndr 2005; 38:329-334, Lippincott Williams and Wilkins

Gielen AC, Fogarty L, O’Campo P, Anderson J, Keller J, et al, Women living with HIV: Disclosure, violence, and social support, 2000, J Urban Health 77:480–491

R. Colombo, The Most Vulnerable Subjects Of Biomedical Research IX General Assembly PAV – publications.

Urmila Thatte, Ethical issues in clinical Research chapter 4, of Basic principles of clinical research and methodology by S K Gupta

Cynthia McGuire Dunn and Gary L. Chadwick, Protecting study volunteers in research, Third edition. Thomson Centerwatch.

Ezekiel J. Emanuel, MD, PhD; David Wendler, PhD; Christine Grady, PhD, What Makes Clinical Research Ethical? , JAMA.2000;283:2701-2711.

Cohen J. Cameroon Suspends AIDS Study. Science, Science Now 2005 Feb: 4.

Singh JA, Mills EJ. The abandoned trials of pre-exposure prophylaxis for HIV: what went wrong? PLoS Med 2005;2: e234

Atatah C. Douala AIDS drug controversy: medical council says trials violated ethical norms. Post News Line 2005. (accessed 15 Jan 2008). (accessed 15 Jan 2008) (accessed 15 Jan 2008)

KIPNIS K., Vulnerability in research subjects: a bioethical taxonomy, in NATIONAL BIOETHICS ADVISORY COMMISSION, Ethical and Policy Issues in Research Involving Human Participants, op. cit., vol. 2, pp. G1-G13, p. G5. (accessed 15 Jan 2008)


Correlation of Mathematics with Other Subjects

“No subject is ever well understood and no art is intelligently practiced, if the light which the other studies are able to throw upon it is deliberately shut out.” – RAMONT

What is correlation?
The meaning of term ‘correlation’ in simplest form is “connect” or “to be connected”. More precisely, ‘Correlation’ means mutual relation of two or more items/things or Mutual relation of two or more than two items/things.
The relation may be inverse or direct. For examle if there are two variables ‘a’ and ‘b’, if there is increase or decrease in one will affect on other. It is really a brainstorming activity which involves lots of efforts to be establishing relationship between school Subjects.
In modern scenario, due to the number of innovation of 21st century involves lots of development in the education. These involve meaningful knowledge of the concept. Here child’s mind is an integrated whole, he wants to receive experiences in a fruitful manner.
“Correlation indicates a joint-relationship between two variables.” Lathrop
“Correlation is concerned with describing the degree of relation between variables.” Ferguson
“Correlation is an analysis of co-variation between two or more variables.” A.M. Taule
“Correlation analysis deals with the association between two or more variables.” Simpson & Kafka
Types of correlation

Positive correlation – when an increase in one variable, increases the value of another variable or vice versa.
Negative correlation – when an increase in one variable, decreases the value of another variable or vice versa.
Incidental correlation — It is not a planned/pre-decided, no deliberate or a systematic attempt made to correlate it. Teacher plays a leading role. E.g. If any teacher has basic knowledge of concepts/elements of versatile or different subjects, he can easily make correlation between two or more subjects. A teacher cannot establish incidental correlation without having knowledge of different subjects.
Systematic correlation – teachers can sit together with his students and how to correlate? While doing systematic correlation, the previous knowledge/content of the student should be related with the current knowledge. To relate the same is called systematic correlation. Here, the student and the teacher have to think about the application of the fact, laws, principles, and correlation of two subjects. After that knowledge becomes interesting.
No correlation – when there is no mutual relationship between the two variables. It is also known as no linear dependent.

Uses of correlation:

The aim of education is “to achieve the all round development of a child”, this cannot be done by teaching only in simple classroom.
In correlation, the practical subjects like maths and science plays important role. Where the correlation with concepts is used in learning of students.
It makes learning permanent and concrete and knowledge to the learner.
It makes the lesson easy and clear for the student.
It enhances the mental abilities like problem solving, logical reasoning, imagination, and analytical power of student, because these can easily correlate acquired knowledge with the other subjects.
It strengthens the skill, complexity of practical subject and makes mastery over the practical subject.
It develops social relationship like – human and social qualities in students.
For teachers; it helps to complete the curriculum within short period of time and provides time for revision.
Knowledge is useful and is maintained so that it can be developed and used in day to day life.

Examples of dependent phenomena include the

Relation between parents and their offsprings.
The correlation between theprice and availabilty of product in the market.
The theoretical aspect of anything explains the practical concept.
Even a crime is also related to wrong addictions.
The negative correlation between age and normal vision.
The positive correlation between the incidence of lung cancer and cigarette smoking.

Correlation of Mathematics with other disciplines
Mathematics is “Science of all Sciences” and “Art of all Arts”. After understanding the basic concept of mathematics, students need to correlate the importance and concept of mathematics with other subjects, so as to understand other subjects easily and establishing relationship. Mathematical knowledge plays a crucial role in understanding the contents of other subjects.

MATHEMATICS WITH GENERAL SCIENCE: Science without mathematics is totally meaningless, because chemical reactions, scientific theories and detail of elements are only generated/ counted with the help of mathematics. Mathematics is used in most of applications like in work, energy, electricity, motion, gravitation, magnetism etc.

MATHEMATICS AND PHYSICS: child should have rich knowledge of mathematics to understand physics. Generally final shape to the rules of physics is given by mathematics; it presents these rules in practically workable form. Mathematical calculations occur in every step of physical science. Charle’s law of expansion of gases is based upon mathematical calculations, numerical problems on liquid, pressure,frictional force, laws of motion, gravitation, momentum etc.

MATHEMATICS AND CHEMISTRY: Molecular weights of organic compounds are calculated with mathematics. To measure the constituents of mixtures and Chemical compounds. To calculate Empirical or molecular formula. In balancing the chemical equations. In electronic configuration of atom of the element. Charle’s law of expansion of gases is based upon mathematical calculations.

MATHEMATICS AND BIOLOGY: Mathematics has very high correlation with biology. The Normal Weight, Caloric value, Rate of Respiration, Nutritive Value of Food, Transpiration, is calculated by Maths. The Growth in Weight of infants’ upto Nine months. To count the number of bones in human being and other different species. To measure blood pressure. To count the number of WBC & RBC in different blood groups. To count Sex chromosomes.

MATHEMATICS AND SOCIAL SCIENCES: After completion of the unit child can read, interpret, and draw the graphs. For example, to compare the Population- students can draw bar graphs, Population Density of various countries, Per Capita Income etc.

MATHEMATICS AND GEOGRAPHY: Geographical figures are explained in the terms of numbers only like seasonal conditions, temperature, humidity, degree, measurement of rain etc. the geographical conditions also defines the economy of a rich/poor country. Many countries like India have agricultural based economy due to its climate, rainfall, rivers and weather prediction.etc.

Certainly Mathematics is used for constituting the map, Formation of Nights & Days, Solar & Lunar Eclipse, Longitude Latitude, Maximum and Minimum Temperature, Barometric Pressure, Height above Sea Level, Surveying, Calculation of International, Local and Standard Time, Instruments etc. And here are also many other calculations. Punjab, Haryana and U.P are very fertile states in India, so contribute to grain stores, industries are established there but in these states there are no mines.

MATHEMATICS AND HISTORY: in history 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 ECONOMICS: Statistical Methods are used to calculate and to know the Volume of Trade, Trend of Import and Exports, Economic Forecasts, Trade Cycles, It helps in calculating various indexes like crop production inflation, etc.

All economists, citizens and the businessmans can get the market trends & economic conditions. Through currencies market, the Current updates of currency and through stock and commodity market the current updates of the stock and commodity of different countries.
Only because of economic reasons certain empires faced liquidation. Similarly, economic events have been influenced or affectd by historical circumstances. In the current scenario the economic condition of India during UPA and NDA.

MATHEMATICS AND FINE ARTS: decides size, Ratio and Proportion while constructing the Similarity, Scale appreciation, Balance and Symmetry, Postulates, Drawing images on cloth and paper, Rhythm in Music etc.


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)

MATHEMATICS WITH AGRICULTURE: Agriculture has close relationship with Maths. Agriculture has correlation with maths like area of crops, which season is suitable for which crop. How much quantity of water may be used in irrigation is also calculated in concern of agriculture by the use of mathematics. Investment, expenditure and saving in sowing specific crop, Division of land, Cost of labour, seed, fertilisers, expenditure in transportation of vegetables to the market, has the use of mathematics. As due to scientific inventions, there is lot of growth of agriculture & economy takes place.

MATHEMATICS WITH COMMERCE/ACCOUNTS: With the rich knowledge of commerce it is possible to study the economy of the country. Only by the knowledge of mathematics, Debit, Credit process & expenditure in accounts of industry, banks firm, etc are determined. The commerce teacher of should try to teachor make understand in such a way that students may relate and explain all specific terms mathematically.

MATHEMATICS AND ICT: The ICT is strongly correlated with mathematics. Computer programmes, applications, software and different languages without mathematics are impossible to operate and follow. Students are taught computers only because of knowledge of mathematics. Computer Provides important software for calculation e.g. SPSS software used in the long statistical calculations for research work. Many mathematical packages are used included Logo, dynamic geometry software, graph plotting etc., which are used in the teaching programmes.

MATHEMATICS WITH ENGINEERING: without mathematics Engineering is like sea without water. Mathematics has very strong correlation with each and every branch of engineering. Mathematics is used in every branch of engineering like Electronics, Electrical, Mechanical, Architect, Civil, Chemical, Computer etc. To get admission in any engineering stream, student must read Mathematics as a subject upto class 12.

MATHEMATICS WITH PSYCHOLOGY: Mathematics has correlation with Psychology for measuring I.Q, S.D, coefficient of correlation, Significance of difference, Measure of central tendency (Mean, Median, and Mode). “Likert Scale” used in psychology to make questionnaire. Mathematics is used in different modes of psychology like industry, army, social etc.

MATHEMATICS WITH ASTRONOMY: Counting of Stars and Planets, No. of moon/satellite of all planets. No. of stars in galaxy. Time taken in revolving at its own orbit. Formation of seasons, Life of star, galaxy etc. And Distance between two planets.

MATHEMATICS WITH PHYSICAL EDUCATION: Mathematics is used to measure structure of the body, blood pressure, the height, weight, rules of the games etc. Temperature of the normal human body, Size of playground, norm and standard of game like boot-ball, hockey, cricket, volleyball, tennis, wrestling, boxing etc.

One more important espect or field

MATHEMATICS WITH INDUSTRY: Mathematics is used in industrial work for example:- weaving, knitting, making furniture, leather work, making paints and fertilisers etc. Mathematical calculations are required to calculate all work and the cost.

PPT by Ms. Namrata Katare Saxena, Asst Prof. PCER, MES
Dr. B. Pandya; Teaching of Mathematics (2007), Radha Prakhashan Mandir, Agra
S.K. Mangal; Teaching of Mathematics, Tondon Publications, Ludhiana