UGC-NET OBJECTIVE

Sample questions UGC-NET (EDUCATION) 1. Education is ________ aspect of philosophy and philosophy is the________ aspect of education. (A) theoretical, practical (B) practical, theoretical (C) dynamic, dormant (D) dormant, dynamic 2. The book “The Life Divine” was written by ___________. (A) Tagore (B) Vivekananda (C) Aurobindo (D) Gandhiji 3. Pragmatism professes for ________ as a school of philosophy. (A) idea (B) action (C) reality (D) programme 4. Secularism means ___________. (A) The State is to give patronage to any one religion. (B) Respect all religions without favouring any one religion. (C) Lacking religious emotion, doctrines and practices. (D) To impose any particular religion upon the rest of the people. 5. ‘Astamarg’ has been practised by the philosophy of ___________. (A) Vedanta (B) Islam (C) Jainism (D) Buddhism 6. “The most important outward factor is the formation of nationalities in the State.” To which philosophy do you attribute this statement ? (A) Marxism (B) Capitalism (C) Fascism (D) Socialism 7. Which one of the following principles is not correct regarding pragmatism ? (A) Pragmatism accepts any definite/eternal truth or principle. (B) According to pragmatists truth is man made. (C) Pragmatists support spiritualism. (D) Pragmatists stress more on acts rather than thoughts. 8. Who has formally initiated the concept of Naturalism in Modern Indian Education ? (A) Tagore (B) Vivekananda (C) Gandhiji (D) Aurobindo 9. “There cannot be educated people without educated women.” This was indicated by ___________. (A) The Resolution of the National Policy on Education (1968) (B) The United Nations Declaration on the Elimination of Discrimination against Women (1967) (C) The University Education Commission (1948-49) (D) New Policy on Education (1986) 10. Analytical School of Philosophy was propounded by (A) Theodor Brameld (B) Bertrand Russell (C) R.S. Piters (D) Vitzenstine 11. “Women are human beings and hence as much right to full development as men have.” This statement was made by ___________. (A) Mahatma Gandhi (B) S. Radhakrishnan (C) Rabindranath Tagore (D) Smt. Hansa Mehta 12. Aim of complete living in Education was propounded by (A) F. Herbert (B) Herbert Spencer (C) John Dewey (D) Plato 13. Who wrote the book “School and Society” ? (A) Auguste Comte (B) John Dewey (C) Emile Durkheim (D) Robert Merton 14. “Educational Sociology is neither education nor sociology alone but joins them in a new Science by applying sociological principles to the whole process of education.” Whose statement is this ? (A) A.K.C. Ottaway (B) George Payne (C) F.J. Brown (D) Herbert Spencer 15. Which of the following is not a subsystem? (A) Political sub system (B) Terrorist outfit (C) Economic organizations (D) Family sub system 16. When does the process of socialization start for a child ? (A) As a school child (B) As a member in the neighbourhood (C) As a member of the family (D) As a member of the society 17. Which of the following is a primary group ? (A) Peer group (B) Classroom group (C) Familial group (D) Basketball group 18. Which of the following is the best mobility multiplier ? (A) Income (B) Education (C) Social status (D) Caste 19. What is horizontal mobility associated with ? (A) Upliftment in the same stratum (B) Upliftment in the upper stratum (C) Change in the stratification (D) Consistency in the stratification 20. From sociological point of view the process of education is supposed to serve two fundamental functions. What are they ? (A) Selection and Allocation (B) Conservation and Creation (C) Preservation and Conservation (D) Creation and Dislocation 21. Arrange the following books in the chronological order in which they appeared. I. Education and Sociology II. School and Society III. Principles of Educational Sociology : An outline IV. Dynamic Sociology (A) IV, II, I and III (B) I, III, IV and II (C) III, II, IV and I (D) II, I, III and IV 22. The term “Untouchability” has been abolished according to an Article in Constitution. What is that Article ? (A) Article 46 (B) Article 17 (C) Article 25 (D) Article 16 23. Why is the school considered a Social Institution ? (A) Because it is concerned with the welfare of the society. (B) It is concerned with burning social issues. (C) It is concerned with social evils. (D) It is concerned with the shaping of the future society. 24. Which of the following stages of cognitive development is not described by Bruner ? (A) Enactive (B) Iconic (C) Heteronomy (D) Symbolic 25. The first intelligence test was developed by (A) Francis Galton (B) Binet and Simon (C) Lavator (D) William Stern 26. Match the following lists : List – I List – II (Specific Characteristics) (Category ofChildren) (a) One who shows i) Creative child consistently remarkable performance (ii) Underachiever (b) One who is more sensitive to environmental stimuli. (iii) Mentally retarded child (c) One who does not show educational iv) Gifted child (v) Delinquent child success commensurate with his abilities. (d) One who shows sub-average general intellectual functioning. Code : (a) (b) (c) (d) (A) (iv) (i) (ii) (iii) (B) (i) (iv) (ii) (iii) (C) (iv) (i) (iii) (ii) (D) (iii) (i) (ii) (iv) 27. Rearrange the following hierarchy of needs as given by Maslow : a. Safety and security needs. b. Physiological needs. c. Self-esteem needs. d. Love and belongingness needs. (A) b, a, d, c (B) d, a, b, c (C) a, b, d, c (D) b, a, c, d 28. According to type theory of personality, a tall, thin and stoop shouldered person will come under the category of (A) Endomorphic (B) Ectomorphic (C) Athletic (D) Pyknic 29 . The concept of emotional intelligence does not involve the ability to (A) understand emotions (B) regulate emotions (C) appraise and express emotions (D) arouse emotions 30. In the formula SER = D × SHR × K – 1, K denotes (A) Habit strength (B) Incentive (C) Drive (D) Excitatory potential 31. The correct sequence of the following items of Gague’s hierarchy of learning is a. Signal learning b. Problem solving c. Rule learning d. Multiple discrimination (A) d, c, b, a (B) c, d, a, b (C) a, d, c, b (D) b, c, d, a 32. Which of the following is not the axiom of learning ? (A) Simple to Complex (B) Specific to General (C) Tangible to Intangible (D) Known to Unknown 33 . Critically judge the following : Assertion (A) : Learning of principles has to be given utmost importance in the classrooms. Reason (R) : Knowledge of principles facilitates transfer of learning to a greater extent. (A) Both (A) and (R) are incorrect. (B) Only (R) is correct. (C) Both (A) and (R) are correct, but (R) is not a correct explanation for (A). (D) Both (A) and (R) are correct and (R) is the correct explanation for (A). 34. Critically judge the following : Assertion (A) : Early admission to school is not scientific. Reason (R) : It is against democratic principles. (A) Only (A) is correct. (B) Only (R) is correct. (C) Both (A) and (R) are correct and (R) is the correct explanation for (A). (D) Both (A) and (R) are correct, but (R) is not a correct explanation for (A). 35. Critically judge the following : Assertion (A) : Classroom instruction should involve variety of strategies. Reason (R) : There are individual differences in Learning styles among students. (A) Both (A) and (R) are correct, and (R) is the correct explanation for (A). (B) Both (A) and (R) are correct, but (R) is not the correct explanation for (A). (C) Only (R) is correct. (D) Only (A) is correct. 36. A researcher studies the effect of peer group interaction on Learning styles. The variable ‘Learning style’ in this study functions as : (A) Independent variable (B) Dependent variable (C) Controlled variable (D) Intervening variable 37. Which of the following may be most appropriately used for measuring self confidence ? (A) An Aptitude test (B) An Archival test (C) An Attitudinal test (D) An Achievement test 38. Which of the following statements is not applicable on the data in a descriptive research ? (A) It may be qualitative, in verbal symbols. (B) It may be quantitative, in mathematical symbols. (C) It may be qualitative and quantitative both. (D) It is only qualitative, never quantitative. 39 . Which one of the following indicates the higher level of significance ? (A) 0.10 (B) 0.001 (C) 0.01 (D) 1.00 40. Which of the following statements is not correct ? (A) A test cannot be valid without being reliable. (B) A test can be reliable without being valid. (C) A test can be reliable and valid both. (D) A test can be valid without being reliable. 41. Two characteristics of Ex Post Facto research are (A) Randomization and comparison of groups. (B) Non-manipulation and randomization. (C) Non-randomization and manipulation of independent variables. (D) Non-manipulation and nonrandomization. 42. Which of the following is a non-parametric correlation ? (A) Product moment (B) Rank difference (C) Point Biserial (D) Partial 43. What percent of IQ scores lie between 85 and 130 in a normal distribution with a mean of 100 and SD of 15 points ? (A) 79.85 (B) 80.85 (C) 82.85 (D) 81.85 44. When is the Type-I error increased ? (A) When alpha-level decreases (B) When alpha-level increases (C) When the sample size increases (D) When the sample size decreases 45. Which of the following poses a threat to internal validity ? (A) Interference of prior treatments. (B) Interaction effect of independent variables. (C) Interaction of treatment variables. (D) Interaction of selection and maturation. 46. If the alpha level of a particular test is lowered from 0.05 to 0.001, then the risk of committing Type-I error will (A) increase (B) remain unchanged (C) decrease (D) not be predictable 47. In case of ANOVA, what is between sum of squares ? (A) The variance caused by treatment variable (B) The variance caused by the difference within subjects (C) The variance caused by the extraneous factors (D) Total variance of the dependent variable 48. Which of the following is not a task of Philosophy ? (A) Speculation (B) Description and Analysis (C) Prescription (D) Observation 49. Which of the following is not a unique feature of education envisaged by Swami Vivekananda ? (A) Cultivation of heart and physical strength. (B) Residential programme of education. (C) Intelligent productive manual labour (D) Importance to concentrations. 50. ‘Intuitive Knowledge’ is attained through (A) External experiences (B) Internal experiences (C) Both internal and external experiences (D) Neither internal or external experiences 51. ‘The child is an integral part of the ultimate universe’ is the view point of (A) Realism (B) Pragmatism (C) Existentialism (D) Idealism 52. Which of the following is not a suited connotation for ‘Equality of educational opportunity’ ? (A) A policy of open access to education to all. (B) Equitable rationing and distribution of available resources to all. (C) Equalisation of educational attainment by providing resources in favour of less able and less motivated group. (D) Investing more funds on education. 53. ‘Learning in communion with nature’ was propagated by (A) Swami Vivekananda (B) Sri Aurobindo (C) Rabindranath Tagore (D) Mahatma Gandhi 54. The founder of Pragmatism was (A) John Dewey (B) William James (C) Kilpatrick (D) Charles Sanders Peirce 55. Rousseau’s conception of ‘freedom’ was not accepted by (A) Pestalozzi (B) Jean Paul Sartre (C) Paulo Freire (D) John Dewey 56. “Discipline through direct consequence” was propagated by (A) Existentialist (B) Pragmatist (C) Naturalist (D) Realist 57. The School of Philosophy which upholds the primacy of ‘mind over matter’ is (A) Existentialism (B) Realism (C) Pragmatism (D) Idealism 58. The teacher is very much concerned with epistemology because his aim is to promote (A) Values (B) Truth (C) Knowledge (D) Skills 59. Which School of Philosophy maintains that the ‘universe is an expression of intelligence and will’ ? (A) Pragmatism (B) Realism (C) Idealism (D) Existentialism 60. “Education according to interest rather than the caste, creed, race or religion” was propagated by (A) Vedantic Education (B) Islamic Education (C) Jainistic Education (D) Buddhistic Education 61. The major constraint of social change is (A) caste (B) education (C) religion (D) poverty 62. Modernisation of ‘educational programmes’ has posed many issues in the society. Which one of the following is not applicable ? (A) Increasing numbers of crimes in teenagers. (B) Increasing number of suicides in students. (C) Misuse of media by youngsters. (D) Reduced status of teachers. 63. Analysis of the sociological processes involved in the educational institutions could be known as (A) Social foundations of Education (B) Sociology of Education (C) Educational Sociology (D) Social Science of Education 64. According to Talcott Parson, social change deals with (A) Spiritual upliftment (B) Economic upliftment (C) Cultural revolution (D) Functional needs of the society 65. Caste system can create a (A) closed society (B) changing society (C) dead society (D) open society 66. It is often complained that there is a ‘brain drain’ in our country. The implication is that (A) the brains of educated persons are being washed in unnecessary pursuits. (B) students’ brains are burdened with education unnecessarily. (C) education today is creating strain to the brains of students. (D) educated and capable people are seeking jobs in other countries for better opportunities and economic benefits. 67. Some sociologists have given importance to the functioning factors of social interaction. These factors are concerned with (A) the proximity and similarity of the societies (B) the purpose and common facts of societies. (C) the needs and past experiences of the societies. (D) goodness, common cause and economy of the societies. 68. National Reconstruction in any country should be based on (A) improvement of adjustability and adaptability of people. (B) familiarising the children with the nation’s culture and philosophy. (C) weeding out the unsocial and unscientific practices at the top level. (D) developing ambitious outlooks among administrator. 69. Which of the following is not an attribute of culture ? (A) Shared (B) Transmittable (C) Innate (D) Learnt 70. The Kothari Commission’s report was entitled as (A) Education and National Development (B) Learning to Be (C) Diversification of Education (D) Education and social change in Democracy. 71. Acculturation is the process of (A) developing qualities affecting the culture of a nation. (B) accepting the innovations required for the development of nation’s culture. (C) being influenced by the cultural imperatives of a nation. (D) following the latest trends of a culture as opposed to the past traditions. 72. The SUPW has been introduced in the school curriculum due to the recommendation of (A) The Kothari Education Commission’s Report (B) The Ishverbhai Patel Educational Review Committee (C) The Secondary Education Commission’s Report (D) The University Education’s Committee Report 73. For Harmonious development of the personality of the child, parents should (A) Over-protect the child. (B) Regularly compare the child with other children. (C) Provide conducive environment at home. (D) Engage qualified teachers for Her. 74 During early phases of Development, Educational Psychology has drawn its content from the researches in (A) Physical Sciences (B) Medical Sciences (C) Social Sciences (D) Natural Sciences 75 Who among the following described the intellectual development as age related development ? (A) Jerome S. Bruner (B) Jean Piaget (C) David Ausubel (D) Hilda Taba 76. Most important factor(s) in the development of child are (A) Physical and moral environment of the child. (B) Social and Economic status of the family. (C) Educational and social status of parents. (D) Socio-economic and intellectual environment of the child. 77 Differences in ‘Learning Styles’ among learners may be attributed to (A) Socialisation process of learner. (B) Thinking strategies adopted by learner. (C) Economic conditions of the family. (D) Parenting of the child. 78. Two-factor theory of intelligence is given by (A) Alfred Binnet and L. Simon (B) C.E. Spearman (C) J.P. Guilford (D) L.M. Terman 79. Children whose mental age is lower than chronological age are called (A) Gifted children (B) Normal children (C) Learning disabled (D) Retarded children 80. Concepts are important vehicles in (A) Learning communication (B) Thinking processes (C) Motivating the learner (D) Achievement of learner 81. The meaningful reception learning was explained by (A) Robert Gagne (B) David Ausubel (C) Jean Piaget (D) Jerom S. Bruner 82. The type of learning explained by Albert Bandura is also known as (A) Insight learning (B) Observational learning (C) Sign learning (D) Verbal learning 83. A child is working very hard for her examination. Her behaviour is an indicator of her (A) Sharp cognitive abilities (B) High achievement motivation (C) Very busy schedule (D) Desire to impress her parents 84. The purpose of instructional theory is (A) Descriptive (B) Instructive (C) Prescriptive (D) Evaluative 85. The quality of questions in a test is assessed by using the method of (A) Item Analysis (B) Task Analysis (C) Content Analysis (D) Trend Analysis 86. The size of a population is 100 and every 5th person is selected to form a sample. This technique of sampling is known as (A) Random (B) Stratified (C) Cluster (D) Systematic 87. If a test measures mastery level achievement in a subject, it is known as (A) Criterion-referenced test (B) Diagnostic test (C) Norm-referenced test (D) Prognostic test 88. In an ethnographical study which of the following technique is most appropriate ? (A) Psychological testing (B) Questionnaire (C) Observation (D) Sociometry 89. The correlation between X and Y is significant. It means that (A) X causes variation in Y. (B) X and Y vary together. (C) Y causes variation in X. (D) X and Y vary independently. 90. If Q1, Q2 and Q3 represent 1st, 2nd and 3rd quartiles respectively and Q semi intrinsic quartile then Q may be written as (A) Q1 – Q3 (B) Q3 – Q1 (C)Q3 + Q1 (D) Q2 – Q1 91. If K is added to every score of a distribution with mean ‘M’ and standard deviation ‘s’, the new standard deviation will be (A) K (B) s (C) s + K (D) Ks 92 . If each z-score of a distribution of scores is multiplied by 10 and the result increased by 50, the standard deviation of the resulting numbers would be (A) 50 (B) 40 (C) 10 (D) 5 93. Which of the following types of test-items make a ‘supply type’ test ? (A) Multiple choice (B) Matching (C) Classification (D) Completion 94 . Which of the following purposes demands Action Research ? (A) Developing a theory (B) Writing a thesis (C) Solving a classroom problem (D) Testing a theory 95 . Median is also known as a. 5% point b. 50th percentile c. 2nd quartile d. 5th decile (A) acb (B) bca (C) bcd (D) cda 96. Match the following List-I with List-II. List-I(Type of Correlation) List-II(Nature of Variables) (a) Biserial Correlation (i) Continuous v/s continuous (b) Pie coefficient (ii) Continuous v/s Dichotomous (c) Point-biserial correlation (iii) Dichotomous v/s Dichotomous (d) Tetrachoric correlation (iv) Dichotomized v/s Dichotomized (v) Continuous v/s Dichotomized Code : a b c d (A) iv i v ii (B) v iii ii iv (C) iii ii v ii (D) v iv ii i 97. Which of the following methods should be used for establishing reliability of the Questionnaire ? (A) Test-retest method (B) Split-half method (C) Parallel form method (D) Rational equivalence method 98. Which of the following is an example of a qualitative research ? (A) Descriptive survey (B) Experimental study (C) Ex Post Facto study (D) Case study ' 99. Two characteristics of ex-postfacto research are (A) randomization and comparison of groups (B) non randomization and manipulation of independent variables © non manipulation and non randomization (D) non manipulation and randomization 100. Preparation of a research proposal involves (A) Using the first person voice in writimg (B) Using a unique format and style © letting the typist decide the format and style (D) Carefully following the required format and style

Graphical Representations of data

Graphical Representation of Data 301 Graphical Representation of Data 28.1 INTRODUCTION Whenever verbal problems involving a certain situation is presented visually before the learners, it makes easier for the learner to understand the problem and attempt its solution. Similarly, when the data are presented pictorially (or graphically) before the learners, it makes the presentation eye-catching and more intelligible. The learners can easily see the salient features of the data and interpret them. There are many forms of representing data graphically. They are (i) Bar graphs (ii) Histograms (iii) Frequency polygons (iv) Ogive (v) Pictographs (vi) Pie charts In this lesson, we shall learn to read and draw Bar graphs, Histograms and Frequency polygons, and graphs related to day-to-day use, like temperature-time graph, velocity-time graph, pressure-volume graph, etc. Other form of graphs are beyond the scope of the present lesson. 28.2 OBJECTIVES After studying this lesson, the learner will be able to z draw bar charts for given data z draw a histogram and frequency polygon for given data z read and interpret given bar charts and histograms z read the relevant information from graphs relating to day-to-day activities, like (i) temperature-time graph302 Mathematics (ii) velocity-time graph (iii) pressure volume graph, etc. z draw graph relating to day-to-day activities, like the ones above. 28.3 EXPECTED BACKGROUND KNOWLEDGE z Knowledge of drawing and marking axes z Knowledge of drawing rectangles and plotting points z Practice of reading graphs. 28.4 BAR GRAPHS A bar graph is a graphical representation of frequency distributions of ungrouped data. It is a pictorial representation of the numerical data by a number of bars (rectangles) of uniform width erected vertically (or horizontally) with equal spacing between them. 28.4.1 Construction of Bar Graphs For the construction of bar graphs, we go through the following steps : Step 1 : We take a graph paper and draw two lines perpendicular to each other and call them horizontal and vertical axes. Step 2 : Along the horizontal axis, we take the values of the variables and along the vertical axis, we take the frequencies. Step 3 : Along the horizontal axis, we choose the uniform (equal) width of bars and the uniform gap between the bars, according to the space available. Step 4 : Choose a suitable scale to determine the heights of the bars. The scale is chosen according to the space available. Step 5 : Calculate the heights of the bars, according to the scale chosen and draw the bars. Step 6 : Mark the axes with proper labelling Let us take some examples to illustrate : Example 28.1 : The number of trees planted by an agency in different years is given below : Years 1997 1998 1999 2000 2001 2002 Total Number of 400 450 700 750 900 1500 4700 trees planted Solution : The bar graph is given below in Fig. 28.1 :Graphical Representation of Data 303 Fig. 28.1 Step 1 : We draw two perpendicular lines OX and OY. Step 2 : On OX, we represent years, from 1997–2002 and on OY we represent the number of trees planted. Step 3 : On OY, we start with 400 and marks points at equal intervals of 200. Step 4 : The height of the bars are calculated according to the number of trees. A kink (~) has been shown on the vertical axis showing that the marking on the vertical axis starts from zero but has been shown to start from 400 as the data needs. Examples 28.2 : The data below shows the number of students present in different classes on a particular day : Classes VI VII VIII IX X Number of 35 40 30 40 50 students present Represent the above data by a bar graph. Solution : The bar graph for the above data is shown in Fig. 28.2.304 Mathematics Fig. 28.2 Example 28.3 : The data regarding causes of accidents in factories are given below: Causes Percentage of Occurrence Faulty Machinery 30% Electrical Disturbance 20% Delay in repairs 35% Mechanical Failure 10% Others 5% Draw a bar graph to represent the above data. Solution : The bar graph representing the above data is shown in Fig. 28.3 below: Fig. 28.3Graphical Representation of Data 305 28.4.2 Interpretation of Bar graphs After drawing a bar graph, we can draw some conclusions, which is called interpreting bar graphs. Let us take some examples and do the same. Example 28.4 : Read the bar graphs given in Fig. 28.1, and answer the following questions : (i) In which year the maximum number of trees were planted ? (ii) What trend the number of trees planted show ? (iii) In which years the number of trees planted differ by 50 only ? Solution : After reading the bar graph, the answers to the above questions are as follows : (i) The maximum number (1500) of trees were planted in the year 2002, as in that year the height of the bar is maximum. (ii) The number of trees planted kept on increasing year after year (iii) (a) The years 1997 and 1998 (b) The years 1999 and 2000 Examples 28.5 : Read the bar graph given in Fig. 28.3 and answer the following questions : (i) Which cause is responsible for maximum accidents in factories ? Which is for minimum ? (ii) Can you think of one of the “other” causes ? (iii) How many percent of accidents could have been avoided by timely action? Solution : (i) Delay in repairs is responsible for maximum (35%) of accidents. “Other causes” are responsible for minimum number of accidents (ii) Carelessness of workers (iii) (35 + 20)% or 55% accidents could have been avoided by taking steps for timely repairs and provision of equipment which can control electrical disturbances. CHECK YOUR PROGRESS 28.1 1. Enlist the possible forms of representing a data graphically. 2. What are the steps needed to represent a data by a Bar Graph ?306 Mathematics 3. For the data on expenditure of a company over different heads, draw a bar graph : Head Percentage of Expenditure Salary of Employees 45% Travelling Allowance 15% Rent of Premises 20% Machinery and materials 10% Other expenditure 10% 4. Given below are data on causes of strikes in mills : Causes Percentage (i) Non fulfillment of economic demands 45 (ii) Overwork 20 (iii) Rivalry in unions 20 (iv) Non-congenial working conditions 10 (v) Others 5 Draw a bar graph depicting the above data. 5. From the bar graph given below, answer the following questions : Fig. 28.4 (i) The names of two steel plants which produced maximum steel in the country during the time period. (ii) What percentage of steel was produced in “other” plants ?Graphical Representation of Data 307 (iii) The steel plant at Durgapur produced how much less steel than at Bokaro? (iv) What percentage of total steel under discussion was produced at Bhalai, Durgapur and Bokaro steel plants ? 28.5 HISTOGRAMS AND FREQUENCY POLYGONS A histogram is a graphical representation of a continuous frequency distribution i.e. grouped frequency distributions. It is a graph, including vertical rectangles, with no space between the rectangles. The class-intervals are taken along the horizontal axis and the respective class frequencies on the vertical axis using suitable scales on each axis. For each class, a rectangle is drawn with base as width of the class and height as the class frequency. The area of the rectangles must be proportional to the frequencies of the respective classes. A frequency polygon is the join of the mid-points of the tops of the adjoining rectangles. The mid-points of the first and the last classes are joined to the mid-points of the classes preceding and succeding respectively at zero frequency to complete the polygon. Let us illustrate these with the help of examples. Examples 28.6 : The following is the frequency distribution of weights of 30 students of class IX of a school. Draw a histogram to represent the data. Classes : 45–50 50–55 55–60 60–65 65–70 Total Frequency : 3 7 12 5 3 30 Solution : For drawing a histogram we go through the steps similar to those of a bar graph. They are given below : Step 1 : On a paper, we draw two perpendicular lines and call them horizontal and vertical axes. Step 2 : Along the horizontal axis, we take classes of equal width : 45–50, 50–55, ...... As the axis starts from 45–50, we take one interval 40–45 before it and put a kink on axis before that Step 3 : Choose a suitable scale on the vertical axis to represent the frequency. It can start from 0 to 12, with a step of 2, i.e., 0, 2, 4, 6, ...., 12, 14 Step 4 : Draw the rectangles as shown in Fig. 28.5.308 Mathematics Fig. 28.5 shows the histogram required. Note : A frequency polygon has been shown in dotted lines, as explained in the steps shown above. Example 28.7 : The daily earnings of 100 shopkeepers are given below : Daily earnings 200-300 300-400 400-500 500-600 600-700 700-800 800-900 (in Rs) No. of shops 3 12 15 30 25 12 3 Draw a histogram and a frequency polygon to represent the above data. Solution : Following the steps suggested in Example 28.6, the histogram and frequency polygon representing the above data are given below in Fig. 28.6 Fig. 28.6Graphical Representation of Data 309 Example 28.8 : Draw a frequency polygon for the following data : Pocket 0–50 50–100 100–150 150–200 200–250 250–300 allowance (in rupees) Number of 16 25 13 26 15 5 students Solution : To draw a frequency polygon without-drawing a histogram we go through the following steps : Step 1 : Draw two lines perpendicular to each other. Step 2 : Find the class-marks of different classes. They are 25, 75, 125, 175, 225, 275 Step 3 : Plot the ordered pairs A (25, 16), B (75, 25), C(125, 13), D (175, 26), E(225, 15) and F(275, 5) Step 4 : Join the points A, B, C, D, E and F and complete the polygon as explained before The frequency polygon is given below : Fig. 28.7 28.5.1 Reading a Histogram Let us explain it with the help of an example Example 28.9. The following histogram shows the monthly wages (in rupees) of workers in a factory310 Mathematics Fig. 28.8 (i) Find the maximum number of workers getting a wage. (ii) Find the least wage and highest wage with no. of workers earning them (iii) How many workers get a monthly wage of Rs. 8000 or less ? Solution : (i) The maximum number of workers is 25 getting wages between Rs (7000 – 8000). (ii) The least wage is between Rs (4000 – 5000) and 4 workers are getting that. The corresponding figures for highest wage are Rs (9000 – 10000) and four workers get that (iii) 50 workers get a wage of Rs 8000 or less as Rs (4000 – 5000) – 4 workers Rs (5000 – 6000) – 10 workers Rs (6000 – 7000) – 12 workers Rs (7000 – 8000) – 24 workers Total – 50 CHECK YOUR PROGRESS 28.2 1. What is the difference between a bar graph and a histogram ? 2. Write various steps in the construction of a Histogram.Graphical Representation of Data 311 3. Draw a histogram for the following frequency distribution : Height of students 135–140 140–145 145–150 150–155 155–160 160–165 (in cm) No. of students 3 5 12 7 5 3 Also draw a frequency polygon for the above data on the same sheet 4. Draw a frequency polygon for the data in Question 3 on a separate paper. 5. Draw a histogram and a frequency polygon for the following grouped data: Annual income 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 (in ten thousand rupees) No. of families 25 20 15 15 13 7 3 2 in a locality 6. Interpret the data represented by the following histogram by answering the following questions : Fig. 28.9 Shirt sale in a week in a shop. (i) The least number of shirts were sold in which class ? (ii) The maximum number of shirts were sold in which class ? (iii) How many shirts were sold upto the 42 shirt size ? (iv) How many shirts of size 44–66 were sold ?312 Mathematics 28.6 GRAPHS RELATED TO DAY-TO-DAY ACTIVITIES In addition to histograms and frequency polygons, we are sometimes faced with graphs of other types. When a patient is admitted in a hospital with fever the doctor/nurses prepare a temperature-time graph, which can be referred to any time for reference. Similarly, the velocity time graph and pressure-volume graph are of day-to-day use. We shall learn to draw these graphs and interpret them in the sections below : 28.6.1 Temperature-Time Graph-Reading and Construction Example 28.10 : The body temperature of a patient admitted in a hospital with typhoid fever at different times of a day are given below : Time of the day 7 9 11 13 15 17 19 21 23 hrs hrs hrs hrs hrs hrs hrs hrs hrs Temperature 102 103 104 103 101 100 99 100 99 (in °F) Draw a graph to represent the above data. Solution : The graph of the above data is given in Fig. 28.10. The graph has been obtained by joining the points corresponding to pairs, like (7, 102), (9, 103), ........., (23, 99) in the rectangular system of coordinates, by line-segments. Fig. 28.10 Note : While drawing the graph it has been assumed that during the time interval in between times, the same trend was present.Graphical Representation of Data 313 Example 28.11 : If the medicine was given to the patient at 9 hours, whose temperature-time graph is shown in Fig. 28.10, answer the following questions : (i) At what time of the day was the temperature highest ? At what time lowest? (ii) After how much time, the action of medicine had started ? (iii) What trend do you observe from the above graph ? Solution : (i) The temperature of the patient was highest at 11 hours and lowest at 19 hrs and 23 hrs. (ii) The action of the medicine started 2 hours after the medicine was given as the temperature started falling after that. (iii) The administered medicine suited the patient as the temperature constantly fell after that, with the exception of period between 19 hrs and 21 hrs when it became slightly higher at 100°F but again fell after that 28.6.2 Velocity Time Graph During a journey from one place to other, the speeds of vehicles keep on changing according to traffic congestions. This can be very well shown by a velocity-time graph. Let us illustrate it with the help of example : Example 28.12. During a journey from city A to city B by car the following data regarding the time and velocity of the car was recorded : Time of the day 6 7 8 9 10 11 12 13 14 15 16 17 (in hours) Velocity 60 60 45 50 60 50 45 60 50 65 40 50 (in km/hour) Represent the above data by a velocity time graph. Solution : As before the graph can be obtained by plotting the ordered pairs (6, 60), (7, 60), ... (15, 65), ..., (17, 50) in the rectangular system of coordinates and then by joining them by line-segments.314 Mathematics Fig. 28.11 Example 28.13 : Read the velocity-time graph given in Fig. 28.11 and reply the following questions : 1. At what time duration of the day, the velocity of the car (i) was lowest ? was highest ? (ii) constant (iii) went on increasing (iv) went on decreasing 2. What was the average speed of the car in the journey ? Solution : 1 (i) At 16 hours; At 15 hours (ii) The velocity was constant at 60 km/hour between 6 hours and 7 hours (iii) Between 8 hours to 10 hours (iv) Between 10 hours to 12 hours 2. The average speed of the car was 60 60 45 50 60 50 45 60 50 65 40 50 12 F + + + + + + + + + + + H G I K J km/hour = 635 12 or 52.92 km/hour.Graphical Representation of Data 315 28.6.3 Pressure-Volume Graph For a fixed quantity of a gas at a constant temperature, is there any relation between pressure and volume of the gas ? Let us see that from the following example : Example 28.14 : The following data pertains to pressure and volume of a fixed quantity of gas : Pressure (p) 60 90 45 30 75 (in Newton) Volume (v) 90 60 120 180 72 (in cm3 ) Draw a graph to represent the above data. Solution : Fig. 28.12 The graph is obtained by joining the plot of the ordered pairs (60, 90), (90, 60), ..... (75, 72) by free hand curve. Example 28.15 : Read the above graph, given in Fig. 28.12, and answer the following questions : 1. Full in the blank : (i) As volume increases, the corresponding pressure ... (ii) As pressure decreases, the volume ... (iii) Pressure × Volume = ...316 Mathematics 2. What will be the pressure when volume is 100 cm3 ? 3. What will be the volume, when the pressure is 100 Newton ? Solution : 1 (i) Decreases (ii) Increases (iii) Constant = 5400 2. We know that pv = 5400 ∴ When volume = 100, p = 54 Newtons as can be seen from the graph at point A 3. When p = 100 Newtons, v = 54 cm3 as can be seen from the graph at the point B. CHECK YOUR PROGRESS 28.3 Represent the data given in each of the questions below graphically : 1. For a town, the maximum temperature for the following months are given below : Months March April May June July August September October Maximum temperature 35 38 38 42 45 40 38 35 (in °C) 2. The body temperatures of a patient admitted in a hospital are given below: Time of the day 8 9 10 11 12 13 14 15 16 17 (in hours) Temperature (in °F) 103 104 105 102 102 100 99 99 100 98 3. The speeds of a car going from station A to station B at different times of the day are given below : Time of the day (in hours) 7 8 9 10 11 12 13 14 15 Speed (in km/hour) 45 45 50 60 60 75 60 60 50 4. The data on pressure and volume of a gas are given below : Pressure (in Newtons) 60 80 50 30 40 20 Volume (in cm3 ) 40 30 48 80 60 120Graphical Representation of Data 317 5. For question No. 1, read the graph and reply the following questions : (i) Find the range of temperature for given months (ii) Which month had the least temperature ? (iii) Which month had the highest temperature ? (iv) In which month was the temperature less than 40°F ? (v) Can you predict the temperature for the next two months ? 6. Read the graph of Question No. 2 and answer the following question : (i) At what time of the day was the temperature of the patient maximum? (ii) If the medicine takes at least two hours to show the effect, at what time of the day was the medicine given ? LET US SUM UP z Bar graphs are the graphical representation of ungrouped frequency data. z Histograms and frequency polygons are the graphical representation of continuous grouped frequency data. z The graphical representation of data from day-to-day life is the join of points corresponding to ordered pairs represented by the data. z The graphical representations show the trends readily and at a glance only. TERMINAL EXERCISE Draw the bar graph for the following data in each case : 1. Height of samplings (in m) 0.5 0.75 1.0 1.25 1.50 1.75 2.00 No. of samplings 15 18 25 40 12 8 7 2. Weight (in kg) 7 8 9 10 11 12 15 No. of baskets of apples 4 5 7 8 5 4 3 3. Number of parcels 120 150 80 60 40 50 received in a post office Weight of parcels (in kg) 1 2 3 4 5 6 4. Interpret the data given in Question 1 and 2.318 Mathematics Draw a histogram and frequency polygon for the data in each case below: 5. Weight (in kg) 40–45 45–50 50–55 55–60 60–65 65–70 No. of students 4 7 8 9 6 3 in the class 6. Daily earning 100-120 120-140 140-160 160-180 180-200 (in rupees) No. of workers 5 7 8 3 2 7. Read the graphs for Question Nos. 5 and 6 and interpret them. 8. The minimum temperatures of a town for a year are given below : Month Jan Feb March April May June July Aug Sep Oct Nov Dec Min. temp. 12 14 16 20 20 24 25 24 22 18 16 12 (in °C) Draw a graph to represent the above data and interpret it. 9. A man left New Delhi for Lucknow by car at 7 AM. The speed of the car at different times of the day is given below : Time of the day 7 9 11 13 15 17 19 21 (in hour) Velocity (in km/hour) 45 50 60 65 70 60 55 40 Represent the above data by a velocity time graph and answer the following questions At what time was the velocity of the car (i) Maximum (ii) Minimum (iii) Between (50–60) km/hour (iv) Can you give hypothesis regarding the places where speed is extreme ? 10. The following data pertains to a gas in a container : Pressure (in Newton) 100 80 50 40 125 200 Volume (in cm3 ) 40 50 80 100 32 20 Represent the above data by a pressure volume graph. What relation do you find between pressure and volume from the data ?Graphical Representation of Data 319 ANSWERS Check Your Progress 28.1 5. (i) Bhilai and Rourkela (ii) 8.33% (iii) 50 (in ten thousand tonnes) (iv) 62.5% Check Your Progress 28.2 6. (i) (44–46) size (ii) (40–42) size (iii) 700 (iv) 50

INTRODUCTION TO THEORIES OF KNOWLEDGE

The branch of philosophy that studies the nature, source and limits of knowledge is known as epistemology. It is the theory of knowledge.The basic questions of epistemology can be put down in the following manner: 1. What is the nature of knowledge: this question asks what does it mean to say that someone knows. How do we distinguish between cases in which someone knows something and cases in which someone does not know something? 2. How do we acquire knowledge: here we try to find the sources and origin of our knowledge. How can we use our various faculties like reason, senses, or other resources to acquire knowledge? We try to find out how we gain the concepts we use in our thought. 3. What is the scope of knowledge or what can we know: this query tries to answer whether there are limits to what we can know. For example, whether there are things which are unknowable for us. Is it possible that we do not know as much as we think we do? This Unit will introduce you to the second question of epistemology, that is, how we acquire knowledge. ORIGIN AND SOURCES OF KNOWLEDGE There are many ways that one might come to know something or acquire knowledge. We acquire our knowledge of empirical facts about physical world through perception, that is, by using our senses. Science is the best example of empirical knowledge with its collection of data. Our everyday knowledge also mostly comes from the senses, as we look, listen, smell, touch, and taste the various objects in our environments. But knowledge is not simply made up of sensations. All knowledge requires some amount of reasoning. Data collected by scientists must be analyzed before knowledge is yielded, and we draw inferences based on what is given to us by our senses. In case of knowledge of abstract or non-empirical facts one has to rely exclusively upon reasoning. Some philosophers regard memory also as a source of knowledge. In memory we come to know something which we knew in the past but which is no longer present to our senses now. Knowledge can also be acquired through testimony, that is, from the words of some trusted person or books that can be believed to be true. THEORIES OF KNOWLEDGE There are four main theories of origin of knowledge. 1. Rationalism: It is a theory that regards reason as the chief source of knowledge. Descartes, Spinoza and Leibniz are advocates of Rationalism. 2. Empiricism: It is a theory that regards experience as the source of knowledge. Locke and Hume are the chief exponents of this theory. 3. Criticism: It is also called the Critical theory of knowledge. It is advocated by Kant. He advocated the view that both experience and reason together yield knowledge. 4. Intuitionism: It regards intuition as the source of knowledge. Henry Bergson is an advocate of this theory. RATIONALISM Rationalism is the theory of knowledge according to which reason or intellect is the main source of knowledge. Rationalism rejects all knowledge derived from sense experience. Socrates and Plato are the earliest rationalist philosophers. According to them, true knowledge originates from reason. The Rationalism that was advocated by these two philosophers became articulate in the philosophy of Descartes, Spinoza and Leibniz. However, the rationalist philosophers differ among themselves regarding how much importance should be given to experience in yielding knowledge. Some rationalists regard experience as wholly misleading while others attach some values to it. They say that the knowledge given by experience is confused knowledge. But inspite of their differences they all agree that reason alone can give us certain and perfect knowledge. Rationalism is also called a priori theory of knowledge as according to this theory, knowledge is prior or independent of experience. Standpoints of Different Philosophers RENE DESCARTES (1596-1650) As it has been mentioned above, modern rationalism begins in the philosophy of Descartes. Descartes is considered as the father of modern western philosophy. Descartes was a mathematician and according to him, the perfect form of knowledge can be gained only through mathematical demonstration. Such demonstration consists in starting with self-evident principles and deducing other truths from these self-evident principles. Descartes divides ideas into three kinds: adventitious, factitious and innate. Adventitious ideas are imposed on the mind from without. They are not clear and distinct. Factitious ideas are created by the mind by the conjunction of ideas. These are created by imagination. They are also not clear and distinct. But innate ideas are clear and distinct. They are implanted in the mind by God at the time of birth. According to Descartes, knowledge is given by clear vision of intellect or reason. Descartes calls it intuition. For him intuition is the undoubted, immediate apprehension of self-evident truth by reason. God imprints certain innate ideas in the mind at the time of birth. They are self-evident. The idea of causality, infinity, eternity, perfect Being or God and the like are innate ideas. They are clear and distinct. Clearness and distinctness is the test of their truth. The development of true knowledge consists in the logical deduction of other truths from these principles. Thus Descartes applies mathematical method to philosophy. Therefore, Paulsen has characterized Descartes’ philosophy as Mathematical Rationalism. According to Descartes, certainty is the criterion of truth. Therefore, he rejects knowledge derived from sensation. He starts with universal doubt. He doubts all knowledge including mathematical demonstration. One can doubt everything, but in doubting one cannot doubt the doubting itself. To doubt is to think. To think is to exist. “Cogito ergo sum”. “I think, therefore, I exist”. Once he establishes the existence of the self, Descartes moves to prove the existence of the external world. Each one of us has the innate ideas of which God is the most important. From this idea of God Descartes proves the existence of God. The idea of God is the idea of infinite Being. But I being finite cannot produce this idea of infinite Being in me. Another human being cannot produce it, as he too is finite. This idea also cannot be produced by addition of finite beings and things as the sum of finite is also finite. So, this idea of the infinite Being must be produced by that which itself is infinite, that is, by God himself. So God must exist. Now God is benevolent and truthful. As such he cannot deceive us. And we have conviction that external things exist. So, they must exist. For otherwise God will turn deceitful. Descartes thus proves the existence of the external world. CHECK YOUR PROGRESS 1. Theory of origin of knowledge is studied in the branch of philosophy known as Metaphysics. True/ False 2. Plato’s philosophy cannot be claimed to be rational in nature. True/ False 3. A priori means ‘knowledge is after experience’. True/ False 4. Innate ideas are implanted in the mind at the time of birth by God. True/ False 5. What are three kinds of ideas according to Descartes? 6. What is the criterion of truth according to Descartes? BENEDICT SPINOZA (1632-1677) Spinoza gave a developed form to the rationalism initiated by Descartes in modern western philosophy. Like Descartes, Spinoza had immense faith in reason. Like a true rationalist Spinoza holds that we can know truth through reason. Reason can give us knowledge of reality because reality itself is rational in nature. According to Spinoza, God himself creates the world rationally and intuition is the realization of true knowledge. It is intuition by which one knows the necessary relations between different phenomena. According to Spinoza, the goal of philosophy is to get complete knowledge of things. He holds that this is possible only by clear and distinct thinking. Like Descartes he believed that if we start with self-evident principles and prove the steps involved in the argument then we will be able to reach certain and universal knowledge. Spinoza uses geometrical method to philosophy to arrive at certain truths. His method is geometrical because he lays down certain definitions, axioms and postulates and from these principles he deduces propositions with proofs. Spinoza starts with the innate principle or idea of God or Substance. According to him, a substance is that which exists by itself and is conceived by itself. This substance is infinite and it has infinite attributes. Out of these attributes we can know only thought and extension which themselves are infinite. They are parallel and co-exist with each other. These attributes are modified into infinite intelligence and will and infinite extension and motion. They are the infinite modes of Substance. Infinite intellect and will are again modified into finite intellects and will or finite minds. Infinite extension and motion are modified into finite extension and motion or finite objects. Thus finite minds and finite objects are modification of the one and same Substance. 1. The method in philosophy used by Spinoza is: a. mathematical b. geometrical 2. According to Spinoza, God has a. two attributes b. three attributes c. infinite number of attributes GOTTFRIED WILHELM LEIBNIZ (1646-1716) Leibniz was a famous mathematician. He held that the world has logical and mathematical order. Laws that govern this world order are rational. Therefore, the world can only be comprehended by reason. Leibniz’s theory of knowledge is based on his metaphysical theory. Leibniz established that the world is composed of dynamic units or immaterial, unextended, simple units of force. These are called monads. According to him, monads are windowless and hence they cannot receive any knowledge from any external source. Leibniz holds that we cannot derive any invariable law concerning the functions of the universe on the basis of sense experience. Knowledge is simply brought out and manifested by experience. He holds that nothing can exist in the intellect that did not first exist in sensation- except, he adds, the intellect itself. The rational laws governing the world are to be found only in reason because the world has been created by God on the basis of reason. EMPIRICISM JOHN LOCKE (1632-1704) Locke revolted against Descartes’ rationalism and criticised his theory of innate ideas. he criticised the theory of innate ideas on the following grounds: 1. If there were innate ideas they should be equally present in all minds. But there are no such innate ideas which are equally present in all minds. For example, we do not find that savages, children or idiots are concious of so called innate ideas like causality, infinity, eternity etc. 2. If there were innate ideas they should be the same in all minds. But the ideas of morality, God and the like are not the same in all minds. Different ideas are held in different socities. Sometimes the same society may hold different view at different times or ages. 3. Even if there were the same ideas in all minds, it would not make them innate on that account. Everybody has the same idea of fire. But all of us get the idea of fire from experience. It is not an innate idea. Universality of an idea does not prove the innateness of it. According to Locke, at the time of birth the mind is a tabula rasa or blank sheet. Mind is a clean slate in the beginning on which expereince writes. According to him, ‘there is nothing in the intellect that was not previously in the senses’. Mind receives ideas from expereince. This expereince is two fold: sensation and reflection. Sensation is the source of our knowledge of the sensory qualities of objects. Reflection is the source of our internal states of mind, such as, perception, belief, thought and reasoning etc. We get our first ideas from sensation and then we reflect upon it. Sensations are the materials on which the mind thinks. According to Locke, the mind is passive in receiving ideas. But it is active in comparing and combining these ideas. The ideas that are passively received by the mind are the simple ideas. these simple ideas are combined by the active power of the mind into varieties to make complex ideas. Locke says that there are four simple ideas: Firstly, the ideas which enter our minds through one sense organ only. For example, colour, sound, taste, heat, cold solidity. Secondly, the ideas which enter the mind by more than one sense organ. For example, space, figure, rest, motion which enter through both sight and touch. Thirdly, the ideas that are received by reflection only. For example, perception, retention, discerning, comparing, compounding, naming and abstracting. Fourthly, the ideas that we receive both through sensation and reflection. For example, pleasure, pain, power, existence, unity, succession and duration. According to Locke, the power that an object has to produce idea in our minds is a quality. But he makes an important distinction between primary and secondary qualities. Primary qualities belong to the objects themselves. They cannot be separated from the object. As such he calls them objective. Examples of primary qualities are solidity, extension, motion, shape, size, impenetrability etc. Secondary qualities on the other hand are mere sensations or ideas in the mind of the knower. They are sensations produced in the mind by the primary qualities. They vary under different conditions. They are subjective. Locke is an empiricist, but he believes in the existence of matter, mind or soul and God though they are not given in experience. He says that we have to assume the existence of matter as the substratum of primary qualities of objects though we do not perceive it. Similarly, the existence of mind is inferred from various mental operations. Its existence must be assumed as the substratum of power of perceiving, thinking, feeling and willing. Similarly, we infer the existence of God as the maker of the external world. Locke being an empiricist refuses to believe that knowledge can be derived from any other source than sense-experience, but he crosses the bounds of empiricism by accepting the existence of matter, mind and God. 1. Why empiricism is called a-posteriori theory of knowledge? 2. Locke maintains that at the time of birth we are born with innate ideas. True/ False 3. Reflection is prior to sensation. True/ False 4. Locke is a thorough going empiricist. True/ False 5. Mind is given in experience and therefore, according to Locke we should believe in its existence. True/ False DAVID HUME (1711-1776) Hume developed Locke’s empiricism to its logical conclusion. Hume is a true empiricist and he does not accept the existence of anything that is not given in experience. As such he denies the existence of mind, matter and God, because these are not given in experience. According to him, all knowledge comes from impressions and ideas. Impressions are lively perceptions and images are their faint copies. There are impressions of sensations or external perceptions and impressions of reflection or internal perception. They constitute the original materials of knowledge. Impressions and ideas are discrete or disconnected from one another. Impressions and ideas are automatically combined with one another by the laws of association, such as law of contiguity, similarity and causality. A picture suggests the object it represents due to law of similarity. An inkpot suggests a pen due to law of contiguity in space. A lightening suggests a thunder due to law of contiguity in time. Fire suggests burning due to law of causation. Thus discrete impressions get connected with one another due to the laws of association. Thus our knowledge is composed of impressions and ideas combined by the laws of association. Our knowledge does not owe anything to reason or intellect. However, these laws are subjective in nature. As such the connection they provide to the impressions are also subjective. Hume rejects the idea of material substance, mind and God, as we do not have any empirical evidence of them. He also rejects all metaphysical entities, as we cannot have any ideas of these entities. Hume admits only particular and contingent truths as they alone are given in experience. It is not possible to go beyond sensation to know reality outside them. Hume’s theory thus lands up in sensationism and scepticism. CRITICISM The doctrine of criticism is synthesis of rationalism and empiricism. As we see neither rationalism nor empiricism is a satisfactory theory of knowledge. By denying the role of experience rationalism has become one sided. Empiricism also is one sided as it denies the role of reason in knowledge. However, rationalism rightly emphasizes the universality or necessity of knowledge. But it is wrong in accepting innate ideas. If we accept innate ideas then we also will have to accept that there is no progress in knowledge as knowledge consists simply in analytical deduction of innate principles. Therefore, empiricists are right in emphasizing that knowledge is acquired through experience. But the problem with empiricism is that it denies universal and necessary knowledge as experience gives us only contingent truths. However, true knowledge should be universal and at the same time it should be novel. Immanuel Kant tries to reconcile rationalism and empiricism in criticism and give a satisfactory view of knowledge that is both universal and contains novelty. MMANUEL KANT (1724-1804) According to Kant, no knowledge is possible without sensation. But he also holds that knowledge is not wholly derived from experience, as it cannot give us universality. The part of knowledge that is not given by experience is a priori. According to Kant, human mind receives sensation from without. The sensations are produced by noumena or things-in-themselves. These are the materials of knowledge. These sensations are discrete or disconnected from one another. As such they cannot give us knowledge unless they are connected with one another by the mind with its synthetic activity. Thus the form of knowledge is supplied by the mind from within itself. According to Kant, both forms and matter of knowledge always go together. In the words of Kant: “Conception without perception is empty; perception without conception is blind”. Kant divides the faculty of knowing into three subordinate faculties: the faculty of sensibility, the faculty of understanding and the faculty of reasoning.Faculty of sensibility: When we perceive a thing, we perceive it in space and time. Space and time are the forms of perception that sensibility applies to the disconnected sensations and converts them to intelligible objects. Space and time do not belong to the things-in-themselves. They are the forms of perception. They are the a priori ways of perceiving things. Faculty of understanding: Categories of understanding are the universal necessary characteristics of experience which are found in all mental experience. Understanding applies its categories, namely, substance, causality, unity, plurality etc., to the sensations that are already arranged in space and time by sensibility. Like the forms of perception they also do not apply to things-in-themselves. Faculty of reason: Reason is the faculty by which the mind tries to employ its innate forms and categories where there is no sensuous experience. Sensations arranged in space and time by sensibility and subsumed under the categories of understanding are co-ordinated by reason. Reason co-ordinates sensibility and understanding according to its ideas of the world, soul and God. These three ideas of reason are regulative ideas. These are the ideas by which reason organizes the facts of experience into a system. The discrete sensations supplied by experience are reduced to a unity by the synthetic activity of the mind. According to Kant, sensations are the materials of knowledge, while the faculties of knowing-forms of sensibility, categories of understanding and Ideas of reason are supplied by the mind itself. Thus our knowledge is confined to phenomena or appearances only. Noumena or the things-in-themselves remain unknown and unknowable. Human mind cannot know them. All thinkers before Kant regarded that our perceptions correspond to the characteristics in the external world. Kant, on the other hand, maintains that objects in order to be known must conform to the constitution of our minds. Thus according to Kant, in knowledge, instead of mind conforming to an independent nature, it is nature that conforms to mind. This is known as the Copernican Revolution in philosophy. 1. Forms of knowledge are a priori. True/False 2. Mind can know only phenomena. True/ False 3. Why according to Kant we cannot know noumena? ANSWERS (I) 1. False 2. False 3. False 4. True 5. Adventitious, factitious and innate. 6. Certainty (II) 1. b 2. c (III) 1. False 2. True (IV) 1. Because according to empiricism, experience is the source of knowledge. 2. False 3. False 4. False 5. False (V) 1. Because we do not have any impressions of mind, matter and God. 2. False (VI) 1. True 2. True 3. Because faculties of knowing do not apply to noumena.

SECONDARY EDUCATION COMMISSION

Let us discuss the background of appointing the Secondary Education Commission. After achieving the independence in 1947, both the public and the Government began to take keen interest in the development of secondary education. Although the number of secondary schools and its enrolment began to significantly increase even before India’s attaining independence, the quality of education imparted was unable to meet the changing socio-economic needs of the country. As such, the need for reform was strongly felt. The university Education Commission also remarked that our secondary education remained the weakest link in our educational machinery and it needed urgent reforms. Meanwhile with the attainment of independence, the political situation of the country also underwent a complete transformation. Education also needed a fresh look, calling for a new outlook which was appropriately voiced by Maulana Abul Kalam Azad, the then Education Minister in his presidential address to the Central Advisory Board of Education in 1948. The Central Advisory Board of Education at its 14th meeting held in January 1948 recommended the appointment of a commission to examine the prevailing system of Secondary Education in the country and to suggest measures for its reorganization and improvement. There were other considerations also before the Government of India for setting up a commission for Secondary Education. In view of these considerations, the Government of India set up, the Secondary Education Commission by Resolution dated 23rd September, 1952, under the Chairmanship of Dr. A. Lakshmanaswami Mudaliar, the Vice-Chancellor of the Madras University. Therefore this commission is also known as Mudaliar Commission. The Commission was inaugurated on 6th October, 1952. It submitted its Report on June 1953. Terms of Reference The terms of reference of this Commission are as follows: a) To enquire into and report on the present position of Secondary Education in India in all its aspects. b) To suggest measures for its re-organisation and improvement with particular reference to - i) The aims, organisation and content of secondary education. ii) Its relationship to primary, basic and higher education. iii) The inter-relation of secondary schools of different types. iv) Other allied problems. So that a sound and reasonable uniform system of secondary education suited to our needs and resources may be provided for the whole country. Method of Enquiry The Commission prepared a questionnaire dealing with the various aspects of secondary education. This was sent out to various educational experts, teachers and educational institutions of India. On the basis of the replies received a good deal of information was collected. The members of the Commission took an extensive tour of the various parts of India and acquired first-hand knowledge of the various educational problems and presented its report running on August 29, 1953. REPORT OF THE COMMISSION Now we shall discuss about the report of the Secondary Education Commission, 1952-53. As the report is a very lengthy one containing 311 pages, it is not possible for us to discuss all aspects in detail. We will confine our discussion to the defects of the prevailing system of secondary education in India and the recommendations given by the Commission regarding its aims, new organizational pattern and the curriculum. Let us discuss all these points one by one. Defects of the Existing System The Commission pointed out the following defects of the existing system - • First, the education given in our schools is isolated from life. The curriculum as formulated and as presented through the traditional methods of teachings does not give the students insight into the everyday world in which they are living. • Secondly, it is narrow and one sided and it fails to train the whole personality of the student. • Thirdly, too much importance has been given to English. Students who did not posses special linguistic ability were, therefore, greatly handicapped in their studies. • Fourthly, the method of teaching generally practised failed to develop in the students their independence of thought and initiative in action. • Fifthly, the increase in size of the classes has considerably reduced personal contact between the teachers and the pupils. Thus the training of character andinculcation of proper discipline have been seriously undermined. • Finally, the dead weight of the examination has tended to curb the teachers initiative, to stereotype the curriculum, to promote mechanical and lifeless methods of teaching, to discourage all spirit of experimentation and to place the stress on the wrong, or unimportant things on education. Its Recommendations on the Aims of Secondary Education The Commission has made the following recommendations in regard to its aims of Secondary Education - Development of democratic citizenship Since India has decided to make itself a democratic republic, the citizens have to be trained to uphold and practice the values of the democratic social order. This can be possible only when the qualities of discipline, tolerance, patriotism, co-operation, equal opportunities for thought, speech and writing, the essence of the world citizenship are inculcated and developed in the students. Secondary education, according to the Mudaliar Commission, should develop all these qualities in the students. Citizens with these qualities can grow into ideal - citizens capable of making Indian democracy a success. In short, the aim of secondary education should be to develop ideal democratic citizens in the country. Improvement of Vocational efficiency : One of the urgent needs of the country is to increase the productive efficiency of its people and to increase the national income. For this, education must aim at increasing the productivity or vocational efficiency of the young students. To achieve this goal, the Secondary Education Commission recommended for fostering the dignity of manual labour and for the promotion of technical skills for the advancement of industry and technology through secondary education. Therefore, secondary education is to be freed from purely theoretical education system and emphasis is to be placed on agricultural, technical, commercial and other practical courses. Education for leadership : Secondary education is a terminal point for majority of the students. Therefore, at the end of the school education, each pupil must be able to enter into various professions independently. “A special function of the secondary school, in the context, is to train persons who will be able to assume the responsibility of leadership - in social, political, industrial or cultural fields - in their own small groups of community or locality.” Development of personality : The secondary education must aim at the development of the personality of the students. It should be so organised that the creative energy in the students should find proper expression. They should also be trained to appreciate their cultural heritage and acquire constructive and valuable interest. They should also be trained to preserve and conserve their cultural heritage. An all-round development of the personality of the student is an essential aim of secondary education. CHECK YOUR PROGRESS 3. Which of the following are the recommendations on the Aims of Secondary Education? Put a (3) for the right answer. i) Education and productivity ii) Education and national integration iii) Development of democratic citizenship iv) Development of personality v) Education and Modernisation vi) Improvement of Vocational Efficiency vii) Development of social, moral and spiritual values viii) Education for leadership Re-organisation of Secondary Education Regarding the organizational pattern of secondary education, the Secondary Education Commission recommended that secondary education should be a complete stage by itself. This stage of education is most important for the students in their preparation for life. To raise the standard of school education the Commission proposed the following organizational pattern: • The duration of secondary education should be 7 years. It should cover the age of group of11-17. • Under the new organizational structure secondary education should commence after 4 or 5 years of primary or junior basic education. • The middle or senior basic or lower secondary stage should cover a period of 3 years. • The higher secondary stage should cover 3 years. • The commission also suggested abolition of the present intermediate classes. The 12th class should be attached to the university and the 11th class should be added to the high school. Thus it pleaded for one year pre-university and 3 year degree courses. • The commission recommended that technical schools should be started in large number and central technical institutes should be established in large cities. • Multi-purpose schools should be established, which would provide terminal courses in technology, commerce, agriculture, fine arts and home sciences. The object of theses institutions was to direct students into different walks of life at the end of the secondary course and this will reduce the pressure upon university entrance. Defects of the Existing Curriculum The Commission has pointed out the following defects in the existing curriculum: • The present curriculum is narrow. • It is bookish and theoretical. • It is overcrowded and does not provide rich and significant contents. • There is no adequate provision for practical and other kinds of activities that should find place in any curriculum at this stage of education. Hence, the curriculum is not able to bring about the education of the whole personality of the child. • It does not cater to the various needs and capacities of the adolescents. • Technical and vocational subjects are very much needed for India today, but the curriculum does not find room for these subjects. • Curriculum is too much dominated by the examination. The Basic Principles of Curriculum Construction The Secondary Education Commission has recommended some principles to be followed in the construction of curriculum. • Principles of totality of experience - According to the Secondary Education Commission, “The curriculum does not include only the academic subjects traditionally taught in the school but it includes the totality of experiences that a pupil receives through manifold activities that go in the school, in the classroom, library, laboratory, workshop, playground and in numerous informal contacts between teachers and pupils.” All types of experiences in the school or planned by the school should be included in the curriculum. • Principles of variety and elasticity - The Curriculum should be elastic and include varieties of subjects and activities to meet the needs of the various types of pupils. The curriculum should be adaptable to meet the needs and interests of the students. • Principles relating to community -The curriculum should be related to the community. There should be community - oriented programmes in the curriculum so that a child can feel that he is an integral part of the local community. The curriculum should bring the child and the community closer. • Principle of training for leisure -The Curriculum should be designed to train the students not only for work but also for leisure. For this purpose there should be a number of activities - social, aesthetic, sporting etc. which should be included in the curriculum. These activities will train the students to use their leisure time properly. • Principle of integration and correlation -The curriculum should not be merely a bundle of subjects and activities. The activities and subjects should be integrated and well - correlated. The curriculum should provide a ‘broad field’ units having direct bearing on life. Curriculum of Different Stages of Secondary Schools 1) Curriculum for Middle Schools 2) Curriculum for High and Higher Secondary Schools. The Commission has laid down the following different curriculum for these two stages in the secondary education. 1) Curriculum for the Middle Schools - The Commission has recommended the inclusion of the following subjects. a) English. b) Social Studies. c) General Science. d) Mathematics. e) Art and Music. f) Craft. g) Physical Education. 2) The Curriculum for High and Higher Secondary Schools- For this stage of education, the commission has suggested that there should be a diversified course. (a) Compulsory subjects or main subjects; and (b) Optional subjects. A) Compulsory Subjects : The Compulsory subjects shall include the following : 1. Mother tongue or regional language or composite course of the mother tongue and a classical language. 2. One other language to be chosen from among the following: i) Hindi for those whose mother tongue is not Hindi. ii) Elementary English (for those who have not studied English in the middle stage). iii) Advanced English (for those who have studied English at the earlier stage). iv) A Modern Indian Language (other than Hindi). v) A modern foreign language (other than English). vi) A classical language. 3. Social studies - General course (for the first two years only). 4. General science, Including Mathematics - General course (for the first two years only). 5. One Craft to be chosen out of the list given below : i) Spinning and weaving ii) Wood Work iii) Metal Work iv) Gardening v) Tailoring vi) Typography vii) Workshop Practice viii) Sewing, Needle Work and Embroidery ix) Modeling B) Optional Subjects : Three subjects from one of the following groups - Group - 1 (Humanities) : (a) A classical language or a third language from A (2) not already taken; (b) History; (c) Geography; (d) Elements of Economics and Civics; (e) Elements of Psychology and Logic; (f) Mathematics; (g) Music; (h) Domestic Science. Group -2 (Sciences) : (a) Physics; (b) Chemistry; (c) Biology; (d) Geography; (e) Mathematics; (f) Elements of Physiology and Hygiene; (not to be taken with Biology). Group -3 (Technical) : (a) Applied Mathematics and Geometrical Engineering; (b) Applied Science; (c) Elements of Mechanical Engineering; (d) Elements of Electrical Engineering. Group - 4 (Commercial) : (a) Commercial Practice; (b) Book-Keeping; (c) Commercial Geography or Elements of Economics and Civics; (d) Shorthand and Typewriting. Group - 5 (Agriculture) : (a) General Agriculture; (b) Animal Husbandry; (c) Horticulture and Gardening; (d) Agricultural Chemistry and Botany Group - 6 (Fine Arts) : (a) History of Art; (b) Drawing and Designing; (c) Painting; (d) Modelling; (e) Music; (f) Dancing. Group - 7 (Home Science) : (a) Home Economics; (b) Nutrition and Cookery; (c) Mother Craft and Child Care; (d) Household Management and Home Nursing. Besides the above, a student may take as his option one additional subject from any of the above groups irrespective of whether or not he has chosen his other options from that particular group. CHECK YOUR PROGRESS 4. Mention any four defects of the existing curriculum. ............................................................................................................... ............................................................................................................... 5. What are the recommendations of secondary Education Commission on the principles of curriculum construction? ............................................................................................................... ...............................................................................................................

Challenges for Secondary Education in India

Education is a Fundamental Right of every citizen of our country. But unfortunately, despite several commissions appointed to improve the state of education in our country since independence, not much headway has been made towards making it relevant to the needs of the time. Parrot learning and reproducing half-baked ideas in the examination halls has been the yardstick of assessing the quality of school goers in all levels whether it is Primary, Secondary or College Education. One of the greatest task before the nation is to expand and extend the outreach of good education to its younger generations, first at the elementary level and then more important emphasis to secondary education. The Constitution of India eloquently highlights the critical significance of these two levels of education. There is an urge to build a society that contribute progress and welfare and at the same time ensure that the next generation inherit a world which would make them proceed ahead further towards better conditions and situations. Education systems are encountering changes everywhere. The issues related to the educational changes have been analysed globally. These need to be understood and analysed. Educationist and educators all over the world come across certain board features which include (i) fast changing technologies and ever increasing impact of information and communication technology (ii) emerging emphasis on self-learning, self directed learning, self motivated learning and as also of co-operative learning (iii) issues related to infrastructures in schools and institution (iv) issues of professional development and growth. These issues related to the educational changes have been analysed globally and the Delors' Commission report, 'Learning The Treasure Within' presents a very comprehensive view of the emerging shapes of education globally. Several significant parameters identified in the report appear irrevocably relevant as these emphasis the indigenous aspects of education and strongly recommend that education must be rooted to culture and committed to progress. The quality and character of the people greatly depend on the education imparted to them at different levels. Mahatma Gandhi had perceived the essence of education as an integral part of life closely related to the requirements of a healthy and productive national life. He felt that an educational system must provide for a proper atmosphere to make the child of fully aware of the responsibility to his family, community and country. Gandhi says: 'By Education, I mean an all round drawing out of the best in child and man Body, Mind and Spirit.' In fast changing world, education needs to respond to the change. In fact education needs to respond everything that is happening in environment external to the process of teaching and learning and the system that is responsible for it. With the unprecedented advent of information and communication technology a global perspective has to be developed and one has to perforce respond to the implication of globalization. To meet the challenge, the new pattern of education, or the New Education Policy of 1986 recommended at the national level, envisages ten years of general education two years of senior secondary and three years degree course. In the first stage of schooling taking ten years, a student is expected to acquire the prescribed minimum proficiency in languages and mathematics. During these days also they are made aware of our cultural heritage and contemporary social, geographical political, economical issues. After this they join the plus two stage before joining college or universities. These systems appears good in appearance. But the system still not been able to make education socially relevant in our society. Education even at this stage really is confined into the four walls of classrooms where the teachers lecture on his specified subject and the students not actively listen to the lectures. The profession of teaching has just been reduced to passing on some information to the students so that the later in turn reproduce it at the time of examination. This fails to involve the students in the learning process and their critical faculties remain untouched. These course of study, patterns of education only brings uncertain future staring in the face of aspiring students. This uncertainty about their future provide potential fodder for the phenomenon known as 'students unrest'. This is the real challenge that lies ahead for secondary education in India. Coming to the context of secondary education in Manipur, the academic atmosphere in the school is haunted by uncertainties. Bandhs and general strikes are called at every moment at every drop of hat. The syllabi, moreover have not undergone any change over the years except some superficial ones. Nearly 95 percent of the grants made to our educational institutions are spent in paying salaries to the teachers and other supporting staff leaving little room for provision of infrastructures like classrooms, laboratories, playgrounds and other facilities to the students. About vocational education, vocationalisation of education. It is not made truly vocational in keeping with the needs of the time. Vocational streams were opened in some higher secondary schools but this is discontinued from this academic session as the Govt fails to provide materials, teachers and feeder colleges after secondary level. So in the end, responding to global and local socio-economic changes, decision makers need to know clearly what the changes and challenges are, why are these going to happen and how will it be tackled. Then the changes and challenges can be approach with confidence and enthusiasm. ________________________________________

PAPER: TEACHING OF MATHEMATICS

Al-Falah School of Education & Training B.Ed. Examination April, 2012 Teaching of Mathematics Paper: VI & VII Gr-B(i) Time: Three Hours Maximum Marks: 100 Note: Attempt any five questions in all, selecting one question from each unit. Question 1 is compulsory. Q.1 Write short notes on any four of the following: 4X5 (i) Diagnostic Testing (ii) Remedial Teaching (iii) Supervised Study (iv) Mathematics Fair Unit-I Q.2 What types of difficulties are faced by the teacher in teaching mathematics? How will you overcome them? Discuss. 20 Q.3. Write notes on: 10,10 (i) Values to be taught through teaching of mathematics (ii) Historical Development of mathematics Unit-II Q.4. What is an Inductive-Deductive method of teaching of mathematics? Explain it with examples. 20 Q.5 Writes notes on: 10,10 (i) Oral Work (ii) Self Study Unit-III Q.6 Writes notes on: 10,10 (i) Application of I.C.T in teaching of Mathematics (ii) Importance and Organization of Mathematics Club Q.7 Prepare a lesson plan on any topic in mathematics for X class. 20 Unit-IV Q.8 Analyze one of the following units in term of Pedagogical analysis: 10,10 (i) Volume (ii) Central Tendencies Mean, Median, Mode Q.9 Writes notes on: 10,10 (i) Criterion and Norm Reference Test (ii) Continuous & Comprehensive Evaluation

PAPER : SECONDARY EDUCATION IN INDIA

Al-Falah School of Education & Training B.Ed. Examination April, 2012 SECONDARY EDUCATIONAL IN INDIA Paper: V Time: One & Half Hours Maximum Marks: 50 Note: Attempt any three questions in all, selecting one question from each unit. Question 1 is compulsory. Q.1 Write short notes on the following: 2X5 (i) Important provision of article 29, 30 & 45 (ii) NAAC (iii) Three Language Formula (iv) Need of in-service teacher education Unit-I Q.2 What is Quality of education? Discuss the different parameters of quality education. 20 Q.3. Write notes on: 10,10 (i) National Curriculum Framework 2005 (ii) Problems and Issues in Secondary Education Unit-II Q.4. Writes notes on: 10,10 (i) What is teacher education? Explain its objectives at secondary level (ii) Role of SCERT and DIETs Q.5 Why today we need to reform our examination system? What is the implication of continuous and comprehensive evaluation?

ICET HOME PAPER APRIL 2012 EXAM

Al-Falah School of Education & Training B.Ed. Examination April, 2012 INFORMATION COMMUNICATION & EDUCATIONAL TECHNOLOGY Paper: V Time: Three hours Maximum Marks: 100 Note: Attempt any five questions in all, selecting one question from each unit. Question 1 is compulsory. Q.1 Write short notes on the following: 4X5 (i) Meaning and Importance of Educational Statistics (ii) Uses and Application of Computer (iii) Co-operative Learning (iv) Net Working Unit-I Q.2 Define Information Communication technology. How do ICT help teachers to make effective teaching learning process? 20 Q.3. Write notes on: 10,10 (i) Multimedia, meaning, importance and use in education (ii) Models and Barriers of communication Unit-II Q.4. Writes notes on: 10,10 (i) Meaning and scope of Educational Technology (ii) Thinking skills Q.5 Writes notes on: 10,10 (i) Flanders Interaction Analysis (ii) Programmed Learning Unit-III Q.6 Writes notes on: 10,10 (i) System approach (ii) Personalized Instructional System Q.7 Writes notes on: 10,10 (i) Inquiry Training Model (ii) Mastery Learning Model Unit-IV Q.8 What is Action Research? Discuss the significance of Action Research in teacher education. 10,10 (i) Volume (ii) Central Tendencies Mean, Median, Mode Q.9 Mention the different types of graphical representation of data. Draw a histogram from the following frequency distribution of the score of 60 students. 20 CI 40-44 35-39 30-34 25-29 20-24 15-19 10-14 5-9 0-4 f 2 5 8 9 12 10 7 4 3