MODULAR METHOD OF TEACHING

Modular method of teaching

     INTRODUCTION

         Modular teaching is one of the most widespread and recognizes teaching learning techniques in United States, Australia and many other Western countries including Asian region. Modular is used in almost all subjects like natural science, especially in biology and medical education and even in social sciences as well as in computers education. All kinds of subjects are being taught through modules. It is a recent development based on programmed learning; a well established and universally recognized phenomenon. It considering the individual differences among the learners which necessitate the planning for adoption of the most appropriate teaching techniques in order to help the individual grow and develop at her/his own pace.

     Definition:-

Module is a unit of work in a course of instruction that is virtually self-contained and a method of teaching that is based on the building up skills and knowledge in discrete units.

     CHARACTERISTICS OF MODULE:-

·         It should be independent.

·         Self-contained.

·         Self instructional.

·         Well defined.

·         Clearly defined objectives.

·         Concern individual differences.

·         Association, structure sequence of knowledge.

·         Systematically organized learning opportunities.

·         Utilization of a variety of media.

·         Active participation by learner.

·         Immediate reinforcement of responses.

·         Mastery of evaluation strategy.

·         Evaluation of the work.

CHARECTERISTICS OF MODULE

·         It should be independent.

·         Self-contained.

·         Self instructional

·         Well defined.

·         Clearly defined objectives

·         Concern individual differences

·         Association, structure sequence of knowledge

·         Systematically organized learning opportunities.

·         Utilization of a variety of media

·         Active participation by learner.

·         Immediate reinforcement of responses

·         Mastery of evaluation strategy

·         Evaluation of the work.

ESSENTIAL COMPONENTS

·         Rationale: An overview of the content of module and explanation of why the learner should study it.

·         Objectives: What is expected outcome of module? This is stated in behavioral/performance terms.

·         Entry Test: To determine if the learner has prerequisite skills needed to enter the module and check.

·         Multi Media Materials: A wide variety of media is used so learners can involve actively and utilize their senses.

·         Learning Activities: Presentation, demonstration, drill, simulation, discovery problem solving etc. may be useful. A wide variety of learning activities increase student interest and cater student needs.

·         Self-Test: This provides a chance to review and check ones own progress.

·         Post Test: To check whether the objectives attained.

      STRUCTURE OF MODULE

·         The title

·         The Introduction.

·         The overview.

·         The instruction to the users.

·         The pre-test evaluation and feedback.

·         The objectives

·         The learning activities.

·         The formative test, evaluation and feedback

·         The summative evaluation and feedback.

    PRINCIPLES UNDERLINE IN PLANNING LEARNING ACTIVITIES

·         Plan learning activities on the basis of entry behavior of the learners.

·         Base learning activities on the terminal behavior 

·         Base learning activities on the needs of learner.

·         Make careful gradation

·         Provide adequate for individual differences.

·         Provide adequate with his progress.

ADVANTAGES

·         Learning became more effective.

·         It establish a system of assessment other than marks or grade

·         Users study the modules in their own working environment.

·         Users can study without disturbing the normal duties and responsibilities

·         Modules can be administered to single use, small group or large group.

·         Modules are flexible so that implementation can be made by a variety of patterns.

·         It is more appropriate to mature students

·         It enables the learner to have a control over his learning and

·         Accept greater responsibility for learning.

·         It already got wider accessibility in the present educational scenario.

DISADVANTAGES

·         Modules are economical in their use.

·         Appropriate only for matured students.

·         This methods demands smart classrooms.

CONCLUSION:-

When we analyzing the modular method of teaching, we can understand that this is more effective, recent and more technology based teaching method in the present educational field. In recent years, the consent of modular curriculum has been under discussion in secondary schools. Modular approach provides more flexibility to distance teaching mode as well to learners.

SIMULAION

SIMULATION

MEANING:

Simulations are a useful teaching strategy for illustrating a complex and changing situation. The Oxford Advanced learners Dictionary explains, “ It is a situation in which a particular set of conditions is created artificially in order to study or experience something that could exist in reality”.

            In a simulation, the learner acts, the simulation reacts, the learner learns from this feedback. Simulation may be defined as a role playing in which the process of teaching is enacted artificially and an effort is made to practise some important skill of communication through this. Under this, the student-teacher and students simulate a particular role and try to develop an identity with the actual classroom environment.

DEFINITION:

R. Wynn(1964): “Simulation is an accurate representation of realistic situation.”

D.R. Cruickshank(1966): “Simulation is the creation of realistic games to be played by participants in order to provide them with life-like problem-solving experiences related to their present or future work.”

W.R. Fritz(1965): “Simulation may be considered as dynamic implementation of a model representing a physical or a mathematical system.”

SIMULATION IN EDUCATION:

            As a teaching technique, it is generally used in management education and training in which a real life situation and values are simulated by substitutes displaying similar characteristics. In teacher education student acts or role play some situation in order to make theory more practically oriented and realistic.

            Examples:        (i) Soldiers engage in mock fighting.

(ii) To perform operations on human beings, doctors are made to learn the operation techniques by experimenting on frogs and rats etc.

SIMULATON IN TEACHER TRAINING:

            Student-teachers are trained in an artificial situation in order to handle the real situation in classroom in a systematic way. Student-teachers are not directly allowed to use school children for practising their teaching skills and modify their teaching behaviours. They are first provided with an artificial situation just like a classroom to achieve the necessary teaching experiences, in which the other teacher trainees or student teachers acts as students. In Simulated teaching, student-teacher plays three important roles: teacher, student and observer. The teacher educator acts as a facilitator for this learning process. The student-teacher and the teacher educator observe the lesson and note down all the good and weak points about the classroom interaction- teaching behaviours, content taught, skills practised and methodology used, etc. After the lesson is over, one free discussion is organised for getting feed back by which the future classroom interaction can be improve.

STEPS IN SIMULATED TEACHING:

            The following steps are usually followed in Simulated Teaching:

                                i.            Orientation of the student-teachers with the concept of simulation, its use in teacher training, steps to be followed in simulated teaching, role of student-teachers as students, teachers and observers and the setting for adopting simulated teaching.

                              ii.            Selection of the specific teaching skills to be practised.

                            iii.            Demonstration lesson by teacher educator.

                            iv.            Formation of groups of student-teachers.

                              v.            Assignment of roles- teacher, student and observer to student-teachers.

                            vi.            Determining the procedure and technique of observation of the classroom interaction.

                          vii.            Delivering the lesson by student-teacher.

                        viii.            Follow up and further modification in the teaching technique.

WHY SIMULATION:

            N.A.Fattu(1966)  gave the following reasons for use of simulation:

                                i.            When an environment cannot be duplicated exactly, then it may be made as realistic as possible.

                              ii.            When a process is to be examined systematically, it may yield information through developing and operating a situation.

                            iii.            When a difficult problem is confronted beyond a teacher’s ability, simulation may help him synthesize and infer a good solution.

                            iv.            The amount of time accomplished is controllable by the simulator.

                              v.            Simulation may also indicate which variables in a complex operation or system are important and how they are related to each other.

                            vi.            Cost may be reduced by simulating rather than by alternative forms of experimenting.

VALUE/ADVANTAGES OF SIMULATION:

Simulation

                                                        i.            Helps to build confidence in the student-teacher.

                                                      ii.            Bridges the gap between the theory and practice.

                                                    iii.            Enables the learner to learn directly from experience.

                                                    iv.            Promotes a high level of critical thinking.

                                                      v.            Simulation game develops in the student-teachers and students an understanding of the decision-making process.

                                                    vi.            Through role playing enables the pupils to empathize with the real life situation.

                                                  vii.            Provides feedback to the learners on the consequences of actions and decisions made.

                                                viii.            Motivates the learners by making real life situations exciting and interesting.

                                                    ix.            Post-simulation analysis enables both the teachers and students to assess the realism of the situation by uncovering misconception.

LIMITATIONS OF SIMULATION:

                                i.            The beginner participants may face some difficulties in clarifying their doubt by asking questions.

                              ii.            During simulation the observer may record incorrectly.

                            iii.            The most common error in serious skill training is the misconception that adults can play the role of pupils.

                            iv.            Simulation attempts to portray real situations in a simple way and which is very difficult.

                              v.            There is a tendency to use the results of a single simulation as the sole basis of generalization.

                            vi.            Commercially developed simulation games are expensive.

ROLE OF THE TEACHER:

                                i.            He plays a relatively non-directive role. Acts as a facilitator.

                              ii.            Keenly observes the teaching of student-teachers.

                            iii.            He guides the students to achieve pre-determined teaching skills.

PRACTICALITIES:

Phase One:  Orientation

-       Explain to your students what simulations are about and for.  (If you mention some common games they play which are simulations, they might start thinking about what real life complex situations the games model, and might learn something about them.)

-       Describe the particular simulation.

-       Ensure the students understand the purpose of the simulation.

-       Outline the rules for the students.

-       Assign roles to the students.

Phase Two:  The Simulation

-       The students participate in the game, playing their roles as assigned.  You, are the coach and referee.  You should stay uninvolved, except when you notice that you can facilitate the educational opportunities the simulation presents.

-       While your students are playing, you could make anecdotal records, or fill in checklists.

Phase Three:  Debrief

For every teaching strategy involving a debrief. There are a number of ways in which debriefs can be done.  Please mix and match the different forms of debriefs you use.

-       Put the students into small groups.

-       Choose three or four learning objectives for the simulation.  Write up these learning objectives as questions for discussion.  One question should be about how the students think the simulation is like the real thing and how it is not like the real thing.  Give each small group of students one question to discuss.

-       Tell the students how much time they have to discuss the questions.

-       Five minutes before the time is up, visit each group with a card which has written on it:  Five minutes until presentation.  “Choose a speaker and write a summary of your discussion for the speaker to present to the class.”

-       An alternative to the above method would be to put groups who have discussed different question together to discuss their different questions and answers.  This way, each group has an opportunity to discuss at least two of the questions.

-       If you use this second method, you could have students write answers to the questions in a learning log instead of having them present to the class.

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