Man made resources & informal learning contexts
- 3. Mathematics is an indispensible part of education. Students are taught many mathematical facts but they are rarely taught what the mathematics process is and how to employ it. The best way to learn the process is to practice it. For the effective practice there are some resources in teaching & learning mathematics. One of them is called man-made resources. They are items or substances that have value to human lives that do not occur in the natural world. That is, a man-made resource is made by human rather than occurring in the nature.
- 4. The man-made resources in mathematics for effective teaching – learning are Mathematics Laboratory. Mathematics Library Mathematics Club
- 5. MATHEMATICS LABORATORY The mathematics laboratory provides an opportunity for individualized instructions, introduction to the use of calculators and computers, etc. The laboratory approach embodies the concept of active learning, pupil’s involvement & participation and relevance. It is the demonstration of the concept of an activity oriented mathematics program.
- 6. Need and Significance It is difficult to understand mathematical concepts as they are abstract in nature. They can be learned through observation of the concrete situations, experiments and manipulation of concrete objects. Students can develop many mathematical concepts by doing laboratory works.
- 7. Importance of Mathematics Laboratory It helps in making clear and understanding abstract concepts. It saves teacher’s time by cutting short certain lengthy explanations. It helps in developing the habit of verification in the students. They accept mathematical truths only after confirming their validity practically. It enables the students to apply mathematical facts and principles in a actual life. It is a multi-sensory approach to learning. Habit of critical thinking and logical reasoning can be developed. Interest in learning mathematics can be developed. Scientific attitude can be developed among the students. Bookish knowledge of the students can be correlated practically with their daily life. Learners can be enabled to construct mathematical knowledge on their own.
- 8. Functions Make mathematics teaching and learning interesting and purposeful for the students. Provide activities that arouse the curiosity of the students and maintain their interest in learning. Enable students to develop proper skills in handling equipments and gadgets. Make students appreciate the practical applicability of mathematical principles and laws. Concretize the abstract mathematical concepts. Help the students develop powers of observation, analysis and drawing inferences. Help the child develop ability for keen observation. Develop in pupils a positive attitude towards problem solving.
- 9. Equipment for Mathematics Laboratory Mathematics laboratory serves not only as a laboratory but also as mathematics room and mathematics museum. Keeping in view the various purposes, it should have the following equipment. (i) Concrete materials: It should be` provided with concrete materials connected with simple arithmetical topics such as beads, sticks, pebbles, ball frames, number cards, seeds, balances, coins, weights, measuring tapes, didactic apparatus which is used in Montessori method, scissors, pins, cardboard, chart paper, graphs, nails, hammers, ropes etc.
- 10. It may also be provided with the following materials: • A number kit: It consists of a set of wooden blocks of different colors, labeling the digits from one to ten. Each block has the numeral and word representing the num eral. • Place value pockets: Is a box having three or four portions labeled as units, tens, hundreds, thousands etc • Fractional parts: Is a series that is divided into halves, thirds, fourths, fifths, etc. • Charts: Charts showing certain geometrical figures. 1
- 11. (ii) Pictures and photographs: • The pictures and photographs of various Mathematicians and their contributions (iii) Models: • Various mathematical models such as those of triangles, squares, solids etc • Various models illustrating Mathematical proofs or principles or statements. (iv) Blackboard and Geometrical Instruments: • The size of blackboard provided in the mathematics room should be larger than ordinary size. • Provision for coloured chalks should be made in the laboratory • A set of geometrical instruments like protractors, compass, rulers etc be kept in laboratory. • Stencils for drawing geometrical figures.
- 12. (V) Bulletin Boards or Display Boards (Vi) Equipments and Materials Concerning Other Subjects: • Equipments illustrating application of mathematics such as barometer, h ydrometer, pendulum etc. should be kept. (vii) Proportional Dividers, Slide Rules, Calculating Machines etc. (viii) Projective Aids: • Devices such as magic lantern, film-strip projector, epidiascope etc
- 13. (ix) Surveying instruments: • Angle mirror: Used for laying out right angles in the field. • Plane table and Alidate: Used for elementary mapping and surveying. • Hypsometer and clinometers: Used for measuring angles of elevation and depression. • Level: Used or finding differences in elevation. • Transit: An angle measurer and leveling instrument. (x) Collections: • Mathematical data from different sources such as data on graphs, budgets etc in the form of cutting, pictures, charts, models etc from various magazines, newspapers, books etc.
- 14. MATHEMATICS LIBRARY Mathematics library is one of the important sources of acquiring vast and varied mathematical knowledge and skills. It serves the purpose of inculcating good reading and study habits which help in promoting self-study and independent work among students.
- 15. Need and Importance A mathematics library provides immediate access to the necessary mathematics book. It facilitates timely use of the book and inculcate reference skills. It promotes efficiency in the organization of library services. It helps the mathematics teacher to get acquainted with the latest developments and ancient contributions of mathematics. It develops the healthy hobby of reading during leisure time. Habit of self study and self education can be developed. It helps to supplement the knowledge learnt in the classroom. Students can improve their general knowledge by reading general books, magazines, etc.
- 16. Functions A mathematical library provides extra information necessary for mathematics. A mathematics library helps in drill and practice. It provides opportunities for filling up the gaps and removing the doubts. It provides facilities for the gifted students to satisfy their curiosity and thirst for knowledge. It provides adequate materials and information necessary for completing the assignments and homework.
- 17. Organization In mathematics library, there should be a good collection of useful books in mathematics. It should be attractive and should provide an atmosphere conducive for reading. It should be decorated with charts, pictures, posters, etc. which tells about the great mathematicians and their contributions. The seating arrangements must be comfortable for the students. When selecting the books, the emphasis should not be merely on quantity, but also on quality.
- 18. Suggestion for Effective Use: The mathematics teacher should take up the responsibility for organizing the mathematics library and be in charge of such a library. It can be situated in a large classroom or in a separate section in the mathematics laboratory. Allot a separate period in the time table for library work especially in higher classes. The mathematics teacher should motivate the students to use the library time more productively. Definite rules should be set up as to when pupils can engage in the various activities and how they are to be checked out.
- 19. Materials for mathematics library The prescribed text-books of mathematics for the different classes. Books on teaching of mathematics meant for teacher such books should be of high standard. Books of recreational activities: Puzzle Mathematics by Gamow published by Macmillan & company. Amusement in mathematics by Dudney published by Nelson & company. Mathematics recreation by Ball & coxeter published by Macmillan & company Mathematical recreation by Maurice published by Dover publication, New York. Riddles in mathematics by Northop published by Nelson & company. Ganit Manoranjan by Kotharia & Om Prakash Published by NCERT.
- 20. Books on Biographies and History of Mathematics: History of Mathematics by Boyer published by John Wiley & Sons. Men of Mathematics by Bell published by Simon & Co., New York. Hindu Ganit ka ithas by Dutt and Singh published by Govt. of U.P., Lucknow. World of Mathematics by Newman published by Simon & Co., New york. Books showing Contribution of Mathematics to other Fields: Mathematical Advantages in Social Science by Davis published by American Mathematical Magazine. Mathematics in Human affairs by Ko Komer Published by prentice Hall. Mathematics for the millions by lance lot published by Norton & Co., New York. Mathematics Journals: The mathematics Teacher Journal, SITU Colony, Madras-28 The mathematics Education journal, P.O. siwan, Distt. Saran (Bihar). NCERT and SCERT Mathematics periodicals and magazines.
- 21. MATHEMATICS CLUB • The mathematics club plays an important role in motivating the students to learn mathematics with interest and involvement. • It provides excellent opportunities for students to break away from the monotony of a rigid and structured classroom environment. • In the mathematics club the students chooses the activities on his own, and pursues them in a free and relaxed manner. • It will create among the students an idea of the practical utility of mathematics in addition to creating their interest in mathematics.
- 22. Need and Importance It inculcates the habit of self-study and independent work among the students and supplements classroom teaching. It acquaints the students with the contribution of great mathematicians in their fields. It stimulates individual interest and initiative in the study of the subject matter. It enhances co-operation between the teacher and the taught. It helps in developing heuristic and problem solving attitude among the students. It provides the students with opportunities to develop their explorative, creative and inventive faculties. It helps to meet individual needs of the students as every member gets an opportunity to work in his areas of interest.
- 23. Functions Organizing recreational activities in mathematics such as games, quiz, puzzles, riddles, etc. Preparing mathematical aids and illustrations. Collecting data and reading mathematical literature and magazines. Organizing mathematical competitions, seminars and career talks related to mathematics Organizing programs that necessitate extra reading and study of mathematics. Arranging mathematical shows, exhibitions, etc. Organizing discussion about the practical applications of mathematics. Celebrating days and events pertaining to eminent mathematicians and history of mathematics.
- 24. Organization A properly organized mathematics club goes a long way in stimulating interest among the students in mathematics. It should be run by the students under the supervision and guidance of the mathematics teacher. To facilitate its smooth functioning, a draft constitution in consultation with the headmaster can be prepared by the mathematics teacher. This draft constitution should provide information about the name of the club, aims and objectives of the club, details regarding membership and the fees etc. Such a club should have the head of institution as its patron.
- 25. One of the senior mathematics teachers be asked to be the sponsor of the club. Membership of the club be open o all the Mathematics students of the school. Associate- membership may be allowed to some other students interested in mathematics. Only a nominal membership fee be charged from the members. The club may have an elected executive committee. Chairman Secretary Assistant secretary Treasurer One or two class representatives from each class. The executive committee should also include a librarian, a store keeper and a publicity officer .
- 26. Informal learning is, any learning that is not formal learning or a non-formal learning, such as self directed learning or learning from the experience. Informal learning is organized differently than formal and non-formal learning, because it has no set objective in terms of learning outcomes . Informal learning is like riding a bicycle, the rider chooses the destination and route. Some informal learning contexts are: Mathematics Exhibitions Mathematics Fairs Field trips
- 27. Mathematics Exhibition Mathematics exhibition is the one of the valuable activities to help mathematics learning. The school should organize mathematics exhibition periodically and the students should be encouraged to display the exhibits prepa red by them individually or in groups. The Mathematics club provides them facilities for making their exhibits. The exhibits displayed and demonstrated in the Mathematics exhibition should be self-explanatory. Each exhibits should be labeled properly and the captions written in bold and distinct letters.
- 28. Purpose To provide students with an opportunity to demonstrate independence and responsibility for their own learning. To provide students with an opportunity to explore multi perspectives. To provide an authentic process for assessing student understanding. To demonstrate how students can take action as a result of their learning. To celebrate the transition of learners primary to middle / secondary education.
- 29. Mathematics Fair Mathematics fair is a non competitive event that gives teachers an opportunity to have their students do problem solving with a particular go al in mind. The mathematics fair can be adapted to almost any curriculum and set of standards, and it will motivate and inspire all of the students. A math fair is to provide a meaningful problem solving experience for all students.
- 30. Educational Importance of Mathematics Fair To provide encouragement and recognition for the bright students who have special talent for mathematics. To popularize the mathematics activities of students among all so that further improvement in standards of performance may be attained. To provide a forum and impetus to mathematics club. To develop among students an inclination to know about developments in various field of mathematics.
- 31. Organization of mathematics fair Organizing Committee: Different committees are formed for performing different duties. List of entrants: A list of entrants is compiled before the date of mathematics fair. It includes name, class, teacher, title and category of projects of each entrant. Time schedule: Time is extremely important factors in planning mathematics fair. A schedule should be made by the committee so that events do not go haphazard.
- 32. Field Trips Field trips and excursions are interchangeably used in educational literature. But in straight sense they are different. An excursion is a school journey involving and organized level made by teachers and students primarily with an educational motive in mind. Field trips organized visits of students and teachers to immediate or distant places to enrich learning experiences and to further instructional purposes of regular classroom activities.
- 33. If learning is to result in the total development of the learners, we must go beyond our school walls into the community as students the chief purpose of field trips is to give students firsthand experience that cannot be had in the classroom. Students can hear, see and handle things and can examine then minutely. Hence field trip is an outdoor lesson in action. Field trips provide opportunities for learning through the use of many techniques other than reading and speaking. Field trips stimulate interest and increase appreciation.