Page 1 1 Guidelines for Mathematics Laboratory in Schools Class IX Central Board of Secondary Education Preet Vihar, Delhi â€“ 110092. Page 2 1 Guidelines for Mathematics Laboratory in Schools Class IX Central Board of Secondary Education Preet Vihar, Delhi â€“ 110092. 2 1. Introduction 1.1 Rationale Mathematics is erroneously regarded as a difficult subject to understand, meant only for persons of â€˜higherâ€™ mental ability. It arouses fear among any students, which in turn creates resistance to learning at and results in an adverse effect on their attainment. But actually, school mathematics is within the reach of any average student. What is needed is to create the right ambience of learning mathematics in every school. Mathematics needs to be learnt with a sense of joy and delight. It needs to be related, where possible, to life-oriented activities, to create interest in the subject. Mathematical faculty and intuition develop not only through theory and problems given in mathematics textbooks but also through a variety of activities involving concrete objects. Activities can be engaging as well as instructive. With this in mind, CBSE has endeavoured to introduce the idea of mathematics laboratory in schools. Some of the ways in which activities in a mathematics laboratory could contribute to learning of the subject are: · It provides an opportunity to students to understand and internalise the basic mathematical concepts through concrete situations. It lays down a sound base for more abstract thinking. · The laboratory gives greater scope for individual participation. It encourages students to become autonomous learners and allows an individual student to learn at his or her own pace. · It helps build interest and confidence among the students in learning the subject. · It provides opportunity to students to repeat an activity several times. They can revisit and rethink a problem and its solution. This helps them develop metacognitive abilities. · It allows and encourages students to discuss, think and assimilate the concepts in a better manner through group learning. · It provides opportunity to students to understand and appreciate the applications of mathematics in their surroundings and real life situations. · It widens the experimental base and prepares the ground for better learning of new areas in the subject. · An activity involves both the mind and hands of the student working together, which facilitates cognition. 1.2 National Curriculum Framework and Boardâ€™s Initiatives. The National Curriculum Framework for school education (NCFSE) developed by NCERT emphasizes that mathematics learning should be facilitated through activities from the very beginning of school education. These activities may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. The Framework strongly recommends setting up of a mathematics Page 3 1 Guidelines for Mathematics Laboratory in Schools Class IX Central Board of Secondary Education Preet Vihar, Delhi â€“ 110092. 2 1. Introduction 1.1 Rationale Mathematics is erroneously regarded as a difficult subject to understand, meant only for persons of â€˜higherâ€™ mental ability. It arouses fear among any students, which in turn creates resistance to learning at and results in an adverse effect on their attainment. But actually, school mathematics is within the reach of any average student. What is needed is to create the right ambience of learning mathematics in every school. Mathematics needs to be learnt with a sense of joy and delight. It needs to be related, where possible, to life-oriented activities, to create interest in the subject. Mathematical faculty and intuition develop not only through theory and problems given in mathematics textbooks but also through a variety of activities involving concrete objects. Activities can be engaging as well as instructive. With this in mind, CBSE has endeavoured to introduce the idea of mathematics laboratory in schools. Some of the ways in which activities in a mathematics laboratory could contribute to learning of the subject are: · It provides an opportunity to students to understand and internalise the basic mathematical concepts through concrete situations. It lays down a sound base for more abstract thinking. · The laboratory gives greater scope for individual participation. It encourages students to become autonomous learners and allows an individual student to learn at his or her own pace. · It helps build interest and confidence among the students in learning the subject. · It provides opportunity to students to repeat an activity several times. They can revisit and rethink a problem and its solution. This helps them develop metacognitive abilities. · It allows and encourages students to discuss, think and assimilate the concepts in a better manner through group learning. · It provides opportunity to students to understand and appreciate the applications of mathematics in their surroundings and real life situations. · It widens the experimental base and prepares the ground for better learning of new areas in the subject. · An activity involves both the mind and hands of the student working together, which facilitates cognition. 1.2 National Curriculum Framework and Boardâ€™s Initiatives. The National Curriculum Framework for school education (NCFSE) developed by NCERT emphasizes that mathematics learning should be facilitated through activities from the very beginning of school education. These activities may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. The Framework strongly recommends setting up of a mathematics 3 laboratory in every school in order to help exploration of mathematical facts through activities and experimentation. With the objective of meeting these national requirements, aspirations and expectations, the Central Board of Secondary Education immediately issued directions to its affiliated schools to take necessary action in this regard. Simultaneously, a document on â€˜Mathematics Laboratory in schools â€“ towards joyful learningâ€™ was brought out by the Board and made available to all the schools. This document primarily aimed at sensitizing the schools and teachers to the philosophy of a mathematics laboratory, creating awareness among schools as to how mathematics laboratory will help in improving teaching and learning of the subject and providing general guidelines to school on setting up and using a mathematics laboratory. Besides, it also included a number of suggested hands-on activities related to concepts in mathematics for Class III to Class X. Teachers were advised to design more activities of similar nature to suit the requirements of the classes and students under their charge. There has been a very encouraging response to this initiative from the schools and a large number of them have already established reasonably functioning mathematics laboratories. However, the Board has been receiving queries and observations from many quarters with the request to provide more detailed guidelines to set up such a laboratory, particularly with regard to its size and design, physical infrastructure, materials required and human resources. In addition to including specific activities and project work for Class IX, the present document aims at clarifying these various matters. 1.3. About the present document The present document has three clear objectives. Firstly, it aims at providing detailed guidelines to schools with regard to the general layout, physical infrastructure, materials and human resources for a mathematics laboratory. This would, it is expected, clear doubts about the minimum requirements for setting up of such a laboratory. Secondly, it includes details of all Class IX syllabus related activities to be done by the students during the academic year. Thirdly, it gives a few specific examples of projects. This is intended to help the schools to have an idea of the nature of project work to be undertaken by the students. Since the schools have already been given directions in relation to setting up of a mathematics laboratory by 31 st March, 2005 through circular Noâ€¦â€¦â€¦â€¦..datedâ€¦â€¦â€¦â€¦.., it is expected that necessary initiatives have been taken and the desired facilities are available in schools. The schools are now expected to extend and expand these facilities to carry out Class IX syllabus activities from the academic session starting April 2005. Another circular Noâ€¦â€¦â€¦datedâ€¦â€¦â€¦has also been issued in relation to the introduction of 20% internal assessment scheme in the subject in Class IX from the ensuing academic session beginning April 2005. The said circular clarifies that the internal assessment is to be given on the basis of performance of an individual in the practical work. The details of assessment in practical work are given in the later sections of this document. Page 4 1 Guidelines for Mathematics Laboratory in Schools Class IX Central Board of Secondary Education Preet Vihar, Delhi â€“ 110092. 2 1. Introduction 1.1 Rationale Mathematics is erroneously regarded as a difficult subject to understand, meant only for persons of â€˜higherâ€™ mental ability. It arouses fear among any students, which in turn creates resistance to learning at and results in an adverse effect on their attainment. But actually, school mathematics is within the reach of any average student. What is needed is to create the right ambience of learning mathematics in every school. Mathematics needs to be learnt with a sense of joy and delight. It needs to be related, where possible, to life-oriented activities, to create interest in the subject. Mathematical faculty and intuition develop not only through theory and problems given in mathematics textbooks but also through a variety of activities involving concrete objects. Activities can be engaging as well as instructive. With this in mind, CBSE has endeavoured to introduce the idea of mathematics laboratory in schools. Some of the ways in which activities in a mathematics laboratory could contribute to learning of the subject are: · It provides an opportunity to students to understand and internalise the basic mathematical concepts through concrete situations. It lays down a sound base for more abstract thinking. · The laboratory gives greater scope for individual participation. It encourages students to become autonomous learners and allows an individual student to learn at his or her own pace. · It helps build interest and confidence among the students in learning the subject. · It provides opportunity to students to repeat an activity several times. They can revisit and rethink a problem and its solution. This helps them develop metacognitive abilities. · It allows and encourages students to discuss, think and assimilate the concepts in a better manner through group learning. · It provides opportunity to students to understand and appreciate the applications of mathematics in their surroundings and real life situations. · It widens the experimental base and prepares the ground for better learning of new areas in the subject. · An activity involves both the mind and hands of the student working together, which facilitates cognition. 1.2 National Curriculum Framework and Boardâ€™s Initiatives. The National Curriculum Framework for school education (NCFSE) developed by NCERT emphasizes that mathematics learning should be facilitated through activities from the very beginning of school education. These activities may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. The Framework strongly recommends setting up of a mathematics 3 laboratory in every school in order to help exploration of mathematical facts through activities and experimentation. With the objective of meeting these national requirements, aspirations and expectations, the Central Board of Secondary Education immediately issued directions to its affiliated schools to take necessary action in this regard. Simultaneously, a document on â€˜Mathematics Laboratory in schools â€“ towards joyful learningâ€™ was brought out by the Board and made available to all the schools. This document primarily aimed at sensitizing the schools and teachers to the philosophy of a mathematics laboratory, creating awareness among schools as to how mathematics laboratory will help in improving teaching and learning of the subject and providing general guidelines to school on setting up and using a mathematics laboratory. Besides, it also included a number of suggested hands-on activities related to concepts in mathematics for Class III to Class X. Teachers were advised to design more activities of similar nature to suit the requirements of the classes and students under their charge. There has been a very encouraging response to this initiative from the schools and a large number of them have already established reasonably functioning mathematics laboratories. However, the Board has been receiving queries and observations from many quarters with the request to provide more detailed guidelines to set up such a laboratory, particularly with regard to its size and design, physical infrastructure, materials required and human resources. In addition to including specific activities and project work for Class IX, the present document aims at clarifying these various matters. 1.3. About the present document The present document has three clear objectives. Firstly, it aims at providing detailed guidelines to schools with regard to the general layout, physical infrastructure, materials and human resources for a mathematics laboratory. This would, it is expected, clear doubts about the minimum requirements for setting up of such a laboratory. Secondly, it includes details of all Class IX syllabus related activities to be done by the students during the academic year. Thirdly, it gives a few specific examples of projects. This is intended to help the schools to have an idea of the nature of project work to be undertaken by the students. Since the schools have already been given directions in relation to setting up of a mathematics laboratory by 31 st March, 2005 through circular Noâ€¦â€¦â€¦â€¦..datedâ€¦â€¦â€¦â€¦.., it is expected that necessary initiatives have been taken and the desired facilities are available in schools. The schools are now expected to extend and expand these facilities to carry out Class IX syllabus activities from the academic session starting April 2005. Another circular Noâ€¦â€¦â€¦datedâ€¦â€¦â€¦has also been issued in relation to the introduction of 20% internal assessment scheme in the subject in Class IX from the ensuing academic session beginning April 2005. The said circular clarifies that the internal assessment is to be given on the basis of performance of an individual in the practical work. The details of assessment in practical work are given in the later sections of this document. 4 2. Mathematics Laboratory 2.1 What is a Mathematics Laboratory ? Mathematics laboratory is a room wherein we find collection of different kinds of materials and teaching/learning aids, needed to help the students understand the concepts through relevant, meaningful and concrete activities. These activities may be carried out by the teacher or the students to explore the world of mathematics, to learn, to discover and to develop an interest in the subject. 2.2 Design and general layout. A suggested design and general layout of laboratory which can accommodate about 30 students at a time is given on pageâ€¦â€¦..The design is only a suggestion. The schools may change the design and general layout to suit their own requirements. 2.3 Physical Infrastructure and Materials It is envisaged that every school will have a Mathematics Laboratory with a general design and layout as indicated on pageâ€¦â€¦â€¦with suitable change, if desired, to meet its own requirements. The minimum materials required to be kept in the laboratory may include all essential equipment, raw materials and other essential things to carry out the activities included in the document effectively. The quantity of different materials may vary from one school to another depending upon the size of the group. Some of the essential materials required are given on page 11. 2.4 Human Resources It is desirable that a person with minimum qualification of graduation (with mathematics as one of the subjects) and professional qualification of Bachelor in Education be made incharge of the Mathematics Laboratory. He/she is expected to have special skills and interest to carry out practical work in the subject. It will be an additional advantage if the incharge possesses related experience in the profession. The concerned mathematics teacher will accompany the class to the laboratory and the two will jointly conduct the desired activities. A laboratory attendant or laboratory assistant with suitable qualification and desired knowledge in the subject can be an added advantage. 2.5 Time Allocation for activities. It is desirable that about 15% - 20% of the total available time for mathematics be devoted to activities. Proper allocation of periods for laboratory activities may be made in the time table. Scheme of Evaluation As an extension of the Boardâ€™s intention to make learning of mathematics a more meaningful exercise, it has been decided to introduce the scheme of internal assessment in the subject. The objective is not merely to evaluate the learner in a public examination and award marks but to promote and encourage continuous Page 5 1 Guidelines for Mathematics Laboratory in Schools Class IX Central Board of Secondary Education Preet Vihar, Delhi â€“ 110092. 2 1. Introduction 1.1 Rationale Mathematics is erroneously regarded as a difficult subject to understand, meant only for persons of â€˜higherâ€™ mental ability. It arouses fear among any students, which in turn creates resistance to learning at and results in an adverse effect on their attainment. But actually, school mathematics is within the reach of any average student. What is needed is to create the right ambience of learning mathematics in every school. Mathematics needs to be learnt with a sense of joy and delight. It needs to be related, where possible, to life-oriented activities, to create interest in the subject. Mathematical faculty and intuition develop not only through theory and problems given in mathematics textbooks but also through a variety of activities involving concrete objects. Activities can be engaging as well as instructive. With this in mind, CBSE has endeavoured to introduce the idea of mathematics laboratory in schools. Some of the ways in which activities in a mathematics laboratory could contribute to learning of the subject are: · It provides an opportunity to students to understand and internalise the basic mathematical concepts through concrete situations. It lays down a sound base for more abstract thinking. · The laboratory gives greater scope for individual participation. It encourages students to become autonomous learners and allows an individual student to learn at his or her own pace. · It helps build interest and confidence among the students in learning the subject. · It provides opportunity to students to repeat an activity several times. They can revisit and rethink a problem and its solution. This helps them develop metacognitive abilities. · It allows and encourages students to discuss, think and assimilate the concepts in a better manner through group learning. · It provides opportunity to students to understand and appreciate the applications of mathematics in their surroundings and real life situations. · It widens the experimental base and prepares the ground for better learning of new areas in the subject. · An activity involves both the mind and hands of the student working together, which facilitates cognition. 1.2 National Curriculum Framework and Boardâ€™s Initiatives. The National Curriculum Framework for school education (NCFSE) developed by NCERT emphasizes that mathematics learning should be facilitated through activities from the very beginning of school education. These activities may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. The Framework strongly recommends setting up of a mathematics 3 laboratory in every school in order to help exploration of mathematical facts through activities and experimentation. With the objective of meeting these national requirements, aspirations and expectations, the Central Board of Secondary Education immediately issued directions to its affiliated schools to take necessary action in this regard. Simultaneously, a document on â€˜Mathematics Laboratory in schools â€“ towards joyful learningâ€™ was brought out by the Board and made available to all the schools. This document primarily aimed at sensitizing the schools and teachers to the philosophy of a mathematics laboratory, creating awareness among schools as to how mathematics laboratory will help in improving teaching and learning of the subject and providing general guidelines to school on setting up and using a mathematics laboratory. Besides, it also included a number of suggested hands-on activities related to concepts in mathematics for Class III to Class X. Teachers were advised to design more activities of similar nature to suit the requirements of the classes and students under their charge. There has been a very encouraging response to this initiative from the schools and a large number of them have already established reasonably functioning mathematics laboratories. However, the Board has been receiving queries and observations from many quarters with the request to provide more detailed guidelines to set up such a laboratory, particularly with regard to its size and design, physical infrastructure, materials required and human resources. In addition to including specific activities and project work for Class IX, the present document aims at clarifying these various matters. 1.3. About the present document The present document has three clear objectives. Firstly, it aims at providing detailed guidelines to schools with regard to the general layout, physical infrastructure, materials and human resources for a mathematics laboratory. This would, it is expected, clear doubts about the minimum requirements for setting up of such a laboratory. Secondly, it includes details of all Class IX syllabus related activities to be done by the students during the academic year. Thirdly, it gives a few specific examples of projects. This is intended to help the schools to have an idea of the nature of project work to be undertaken by the students. Since the schools have already been given directions in relation to setting up of a mathematics laboratory by 31 st March, 2005 through circular Noâ€¦â€¦â€¦â€¦..datedâ€¦â€¦â€¦â€¦.., it is expected that necessary initiatives have been taken and the desired facilities are available in schools. The schools are now expected to extend and expand these facilities to carry out Class IX syllabus activities from the academic session starting April 2005. Another circular Noâ€¦â€¦â€¦datedâ€¦â€¦â€¦has also been issued in relation to the introduction of 20% internal assessment scheme in the subject in Class IX from the ensuing academic session beginning April 2005. The said circular clarifies that the internal assessment is to be given on the basis of performance of an individual in the practical work. The details of assessment in practical work are given in the later sections of this document. 4 2. Mathematics Laboratory 2.1 What is a Mathematics Laboratory ? Mathematics laboratory is a room wherein we find collection of different kinds of materials and teaching/learning aids, needed to help the students understand the concepts through relevant, meaningful and concrete activities. These activities may be carried out by the teacher or the students to explore the world of mathematics, to learn, to discover and to develop an interest in the subject. 2.2 Design and general layout. A suggested design and general layout of laboratory which can accommodate about 30 students at a time is given on pageâ€¦â€¦..The design is only a suggestion. The schools may change the design and general layout to suit their own requirements. 2.3 Physical Infrastructure and Materials It is envisaged that every school will have a Mathematics Laboratory with a general design and layout as indicated on pageâ€¦â€¦â€¦with suitable change, if desired, to meet its own requirements. The minimum materials required to be kept in the laboratory may include all essential equipment, raw materials and other essential things to carry out the activities included in the document effectively. The quantity of different materials may vary from one school to another depending upon the size of the group. Some of the essential materials required are given on page 11. 2.4 Human Resources It is desirable that a person with minimum qualification of graduation (with mathematics as one of the subjects) and professional qualification of Bachelor in Education be made incharge of the Mathematics Laboratory. He/she is expected to have special skills and interest to carry out practical work in the subject. It will be an additional advantage if the incharge possesses related experience in the profession. The concerned mathematics teacher will accompany the class to the laboratory and the two will jointly conduct the desired activities. A laboratory attendant or laboratory assistant with suitable qualification and desired knowledge in the subject can be an added advantage. 2.5 Time Allocation for activities. It is desirable that about 15% - 20% of the total available time for mathematics be devoted to activities. Proper allocation of periods for laboratory activities may be made in the time table. Scheme of Evaluation As an extension of the Boardâ€™s intention to make learning of mathematics a more meaningful exercise, it has been decided to introduce the scheme of internal assessment in the subject. The objective is not merely to evaluate the learner in a public examination and award marks but to promote and encourage continuous 5 self-actualised learning in the classroom and in the extended hours of schooling. This internal assessment will have a weightage of 20 marks as per the following break up : Year-end Evaluation of activities : 10 marks Evaluation of project work : 05 marks Continuous assessment : 05 marks The year-end assessment of practical skills will be done during an organized session of an hour and a half in small groups as per the admission â€¦â€¦â€¦â€¦â€¦. convenience of the schools with intimation to the Board. The break up of 10 marks could be as under : Complete statement of the objective of activity : 1 mark Design or approach to the activity : 2 marks Actual conduct of the activity : 3 marks Description /explanation of the procedure followed : 2 marks Result and conclusion : 2 marks Out of all the activities given in the document, every student may be asked to complete a minimum of 15 marked activities during the academic year and be examined in one of these activities. He/she should be asked to maintain a proper activity record for this work done during the year. The schools would keep a record of the conduct of this examination for verification by the Board, whenever necessary, for a period of six months. This assessment will be internal and done preferably by a team of two teachers. Evaluation of project work Every student will be asked to do one project based on the concepts learnt in the classroom but as an extension of learning to real life situations. This project work should not be repetition or extension of laboratory activities but should infuse new elements and could be open ended and carried out beyond the school working hours. Five marks weightage could be further split up as under : Identification and statement of the project: 01 mark Design of the project 01 mark Procedure /processes adopted 02 marks Interpretation of results 01 markRead More

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