Guidelines for Mathematics Laboratory in Schools - Math, Class 9 Class 9 Notes | EduRev

Class 9 : Guidelines for Mathematics Laboratory in Schools - Math, Class 9 Class 9 Notes | EduRev

 Page 1


1
Guidelines for
Mathematics Laboratory in Schools
Class IX
Central Board of Secondary Education
Preet Vihar, Delhi – 110092.
Page 2


1
Guidelines for
Mathematics Laboratory in Schools
Class IX
Central Board of Secondary Education
Preet Vihar, Delhi – 110092.
2
1. Introduction
1.1 Rationale
Mathematics is erroneously regarded as a difficult subject to understand, meant only
for persons of ‘higher’ 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 Board’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 – 110092.
2
1. Introduction
1.1 Rationale
Mathematics is erroneously regarded as a difficult subject to understand, meant only
for persons of ‘higher’ 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 Board’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
‘Mathematics Laboratory in schools – towards joyful learning’ 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
No…………..dated………….., 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 No………dated………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 – 110092.
2
1. Introduction
1.1 Rationale
Mathematics is erroneously regarded as a difficult subject to understand, meant only
for persons of ‘higher’ 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 Board’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
‘Mathematics Laboratory in schools – towards joyful learning’ 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
No…………..dated………….., 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 No………dated………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 page……..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 page………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 Board’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 – 110092.
2
1. Introduction
1.1 Rationale
Mathematics is erroneously regarded as a difficult subject to understand, meant only
for persons of ‘higher’ 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 Board’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
‘Mathematics Laboratory in schools – towards joyful learning’ 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
No…………..dated………….., 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 No………dated………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 page……..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 page………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 Board’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 ……………. 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 mark
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