The Purpose of the Mathematics LaboratoryNational Policy on Education (1986) states “Mathematics should be visualisedas a vehicle to train a child to think, analyse and articulate logically”. NationalCurriculum Framework - 2005 brought out by NCERT states that the main goalof Mathematics education is mathematisation of child’s thought process. Theseobjectives can only be achieved if there is an opportunity of creating a scope ofexploring, verifying and experimenting upon mathematical results by studentsthemselves. Thus, there is need of adopting activity — oriented process ratherthan merely concentrating upon mastery of rules and formulae so as to domathematical problems mechanically and pass out the examinations. There isneed to provide the learners the scope for interaction, communication andrepresentations of mathematical ideas by practising processes.No doubt a laboratory is a place where scientific research and experimentsare conducted for verification, exploration or discovery. Specifically, inmathematics the role of laboratory is helpful in understanding the mathematicalconcepts, formulae through activities. It is worth mentioning that pattern iscentral theme in mathematics which we need to develop practically to get insightinto the mathematical concepts/theorems/formulae. Mathematics laboratoryshould not be solely a store house of teaching aids but in turn emphasis has tobe laid on organising activities by students/teachers to rediscover the truthunderlying the mathematical concepts. However, there may be a few interestingreadymade geometrical and other models to motivate students. Moreover thesemodels should be manipulative and dynamic.A mathematics laboratory can foster mathematical awareness, skill building,positive attitude and learning by doing experiments in various topics ofmathematics such as Algebra, Geometry, Mensuration, Trigonometry, Calculus,Coordinate Geometry, etc. It is the place where students can learn certainconcepts using concrete objects and verify many mathematical facts andproperties using models, measurements and other activities. It will also providean opportunity to the students to do certain calculations using tables, calculators,etc., and also to listen or view certain audio-video cassettes relating to, remedialinstructions, enrichment materials, etc. Mathematics laboratory will also providean opportunity for the teacher to explain and demonstrate many mathematicalconcepts, facts and properties using concrete materials, models, charts, etc.24/04/18

The teacher may also encourage students to prepare similar models and chartsusing materials like thermocol, cardboard, etc. in the laboratory. The laboratorywill act as a forum for the teachers to discuss and deliberate on some importantmathematical issues and problems of the day. It may also act as a place forteachers and the students to perform a number of mathematical celebrationsand recreational activities.Mathematics laboratory is expected to offer the following opportunities tolearners: To discover the pattern for getting insight into the formulae To encourage interactions amongst students and teachers through debateand discussions. To encourage students in recognising, extending, formulating patterns andenabling them to pose problems in the form of conjectures. To facilitate students in comprehending basic nature of mathematics fromconcrete to abstract. To provide opportunities to students of different ability groups in developingtheir skills of explaining and logical reasoning. To help students in constructing knowledge by themselves. To exhibit relatedness of mathematics with day to day life problems.2To visualise algebraic and analytical results geometrically.To design practical demonstrations of mathematical results/formulae or theconcepts.To perform certain recreational activities in mathematics.To do certain projects under the proper guidance of the teacher.To explain visually some abstract concepts by using three dimensionalmodels.Laboratory Manual24/04/18

Role of Mathematics Laboratory in Teaching-LearningMathematics at Senior Secondary stage is a little more abstract as compared tothe subject at the secondary stage. The mathematics laboratory at this stage cancontribute in a big way to the learning of this subject.Some of the ways are: Here the student will get an opportunity to understand the abstract ideas/concepts through concrete objects and situations. The concepts of relations and functions can be easily understood by makingworking models and by making arrow diagrams using wires. Three dimensional concepts can only be conceived by three dimensionalmodels in the laboratory, where as it is very difficult to understand theseconcepts on a black board. The concept of function and its inverse function, becomes very clear bydrawing their graphs using mathematical instruments and using the conceptof image about the line y x, which can be done only in the laboratory. It provides greater scope for individual participation in the processes oflearning and becoming autonomous learner. In the laboratory a student is encouraged to think, discuss with others andwith the teacher. Thus, he can assimilate the concepts in a more effectivemanner. To the teacher also, mathematics laboratory enables to demonstrate andexplain the abstract mathematical ideas, in a better way by using concreteobjects, models etc.24/04/18

Management and Maintenance of LaboratoryThere is no second opinion that for effective teaching and learning ‘Learning bydoing’ is of great importance as the experiences gained remains permanentlyaffixed in the mind of the child. Exploring what mathematics is about and arrivingat truth provides for pleasure of doing, understanding, developing positiveattitude, and learning processes of mathematics and above all the great feelingof attachment with the teacher as facilitator. It is said ‘a bad teacher teaches thetruth but a good teacher teaches how to arrive at the truth.A principle or a concept learnt as a conclusion through activities under theguidance of the teacher stands above all other methods of learning and the theorybuilt upon it, can not be forgotten. On the contrary, a concept stated in theclassroom and verified later on in the laboratory doesn’t provide for any greatexperience nor make child’s curiosity to know any good nor provides for anysense of achievement.A laboratory is equipped with instruments, apparatus, equipments, modelsapart from facilities like water, electricity, etc. Non availability of a singlematerial or facility out of these may hinder the performance of any experimentactivity in the laboratory. Therefore, the laboratory must be well managed andwell maintained.A laboratory is managed and maintained by persons and the materialrequired. Therefore, management and maintenance of a laboratory may becategorised as the personal management and maintenance and the materialmanagement and maintenance.(A) PERSONAL MANAGEMENT AND MAINTENANCEThe persons who manage and maintain laboratories are generally calledlaboratory assistant and laboratory attendant. Collectively they are known aslaboratory staff. Teaching staff also helps in managing and maintenance ofthe laboratory whenever and wherever it is required.In personal management and maintenance following points are considered:01.CleanlinessA laboratory should always be neat and clean. When students performexperiment activities during the day, it certainly becomes dirty and24/04/18

things are scattered. So, it is the duty of the lab staff to clean thelaboratory when the day’s work is over and also place the things at theirproper places if these are lying scattered.2. Checking and arranging materials for the day’s workLab staff should know that what activities are going to be performed ona particular day. The material required for the day’s activities must bearranged one day before.The materials and instruments should be arranged on tables before theclass comes to perform an activity or the teacher brings the class for ademonstration.3. The facilities like water, electricity, etc. must be checked and madeavailable at the time of experiments.4. It is better if a list of materials and equipments is pasted on the wall ofthe laboratory.5. Many safety measures are required while working in laboratory. A listof such measures may be pasted on a wall of the laboratory.6. While selecting the laboratory staff, the school authority must see thatthe persons should have their education with mathematics background.7. A days training of 7 to 10 days may be arranged for the newly selectedlaboratory staff with the help of mathematics teachers of the school orsome resource persons outside the school.8. A first aid kit may be kept in the laboratory.(B) MANAGEMENT AND MAINTENANCE OF MATERIALSA laboratory requires a variety of materials to run it properly. The quantityof materials however depends upon the number of students in the school.To manage and maintain materials for a laboratory following points mustbe considered:1. A list of instruments, apparatus, activities and material may be preparedaccording to the experiments included in the syllabus of mathematics.2. A group of mathematics teachers may visit the agencies or shops tocheck the quality of the materials and compare the rates. This will helpto acquire the material of good quality at appropriate rates.5Mathematics24/04/18

3. The materials required for the laboratory must be checked from timeto time. If some materials or other consumable things are exhausted,orders may be placed for the same.4. The instruments, equipments and apparatus should also be checkedregularly by the laboratory staff. If any repair is required it should bedone immediately. If any part is to be replaced, it should be ordered andreplaced.5. All the instruments, equipments, apparatus, etc. must be stored in thealmirahs and cupboards in the laboratory or in a separate store room.6Laboratory Manual24/04/18

Equipment for Mathematics Laboratory at the Higher Secondary StageAs the students will be involved in a lot of model making activities under theguidance of the teacher, the smooth running of the mathematics laboratory willdepend upon the supply of oddments such as strings and threads, cellotape, whitecardboard, hardboard, needles and pins, drawing pins, sandpaper, pliers, screwdrivers, rubber bands of different colours, gummed papers and labels, squaredpapers, plywood, scissors, saw, paint, soldering, solder wire, steel wire, cottonwool, tin and plastic sheets, glazed papers, etc. Besides these, some models,charts, slides, etc., made up of a good durable material should also be there forthe teacher to demonstrate some mathematical concepts, facts and propertiesbefore the students. Different tables, ready reckner should also be there (in thelaminated form) so that these can be used by the students for different purposes.Further, for performing activities such as measuring, drawing and calculating,consulting reference books, etc., there should be equipments like mathematicalinstruments, calculators, computers, books, journals mathematical dictionariesetc., in the laboratory.In view of the above, following is the list of suggested instruments/modelsfor the laboratory:EQUIPMENTMathematical instrument set (Wooden Geometry Box for demonstrationcontaining rulers, set-squares, divider, protractor and compasses), somegeometry boxes, metre scales of 100 cm, 50 cm and 30 cm, measuring tape,diagonal scale, clinometer, calculators, computers including related softwareetc.MODELS FOR DEMONSTRATION OF–SetsRelations and FunctionsQuadratic functions with the help of linear functionsSequence and seriesPascal's triangleArithmetic Progression24/04/18

Conic SectionsIncreasing, decreasing functionsMaxima, minima, point of inflectionLagrange's minima, point of inflectionRolle's theoremDefinite Integral as limit of sumAngle in semicircle using vectorsConstruction of parabola when distance between directrix and focus is givenConstruction of ellipse when major and minor axes are givenOctantsShortest distance between two skew linesGeometrical interpretation of scalar and vector productEquation of a straight line passing through a fixed point and parallel to agiven vectorEquation to a planeAngle between two planesBisection of the angles between two planes by a third planeIntersection of three planesProjection of the line segmentSample spacesConditional ProbabilitySTATIONERYAND ODDMENTSRubber-bands of different colours, Marbles of different colours, a pack ofplaying cards, graph paper/ squared paper, dotted paper, drawing pins, erasers,pencils, sketch pens, cellotapes, threads of different colours, glazed papers,kite papers, tracing papers, adhesive, pins, scissors and cutters, hammers, saw,thermocol sheets, sand paper, nails and screws of different sizes, screw drivers,drill machine with bit set, and pliers.8Laboratory Manual24/04/18

Activities forClass XI24/04/18

Mathematics is one of the most important culturalcomponents of every modern society. Its influence anothercultural element has been so fundamental and wide-spreadas to warrant the statement that her “most modern” waysof life would hardly have been possilbly without mathematics.Appeal to such obvious examples as electronics radio,television, computing machines, and space travel, tosubstantiate this statement is unnecessary : the elementaryart of calculating is evidence enough. Imagine trying to getthrough three day without using numbers in some fashionor other!– R.L. Wilder24/04/18

Activity 1OBJECTIVEMATERIAL REQUIREDTo find the number of subsets of agiven set and verify that if a set has nnumber of elements, then the totalnumber of subsets is 2n.Paper, different coloured pencils.METHOD OF CONSTRUCTION1. Take the empty set (say) A0 which has no element.2. Take a set (say) A1 which has one element (say) a1.3. Take a set (say) A2 which has two elements (say

The Purpose of the Mathematics Laboratory National Policy on Education (1986) states “Mathematics should be visualised as a vehicle to train a child to think, analyse and articulate logically”. National Curriculum Framework - 2005 brought out by NCERT states that the main goal of Mathematics education is mathematisation of child’s thought process. These objectives can only be achieved if .