MATHEMATICS LABORATORY IN SCHOOLS

MATHEMATICS LABORATORY IN SCHOOLScreativity, scientific development of the brain of the
It is a place where:children, and satisfies their zeal to do something new
1)      Students do experiments with numbersand unique.
and geometrical shapes and try to generalize theseRaw Materials:
patterns.To enable the students to work in a mathematics
2)    Students do most of their calculations withlaboratory, there should be a few cupboards to store
the help of scientific calculators.raw materials, which can be issued to the students
3)    Students draw graphs of large number ofwhen they come to the lab for doing practical work.
functions with the help of scientific or graphicThe list of some of the essential raw materials is as
calculators and try to become familiar with graphs ofunder:
all the functions they usually deal with.I)                 Circular discs: Plates of
4)    Students solve real life problems with realdifferent diameters may be cut on thermo Cole
data because complex calculations are no longer asheets or may be plastic metal discs purchased from
major consideration.the market to determine the value of ? or such
5)    Students express their answers toother experiments.
mathematics problems in decimal numbers and not inII)            There should be square
symbols and have a good idea about theirrectangular plates cut from thermo Cole sheets,
magnitudes.different solids like cone, cylinder for drawing
6)    Students get practice in estimating orders ofdifferent shapes and making observations for various
magnitudes and obtaining approximate answers whencomputations.
exact answers are difficult to find.III)        A thick card sheet, capable of folding,
7)    Students make charts and models to illustrateto prepare packing boxes, envelops etc or other
mathematical ideas.small objects.
8)    Students do almost all the work themselves,IV)            The students will be required to
of course under the guidance of teachers, but theuse drawing sheets, graph papers, cutting tools,
students are active all the time and are involved withthread, small balls made of different materials, ready
what they are doing.reckoners, rubric cube, calculators etc.
9)    The creativity of students is allowed freeMeasuring Equipment:
play.1)      Measuring tapes 30m; 10m; 2m; 1m and
10) Students solve graphically equations involving allsmaller lengths, arrows (iron wire nails 20 to 30 cm
types of functions.long; 2.5 mm in diameter)- they act as pegs to mark
11)  Students are free to discuss among themselvespoints on the field ; pipe hole 1m long ; 10 mm in
and with the teachers; in fact students and teachersdiameter, pointed at one end; painted with red and
form joint investigating teams.white strips- used for making solar observations and
12) Students find areas and volumes of both regulardetermination of N-S direction at a place and also
and irregular solids.finding out the angle of elevation of the Sun at any
13) Students undertake projects both in mathematicstime.
and its applications.2)    Plain mirror, plum bob suspended from a
14) The concepts and theorems are not given to thehook, drawing board , mini drafter, vernier calipers ,
students; these arise naturally from theirworking models to verify law of parallelogram of
investigations.forces, triangle of forces etc.
15) Interfaces between algebra, geometry;Display models:
probability; calculus etc are freely investigated and1)      Children are assigned task to imagine
discussed.suitable design data to prepare models and keep
16)  Attempts are made to interpret every symbolicthem for display in the lab. This includes different
solution.types of packing boxes; tents-pyramid shaped;
17) The process of mathematics is emphasized muchcircular and dome shaped etc.
more than the product of mathematics.2)    Storing typical shaped tin cans or paper
18) Students are encouraged to find alternativepackets like a tetrahedron; prism; cylindrical shaped
solutions and alternative methods of solving problems.which are available in the market for packing milk or
19) Students enjoy learning mathematics.juice. The children are assigned task to imagine
Before we proceed further, let us explore as to whysuitable design data to prepare attractive packets for
students do not fair well in mathematics. The reasonsliquid contents.
are not difficult to find.3)    Certain models are prepared to demonstrate
It is not because:i)                  the principles used in making some scientific
Students are unable to solve certaininstruments, e.g. optical square; cross staff;
problems,ii)                Or, students areperiscope; kaleidoscope etc. The students thus come
not able to memorize formulae etc.to know the use of such scientific equipments.
But, it is due the fact that there are some inherentWorking Models:
weaknesses in the teaching of present day1)      Plane co-ordinatograph: It is a model
mathematics. These are listed below:prepared in the lab and used for making observations
1)      Mathematics is taught as an abstractof co-ordinates of various points in a plane. This is of
subject.great help to explain the basic concepts of
2)    Mathematics education is far removed fromco-ordinate geometry in two dimensions. Students
applications.are asked to take observations of points and write
3)    Mathematics is taught as an isolated subject.equations of incident ray; reflected ray; equations of
4)    There is too much emphasis on symbols andcircles; parabola; plane; straight lines; tangent lengths
their manipulations and relatively little on problemetc on the basis of co-ordinates observed on the
solving.working model. The students can understand the
5)    Too much time is spent on routinetransformation of one system of co-ordinates into
monotonous drill type arithmetical calculations.the other, trigonometric ratios and their applications
6)    The goal of mathematics education appearsetc.
to be passing examinations in mathematics and not2)    Plane Space Co-ordinatograph: It is a model
understanding mathematics and its applications orprepared in the lab and used for making observations
developing capacity to think mathematically.of co-ordinates of various points in the space above
7)    Instead of developing creativity, mathematicsthe surface. This is of great help to explain the basic
education encourages conformity to standardconcepts of co-ordinate geometry in three
methods.dimensions. Students are asked to take observations
8)    It trains students to think that there shouldof points in space; write equations of straight lines in
be only one method of solving mathematicsspace and locate points in space. The students can
problems.understand the transformation of one system of
9)    It trains students to think that there can beco-ordinates into the other. With such experiments,
only one solution to a problem.children come to know how to determine the
10) Mathematical proficiency is often confused withdistances of cloud; sun; moon; space craft at the
proficiency in making arithmetical calculations.time of Arial photography etc.
11)  The process by which mathematics is created is3)    Dip Measurement Model: It is a model made
seldom taught or emphasized.out of transparent plastic cylinder to represent
12) Mathematics is presented as a purely deductiverailway tanker. This demonstrates how easily the
science though it is also as much an experimentalliquid contents or the volume can be determined in
science as physics or biology.case of cylindrical tanker making few observations.
13)  Geometric and Physical visualizations remain4)    Water analog model: It is a model to take
very weak.observations for filling the pool by different taps
14) Even geometric objects become just relationshaving different rates of discharge. Such observations
between symbols and are not curves or surfaces.enable the students to formulate quadratic equations
15)  It convinces the students that the only lawand find out their solutions. Such working models
which matters is the linear law.analogy can be applied in solving different types of
16)  Students develop no idea of the order ofproblems related to the formation of quadratic
magnitude of the results they get.equations on the basis of given conditions. Also the
17)  Students are passive learners.observations may be used to tackle problems based
18)  Students do not talk mathematics, discusson dispersion theory and determination of the most
mathematics or think mathematics.probable value in a set of observations.
19)  Mathematics is taught as a collection of topics.5)    Model To Make Observations of Time Periods:
20)                       The historicalA pendulum is suspended in the lab and time period
development of mathematics is never emphasized.for the oscillations are observed. This leads to the
Thus the objective of a mathematics laboratory isvalue of g, the acceleration due to gravity.
to:a)     Remove the weaknesses of present day6)    Equilibrium Forces Analog Model: This model is
mathematics education which the mathematicsused to formulate the equations of equilibrium.
laboratory and the mathematics laboratory alone canThe Concept:
do it.b)    To develop the much needed confidenceOn the lines of science laboratory, the concept of
in students.c)     To generate interest in themathematics laboratory may be visualized and
subject.d)     To make the students divergentdeveloped. It is a place where every one should get
thinkers.an opportunity to establish correlation of one subject
Having seen “WHAT” and “WHY” ofwith allied subjects.
a mathematics laboratory let us now discuss theThe basic linear equation answering the needs of
“HOW” of it.mathematics laboratory is:
Time-table Re-scheduling:Ml = aiXi + bi Ym + ciZo ; where:
While preparing class-wise time-table, in JNVs, theMl denotes activities in mathematics laboratory.
provision for mathematics practical periods may beXi denotes necessary infra structure.
made in the following manner:The coefficients are:a1 denotes library and reference
From classes VI to X, there is a provision of onebooks.a2 denotes furniture layout.a3 denotes
theory period of mathematics in each class in everylaboratory equipment- Computers; Calculators;
day working time-table. Also in each class twoGeometry Box; Cutting Tools; Letter-Stencils;
periods for “ART” are allotted per week. ItDrawing Equipment; Mathematical Charts; Logarithm
is suggested that one theory period of mathematicstables etc.
may be combined with one period of art and theYm denotes necessary mode of working and
combined periods may be re-named asmanagement tools.
“MATHEMATICS PRACTICAL PERIODS”.The coefficients are:b1 denotes Computations leading
This way in five days each class will have anto desirable outputs.b2 denotes Making drawings and
opportunity to visit the laboratory. As regards classessketches to explain the procedure.b3 denotes
XI and XII are concerned, the students normally optAnalysis and decision from set of observations.b4
either mathematics or biology. The students optingdenotes Field layout and model making to achieve
mathematics can be taken to the laboratory duringthe objectives.
the practical periods for biology.Zo denotes the number of objectives associated
Layout of a mathematics laboratory:with the activity.
The ideal mathematics laboratory will have theFor example: an activity for determining the nature of
following sections:? may have the following objectives:c1 denotes :
1)      Section for job discussion and planning theWhat is ??c2 denotes: What is the value of ??c3
solution.denotes : Whether ? is rational or irrational?
2)    Section for making sketches, drawings forNow finally I suggest some activities which can be
taking observations.done in the mathematics laboratory:
3)    Section for reporting the results.1)      Mathematics laboratory- Definition.
4)    Section for making the working models as2)    Activity 1: Mathematics laboratory-
per job specifications.Introduction.
5)    Computer section for doing experiments of3)    Activity 2: Half Life.
mathematics on computers.4)    Activity 3: One-Less.
The above sections (steps to be performed by5)    Activity 4: Doubling.
students) need be discussed by the teacher6)    Activity 5: Span.
in-charge, in the laboratory. Before the children are7)    Activity 6: Roller.
asked for execution, the teacher should explain the8)    Activity 7: Center-Point.
planning part as well as he/she should help them in9)    Activity 8: Bigger.
identifying the appropriate solution in respect of10)  Activity 9: Equals.
choice of proper tools and their use in execution. The11)  Activity 10: Side by Side.
teacher should also explain the use of computers in12)  Activity 11: Paper art.
finding the solution and the method of checking the13)  Activity 12: Cut Away
accuracy of the solution already found in the14)  Activity 13: Impossible Challenge.
laboratory.15)  Activity 14: Get triangle equal in area to a
Furnishing Mathematics Laboratory:parallelogram.
Sufficient furniture should be provided in the16)  Activities 15, 16: Quick Calculations.
laboratory to do experiments and at the same timeThis is not the exhaustive list of activities to be
for displaying the working models and other meansperformed in the laboratory. Many more activities
of taking observations; to carry out experiments andmay be thought of and performed in the laboratory.
make a clear understanding about the use ofThe details of the above mentioned activities are
procedural tools in engineering projects.  Theseavailable in the accompanying CD. These can be
models are made out of discarded toys and wasteviewed using Microsoft Power Point and clicking to
articles found around us. This approach boosts theview slide show.