Mathematics has always been considered a dreadful subject and you might not have heard the word phobia associated with other subjects except Mathematics. The main reason is we fail to associate mathematics with the daily life situation. A concept can only be termed as permanent if it attracts the learner. Since the birth of an individual we start calculating weight, timing, diameter of head etc. that is nothing but a part of hidden mathematics but as we grow, we start hating mathematics despite the fact that it is the integral part of every individual.
Now to link mathematics with the daily life situation, to engage the students to have a feeling of exploring the knowledge by doing a concept of laboratory has been introduced in curriculum. The mathematics laboratory is a palace where anybody can experiment and explore patterns and ideas because mathematics is nothing but the pattern recognition, playing with numbers to enjoy the inner beauty of mathematics.
A world where student can discover what mathematics is all about and explore the previous knowledge to give a new breakthrough by means of games, puzzles, three dimensional objects, theorem in geometry etc. All such activities create interest among students who wants to explore and test some of their ideas, beliefs about mathematics. It provides and opportunity to discover through doing. The activities help students to visualize, manipulate and reason out conjectures and test them, and to generalize observed patterns. It is a place where anyone can generate problems and struggle to get an answer, design new mathematical activities.
Saying all the above, I am of the opinion that mathematics is omnipresent and it can’t be learnt in a confined area that is now termed as Mathematics laboratory. Mathematics learning can take place everywhere even in the garden, park, playground, the shapes, number around us.
1. A symmetry pattern can be learnt in nature by observing the leaves symmetric.
2. A Fibonacci pattern can be understood by cutting the cross section of oranges, counting the anti-clock wise and clockwise lines on pine apples, counting the pattern in sunflower etc.
3. The concept of mathematics applied in Football shape having pentagon and hexagons can be understood in the field itself.
4. Nature can teach us many mathematical phenomena and for that we don’t need any laboratory as such but for the practical purpose it is not feasible to do all such experiment in open.
Importance of Mathematics Lab: -
a) Lab offers more scope for individual participation through different activities. It encourages independent learners and allows them to learn at their own pace.
b) It widens the experimental base and lays groundwork for later learning applicable in new learning.
c) It helps in developing meta cognitive abilities as a student attempts several times without any interference from time constraints.
Few mathematical lab instruments and its applications: -
1) Tower of Hanoi: - It is easy to construct with the help of rubber sheet and rods but it has practical implication not only for the purpose of entertainment but it has its history associated with Vishwanath Temple Varanasi. If there are 5 discs chosen then minimum number of moves required to transfer the discs to one of the other rods using the third rod is 31. If the number of discs is more than number of moves will be 2^n – 1. This puzzle will help students to find the number of moves starting from 2 discs and increasing the discs one can understand the concept of COMBINATIONS. Moreover, students can also raise questions like – a) Why we need three rods not two rods? b) What would happen if we add one more rod?
2) Circle: - In Primary level we have the different components of circle like – diameter, chord, sector, arc length etc. In addition to this in secondary level we study the different theorems based on segments, cyclic quadrilateral, tangents etc. All such concepts can be understood with the help of mathematical laboratory. A) Finding the area of circle b) relation of sides and radius in circum-circle, incircle etc. c) tangential circle d) angle subtended by an arc of a circle e) equidistant equal chords etc.3) Graph: - A student can’t be taught the graph on a normal blackboard. The concept of ordinate, abscissa and co-ordinate can be taught to a student in laboratory,
4) Polygon and Polyhedron: - In mathematical laboratory a student visualize the three-dimensional pattern that he /she can’t feel in the book or when drawn on blackboard. The Euler’s relation between Edges, Vertices and Face can only be understood with the proper visualization of the object.
5) Poster and Chart: - Mathematics can be made inspiring by letting the students know about the story and achievement of mathematician. Importance of mathematical days like – Pie day (14th March), Pi Approximation day (22nd July), National Mathematics Day (22 December). Besides that poster of mathematicians with some information and tidbits can be kept in laboratory.
6) Surveying Instruments: - In geometry and especially in trigonometry measuring the height of an object from a distant point depends on the angle of elevation or depression and it can be understood if we use – 1) angle mirror 2) plane table 3) hypsometer and clinometers 4) astrolabe 5) sextant 6) ellipsograph 7) opisometer can come handy to understand the concept of height and distance.
7) Conic Section: - In geometry the concept of parabola, hyperbola, ellipse can’t be easily explained on blackboard. The concept of focus, latus rectum, eccentricity can be explained in lab with proper explanation and experiment to students.
8) Mathematical models: - Various models on plane geometry, three-dimensional geometry can be stored in a lab to understand the abstract mathematical proofs, principles or statements in mathematics. Moreover, the concept of symmetry, rotational symmetry can be explained in laboratory.
9) Algebraic/ Geometrical proof: - Mathematics is all about knowing the proofs of identities. In algebra there are many identities that can be explained with the help of some puzzles. Even theorems can be explained in lab.
There are 100 of mathematical activities that can be explained in laboratory. Even working models can be explained or students can be encouraged to make mathematical models.
Dr Rajesh Kumar Thakur