The teaching and learning of this seemingly difficult subject can be made easy and interactive
A mathematics laboratory or activity centre is a place where we find a collection of games, puzzles, teaching aids and other materials for carrying out activities. The concept of Mathematics Activity Centre has been introduced with the objective of making teaching and learning of the subject interactive, participatory, fun filling and joyful from primary stage of schooling up to higher secondary. The other purpose could be strengthening the learning of mathematical concepts through concrete materials and hands-on-experiences.
Maths Activity Centres could also be helpful in relating classroom learning to real life situations and discourage rote and mechanical learning. A mathematics laboratory provides an opportunity for the students to discover through doing. In many of the activities, students learn to deal with problems while doing concrete activity, which lays down a base for more abstract thinking. It gives more scope for individual participation. It encourages students to become autonomous learners and allows a student to learn at his or her own space. It widens the experiential base, and prepares the ground for later learning of new areas in mathematics and of making appropriate connections. In various puzzles and games, the students learn the use of rules and constraints and have an opportunity to change these rules and constraints. In this process they become aware of the role that rules and constraints play in mathematical problems. Because of the larger time available individually to the student and opportunity to repeat an activity several times, students can revise and rethink the problem and solution. This helps to develop meta-cognitive abilities. It builds up interest and confidence in the students in learning and doing mathematics. Importantly, it allows variety in school mathematics learning.
Not much hardware is required for developing maths activity centre. Some charts, Pictures, Geoboards, Connectable Plastic cubes, Net diagrams for solid shapes, special types of paper such as isometric dot paper, grid paper, origami paper, squared paper, card board, full protractor, plastic ruler, thread, rubber bands and match sticks or tooth picks are sufficient to start hands on math endeavour.
Tangrams, Tessellation and Origami are very good activities to initiate child towards geometry and creative learning in maths. The seven pieces that make up a tangram can be cut from a single square. There are thus two small triangles, one medium size triangle, two large triangles a square and a lozenge shaped piece. The medium sized triangles and the square and the rhomboid are all twice the area of one of the small triangles. Each of the large triangles is four times the area of one of the small triangles. All the angles in these pieces are either 900, or 450 or 1350.The puzzle lies in using all seven pieces of the Tangram to make alphabets, birds, houses, boats, people and geometric shapes. Tangrams have fascinated mathematicians and lay people for ages.
A tessellation or tiling of the plane is a pattern of two dimensional figures that fills the plane with no overlaps and no gaps. A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. The traditional Kashmiri art Khatambands are practical application of tessellations.
Origami (Ori-folding, gami –paper) is the traditional Japanese art of paper folding. Using just square sheets of paper, a variety of three dimensional objects are formed. It is the art of creating a structure by folding a single sheet of paper according to a pattern without cutting. Its educational value specially teaching geometry, algebra and trigonometry through origami is undisputed. Some of the origami patterns are geometric, and they make it possible to see geometry in the principles of origami. By systematically folding a paper one could fold lots of angles, polygons, curves and 3D polyhedra. In some way Origami can be considered as a stepping stone towards appreciation and building up of mathematics lab at schools. ‘Origami – Fun and Mathematics’ by VSS Sastri and ‘Square pegs in round hole’ by Arvind Keskar demonstrate how children can learn to make different geometric models through paper folding in an enjoyable manner. Origami is a wonderful way to learn practical geometry. These books also serve as a manual for developing teaching aids in mathematics.
One can make flexa hederon and mobius strips and play with them for hours. As one turns felxahederon paper sculpture inside-out, it changes colors. First yellow, then blue, then red, then green, and then yellow again. One can keep turning it inside-out, cycling the colors, as long as one likes.
The Möbius strip is a surface with only one side and only one boundary component. It is a non orientable surface. A model can easily be created by taking a paper strip and giving it a half-twist or full twist and then joining the ends of the strip together to form a loop. It has several curious properties. A line drawn starting from the seam down the middle will meet back at the seam but at the "other side". If continued the line will meet the starting point and will be double the length of the original strip. Cutting the Möbius strips along the center line yields two entirely different but interesting results.
Apart from the above mentioned toys and activities, full protractors, plastic rulers, rivets and nuts also come handy for mathematical activities. Two crossed plastic rulers could be riveted in the centre of full protractors and the adjacent and opposite angles could be measured to find various relationships. Similarly three rulers could be riveted to make triangles and three full protractors could be used to read internal and external angles to find the relationships between various angles. Pythagoras theorem and algebraic equations like (a+b)2 = a2+b2+2ab can also be visualised with the help of colourful paper sheets.
(Dr Seemin Rubab is Associate Professor, Physics, NIT, Srinagar).