hands on Maths

In our times there was no concept of Maths lab but now a days the idea of hands on math is picking up. The math lab could be developed for primary, middle, secondary and higher secondary level. The concept of Mathematics Laboratory 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 lab could also be helpful in relating classroom learning to real life situations and discourage rote and mechanical learning. Not much hardware is required for developing primary and middle level maths lab or even secondary level math lab. Some special types of paper such as isometric dot paper, grid paper, origami paper, squared paper, card board, full protractor, plastic ruler,  thread 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 birds, houses, boats, people and geometric shapes. Tangrams have fascinated mathematicians and lay people for ages.

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. These authors conduct workshops on ‘Maths through Origami’. If you think  origami is  for school kids, then you are mistaken there is now research on applying paper-folding techniques to engineering in a field dubbed as "origami engineering."  The Japan Society for Industrial and Applied Mathematics has set up a research group called Mathematics of Origami Engineering.

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. Khatambands are practical application of tessellations.

One can make flexahederon  and mobius strips and play with them for hours. As one turns fexahederon  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. For making a flexahederon one may consult the site www.sci-toys.com

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 above two Möbius strips along the center line yields two entirely different but interesting results.

Apart from the above mentioned toys and activities, full protractors,  plastic scale and nuts also come handy for mathematical activities. Two crossed plastic scales could be riveted in the centre of full protractors and the adjacent and opposite angles could be measured to find various relationships. Similarly three scales 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. Algebraic equations like (a+b)² = a²+b²+2ab can also be visualised with the help of paper sheets. I urge students to experience hands on mathematics this winter rather than going for a maths tuition.