World of Puzzling Patterns
Have you ever tried to see math in all the amazing shapes and patterns in the world around us? Mathematics and nature look like two different realms. But they are very well connected. Math was developed to describe patterns in nature. Early Greek philosophers like Plato, Pythagoras and Empedocles attempted to explain the orders and patterns in nature. The modern understanding of visible patterns was developed gradually over time. For many, math can be frustrating, boring, and hard. Still, we cannot deny the fact that Math is all around us! Galileo Galilei had said that "To understand the universe, you must understand the language in which it's written, the language of Mathematics."
Nature often displays models and patterns we see in mathematics. Even the vast majority of animals on earth display at least some form of symmetry. Spider Webs, Honeycombs, Nautilus Shell, Snow Flakes, Moon and Sun, and Sunflowers are some of the examples in which we can find some familiar math concepts.
Pallikkutam has reached out to some experts in Mathematics, on the shapes and patterns fascinate them while exploring maths.
Chandran Nair, Chief Executive Officer at AEM Holdings, Singapore, says, mathematics helps in recognising patterns. For example patterns in speed, patterns in digital transformation. Mathematics can be used as a great tool in many sciences. Chandran Nair has previously held key positions in National Instruments in Singapore and holds an MS in Mathematics from Arizona State University.
He continues, "I am by nature good at abstract thinking and mathematics was quite easy for me. Both my children differ in mathematical abilities." There are three kinds of students a teacher may encounter in a class. One is the abstract thinking type who is quite comfortable with mathematics and easily understands the theorems and equations.
The second type of students require representations of say geometry or trigonometry to understand concepts. And the third category doesn't like maths at all. Very few teachers commit to addressing the third category while the first category will learn on their own as they are intrinsically motivated and driven by abstract thinking. The challenge is to make children in the third category who don't like maths to start loving it. A good understanding of the fundamentals of maths is required for everyone. There is talk of integration of mathematics in various sciences including humanities. But it all depends on how best mathematics is used as a tool and teach students how it integrates into the domain rather than teaching the entire concepts as it is taught to a student specialised in mathematics.
In schools and colleges, it all depends on whether teachers are well paid and hence able to attract the best talent or whether they become teachers as a last resort because it isn't a remunerative profession.
The geometry of Sri Chakra
Subha Rakesh, a specialist in Vedic Mathematics and Chess says, “Mathematics is the beautiful language of the Universe. When we look around, we can see that everything in our life is related to Mathematics, starting with the fraction of a second of our lives. Another interesting thing we can observe is the occurrence of patterns. We can see patterns in Stars, Seasons, in the number of petals in flowers etc.
“One of the important and higher-level mathematical relations I have seen, is in Sri Chakra or Sri Yantra, in Hinduism. Sri Chakra is an ancient geometrical construction based on interlocking triangles. It is a 2-dimensional ancient sacred diagram used in mediation and prayers. It consists of nine interwoven isosceles triangles that surround a central point. These triangles represent the cosmos and the human body. It is surrounded by 8 and 16 petalled loti. The intersection of the 9 triangles results in the formation of 43 small triangles organized in 5 concentric levels.
When the diagram is represented in 3 dimensions, it is called Mahameru. The diagram looks simple, but it involves a very high level of mathematical calculations. We can also see a relation to some calculations involved in the Great Pyramids in Egypt. When we analyse the patterns and the geometry involved, we wonder how such a difficult geometric expression could be invented. Sri Yantra is a visual masterpiece of abstraction.”
National Mathematics Day
India celebrates National Mathematics Day on 22 December every year to mark the birth anniversary of legendary Indian mathematician, Srinivasa Ramanujan. This was announced by Prime Minister Manmohan Singh on 26 February 2012 at Madras University, to mark the 125th anniversary of the birth of Srinivasa Ramanujan. Since then, India's National Mathematics Day is celebrated every 22 December with numerous educational events held at schools and universities throughout the country. This year also, the day has been celebrated all over India raising awareness among people about the importance of mathematics for the development of a country.
One such event was organised by the Regional Institute of Education, Bhopal on 20th December on virtual mode.
The National Council of Educational Research and Training (NCERT) is preparing a working paper on teaching mathematics to develop computational thinking in school students, said Prof SreedharSreevastava, Director of NCERT, inaugurating the event. Prof Sreevastava added that the New Educational Policy 2020 would enable students to schools and colleges to put mathematics in a basket of courses and not confined to engineering or science courses alone. It can now be combined with humanities, social sciences, psychology, Sanskrit or other languages or arts.
Compared to other subjects mathematics is abstract and hence an interest in learning has to be developed by teachers so that students experience an inner motivation to learn, understand and apply them by observing the surroundings.
Mathematics in ‘Kolam’
Prof R Ramanujam, Professor of Theoretical Computer Science at Institute of Mathematical Sciences, Chennai explains math in 'Kolam', the traditional designs drawn by women especially in Tamil Nadu, Karnataka and Kerala in front of the houses or courtyards. They should be admired for its aesthetics as well as the mathematics behind it. For mathematicians, it lends itself to a deep analysis of the several mathematical shapes and patterns said Prof R Ramanujam while delivering the keynote address titled 'Guide maps for Mathematical Exploration' at 9th National Conference on Mathematics Education organised by the Regional Institute of Education, Bhopal, and being held from December 20 to 22 via a virtual platform. Prof Ramanujam said that it was amazing to analyse the squares, triangles, Fibonacci and Pascal patterns or curves and dots used by women to draw such 'Kolam.' They are drawn using white rice powder, chalk powder or rock powder and is believed to attract goddess of wealth 'Lakshmi' and it also welcomes birds and insects thus bringing nature to home surroundings.
Prof Ramanujam said that analysing and classifying 'Kolam' has been an integral part of the curriculum at the Institute of Mathematical Sciences. You can give fifty sheets with 'Kolam' drawn in different shapes and ask students to analyse. There are various types of symmetry such as diagonal symmetry, mirror symmetry seen in 'Kolam'.
The analysis is a four-step process involving classification, analysis, finding the symmetry and transformation, and finding the curvature of the 'Kolam'. The problem of orbits in 'Kolam' takes you straight to algebraic geometry and he said that his student at Princeton University has researched 'Geometry of Kolam.'
Learning mathematics should be an exploratory journey for the student. It involves visualisation, representation, argument (not proof). He said the conventional style of mathematics teaching was to have problems and solutions but every solution should end only by raising a new problem. For exploratory learning knowledge, skills, aptitude and disposition are needed.
He also touched upon the three types of exploration- question-driven, concept-driven, and goal-driven. Mathematics has to be taught in a manner that children raise more and more questions that aids learning, he adds.
Nurturing Math Skills in Children
Developing mathematics skills begins long before children enter formal schooling. Preschool and toddler-aged children are constantly playing with math. They naturally sort and organize. They build and design. These are mathematical skills children have a natural interest in and their beginning development comes through the very natural act of playing. We can use nature to teach them.
Tips to Explore Mathematics in Nature:
· Go outside
· Observe the world around you
· Think mathematically
· Record data
Math-in-Nature Tasks for Children:
We have sorted out some popular math concepts with real examples in nature. You can ask your child to try these simple math-in-nature activities at home:
Definition: A three-dimensional object, completely round in shape
Task: Find five examples of spheres in nature.
Definition: One half of an object is the mirror image of the other half.
Task: Prepare a list of 10 things in nature that have symmetry.
Definition: A number that shows the amount of something.
Task: Take your child for a walk in a park. Get a measuring tape, a pencil, and a notebook. Ask your kids to measure different things like tree stumps, flowers, sticks, and stones. Ask them to write their findings in a notebook.
Definition: A 6-sided polygon (a flat shape with straight sides).
Task: Find three examples of nature using hexagons
Definition: The act of determining the quantity or the total number of objects in a set or a group.
Task: Walk outside and count the number of trees with a simple leaf and compound leaves.
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