UNIT-1
Mathematics as an intrinsic and natural part of life.
When most people think about Mathematics, they think about it as a dreaded subject, which only some are good at and they also think that such people are specially intelligent. This is the common view, but this view could be termed as the greatest irony when it comes to subjects.
This is because mathematics is an intrinsic and natural part of life and in fact every aspect of living contains mathematics implicitly.
Let us see how Mathematics comes into play, implicitly, intrinsically, naturally as a child grows from birth to the age of three. It is, in fact, a tremendous growth that by the age of three, a child learns naturally and absorbently a great deal of information, so much so that by three he feels at home in his surroundings and develops a language and even a distinctive sense of being, a personality and an identity!
The point is that this tremendous development actually is accompanied intrinsically by a mathematical sense of --
Implicit measurements, Pattern recognition, Awareness of cycles, Complex relationships of a variety of things between two or more things
Comparison by similarities and differences,
Matching of complementary things, Sorting and classifying Development of fine discrimination's of sensory differences in seeing, hearing, touching, tasting, smelling innumerable things.
Discrimination of touch senses to develop, fine, and gross motor skills,
And many, many more skills, observations.
All of these can be actually rooted to a mathematical measuring sense.
Let us concretise the above processes by some examples to make it fully clear how mathematics can come in operation in every single action that you observe in the world.
A child tremendously desires to learn and he or she is extremely sensitive and absorbent. This was explained and brought to light first and deeply by Maria Montessori, a century back. She urged us “to discover the child”.
What is a child? Especially in the first three years of his life.
A child is curious, active and deeply hungry to use his body and mind and its potential capacities. This manifests as being non-stop active which many interpret as hyperactivity or even being naughty,
In his natural surroundings a child observes innumerable things with high sensitivity and absorbs this information and makes it part of his own.
Sensory Observations
Let us look at all the sensory observations he makes with his sensitive intelligence and how a mathematical discrimination comes naturally into play.
He observes, for example, the cycle of night and day and within that, he knows the gradations from early morning, to afternoon, to evening, to night,
He senses time, implicitly also,
And also seasons and weather.
He's measuring the gradations of heat so that he can know whether it's early morning or afternoon. He is ordering the time,
As we can see, all these are actually measurement processes, mathematical processes.
Same thing happens when he hears sounds, whether it's loud or soft, also he can listen sharply to music, he can even understand whether it's something sad or happy or light on his own level. He listens to music of of all kinds.
He listens to voices of human beings of his mother, father, all the people around him, children, adults
He learns again. Measuring, ordering, comparing, matching all the sounds made by all the things whether it's vessels or wind or bus or car, bike TV , actually hundreds and hundreds of things, he listens to them, he can observe and measure their pitch and loudness and quality.
In all of this, he is implicitly and sharply aware and measures the pitch and loudness and even quality
The child is also comparing and matching and ordering and classifying, for example, he knows human sounds are different from cat sounds and these are different from dog's sounds, etc.
All the sounds in the world around him have been sorted, classified, ordered, learnt and stored within his mind! This is a mathematical feat!
The same happens with sight, he knows the colors of everything implicitly, and the gradations of color eg light blue, dark blue, medium blue.
He knows the degrees of each color.
He knows the colors of every single thing and the types of colors they can have. For example, faces, clothes, trees, animals, vehicles, food stuff and all the things around him.
He knows all the touch feelings whether it is hot, cold, and all kind of touch sensations which he can feel around him. For example, he knows the touch of his father and mother, of his doll, of his dog, water, carpet, bed, etc.
The same thing happens with smells about all kinds of things in his environment.
In fact, a child is very sharp with all his senses and through his senses he learns through the processes again of measuring, of ordering, of matching, of classifying.
Learning By Doing
Also, he learns to DO things to find out how things work, and what things are,
So he not only observe by his senses, he needs to EXPERIMENT with things to learn about the world, so he has to use his hands, his body along with his mind and senses, to learn about the world,
We observe children do a variety of activities with their hands and bodies and they are non-stop active, which is what exasperates adults
For example, he bangs his doll or takes out his toy apart.
He always wants to play, and play for him means simply to experience and experiment with everything.
For example, moving a ball, bending his spoon, banging his spoon with a vessel, breaking things, playing with water, using a pen, even eating things. He is all the time trying to learn about the properties of all things through doing and playing!
Thus he is using his hands and the body. Here the examples are infinite and finally a day comes when there is nothing that he has not become acquainted with.
He has learned, by touching or playing, with a purpose, everything.
Especially if he's given more freedom, he learns more sharply, more perfectly.
In fact, a child would love anybody who would give him things to play with, who would guide him to play with, who would help him to play with, he would then play endlessly and without stop.
He would repeat the same thing endlessly!
This is clearly observable by anybody.
Why? What is he doing? Why is he doing that?
He's doing that because he's learning, there's a tremendous need
biocentrically within him, to feel at home, in this world, to feel comfortable in this world, to feel powerful in this wonderful world and to feel confident in this world.
This is a need, and not just a luxury, it's a need bio-centricity and deeply
A child has the curiosity and the desire to know, to grow, to become powerful and to become confident.
It is inherent intrinsically, a part of a human being. This is the great insight which all great educationists.
We can easily see that the child is again implicitly relating one thing with another, observing many things and while observing he is sensing the implicit measure of all dimensions
So obviously, he's relating one thing with another via implicit measuremrnts.
He understands that this is what he has to do.
Another remarkable thing is that he learns the names of all the things and he names all the actions also, in fact all the words, and his absorbent mind grasps all kinds of words and sentences and idioms and phrases in his local language and with no book, only by hearing and watching people and their expressions and body language, he learns something so tremendous as a language, a complex language!
It is in fact an intellectual and mathematical feat!
We all know how much a three year old learns but we take it for granted.
But what we must note here is that a mind, a mathematical mind, deeply and sensitively, connected to senses and guided by a powerful absorbent mind is doing its work non-stop.
Thus, we see a mind, a human being is absorbent. A human being has a discriminatory capacity to observe and order, classify, sort and match by implicit measurements.
Man is a measure of all things. Many people have said, but many great philosophers have also said, man measures all things implicitly.
Now we can see clearly that mathematics is not an abstract detached subject which only some are good at.
Now, we can see the irony of thinking that way.
Mathematics is actually a natural and intrinsic part and parcel of life, living your whole life with such an ability, at least potentially.
Now, we are ready and can ask the real questions with respect to the subject of mathematics.
When so much can and has been learned by three years itself, when so much is part and parcel of the mind itself, the mathematical intellectual mind to observe via sharp sensory abilities and absorbent mind, then what should happen next?
What should the child learn in mathematics When he enters schools?
What is the task in Mathematics in the pre primary and primary levels?
And in the higher levels. How should mathematics be used in life?
What IS really the subject matter of mathematics? What are the topics of mathematics?
And why only those?
And why should they be learned?
Should the same processes detailed in this chapter be carried out but explicitly ?
Now we are looking at mathematics in a totally different way, yet totally real way, connecting it TO life, making it an intrinsic part of life.
In fact, mathematics becomes a way of life and living!
The above questions specifically on formal Mathematics would answered in the next 2 UNITS.