Blog on Kids Education, Learning and Parenting Tips

How often have you said to yourself, “I don’t give a damn what others say! I know what I know!” Chances are that you would be applauded for your fiercely held self belief. This article is not to make a dent into your self belief. This article is about consequences of others perception, specifically a teacher’s perception of a child’s ability.

In 1948, an article by Robert Merton appeared in The Antioch Review.

But is that possible? Can we learn to become conscious of the signals that we send out unconsciously? And optimise it to our benefit? A study of Clever Hans or Der Kluge Hans seems to suggest otherwise. But that is the topic of another discussion: The Horse that knew how to do Maths!

Children interpret their surroundings with their different strokes; whether, while playing, it is lines drawn with a stick on the ground to represent no-go areas or the representation of the three stumps of the cricket game by drawing three lines on the wall with a thick charcoal , they interpret their everyday life in various ways. Children put down their impressions of their environment in sketch books as well. A good deal of study has gone into the interpretation of children’s drawings. The drawings have even helped experts in diagnosis of children behaviour.
Interpretation of children’s drawing was famously shown in Shekhar Kapur’s movie “Masoom”. An illegitimate child’s yearning for place in a family was poignantly depicted through the child’s story board.
There are other interesting aspects of children’s drawing, visual realism is one example. In this article let us see this interesting aspect as we trace the progress of visual realism in children’s drawings, as they become older. In particular, we will see how children deal with transparency in drawings. We will see this with examples of children’s drawings of floating objects like ships, boats and yachts.
Below is a 5 year old child’s drawing. Notice that a person has been placed right at the bottom of the hull of a ship by this child. Also, we are able to see this person placed inside the hull as if the hull were transparent. The child’s comprehension of space and its translation onto paper is interesting. The child’s depiction of transparency of the hull is worth noting.

Image courtesy Joseph H. Di Leo’s book on ‘Interpreting children’s drawings’

Let us move to the next stage. Here the child who drew the picture below is a few months older. The child’s sense of space is more keener but she still hasn’t quite grasped the transparency issue

Image courtesy Joseph H. Di Leo’s book on ‘Interpreting children’s drawings’

Here is the third stage. The drawer is 6 years old. The boy drawing the below picture has made a compromise between spatial positioning and transparency. He has placed a person on the deck. This is how he is trying to bring the picture closer to visual reality.

Image courtesy Joseph H. Di Leo’s book on ‘Interpreting children’s drawings’

The next stage almost mimics visual reality. The person’s trunk is hidden in the boat’s hull. The drawer is a boy of 6 plus years. He recongnises that the face is the most important item that he wants to show. So even though the person wears a beard he has made sure that the face can still be seen by making the beard semi transparent.

Image courtesy Joseph H. Di Leo’s book on ‘Interpreting children’s drawings’

Our drawer has grown older. S/he has opacity and spatial sense. This seven and a half year old depicts a man in a sailing boat. As an adult would imagine, the trunk of this person’s body is not seen. The partly submerged boat is also correctly depicted. The child has now a keen grasp of visual realism.

Image courtesy Joseph H. Di Leo’s book on ‘Interpreting children’s drawings’

The point we are trying to make is that the transparency and spatial sense of a child is progressive. Would it not be fun to watch the transformation as your child goes from subreal to real to surreal?

My son, when he was a kindergartner, was always fascinated by the cawing of crows. I am not sure if the raucous call was music to his ears but his fascination for crows was unwavering. I recall a time when the family went out to the zoo on a Sunday afternoon.  My wife was trying to get him excited about the big cats that were gnashing their teeth and circling in their pens. But his interests lay elsewhere. He ran after a crow that took off from the back of a hippopotamus. He was looking up and running, tracing the flight of the crow. The nice family outing ended when he ran into a puddle and submerged himself in mud.

Not long after this fascinated-with-crow incident, we had another fascinated-with-crow incident. His mother was reading him out a story of a king and queen when a crow started cawing outside our window. My son’s ears cocked up. And suddenly he recited the following lines:

            The crow was flying high and high

            Pecked the Queen

            The King was angry

            The crow was jealous

Now, how in the world did he blurt out these lines? To this day I don’t know. But that day I was absolutely convinced that my son is going to be a literary sensation. My wife quickly jotted these lines down in her diary lest his literary awakening was lost forever.

But after that nothing happened. Not a single verse came out from his pencil, pen or ballpoint-pen. We cajoled him and coaxed him but to no avail.  He and verse, the twain did not meet ever again. Mind you, he often got stars for his compositions in school. But we could never coax out a verse from his pen ever.

So, what had happened? I know one verse does not a poet make. But he had imagination –which indeed he still has in abundance- and a huge enthusiasm for reading. So why did he not carry on from his King and Queen poem? Was there something which I and my wife, as parents, should have done differently? Was there something which his teachers should have done differently? Or, was he not wired to be a poet at all?

I do not have the answers.

 What do you think? Do you have the answers? Or perhaps some pointers where I and others could find the answers?

As a parent, I admit that I am a little technologically challenged. My son never misses a chance to call me that whenever I fumble with my new mobile or I get horribly entangled in the workings of a new gizmo. But this is only one among the many challenges that I have faced. Long before I was called technologically challenged, I realized that I was numerically challenged (my taxonomy) as well. While my fellow first graders added up a given sum like a breeze, I struggled to keep up. So, what made my other fellow first graders tick? It turns out there is this thing called ‘number sense’ that was not quite prewired into me. But the good news is that the challenge can be met by intervention and support. In other words, once numerically challenged does not mean always challenged likewise.

So, what is number sense? A definition given by Kalchman, Moss and Case says:

“The characteristics of good number sense include: a) fluency in estimating and judging magnitude, b) ability to recognize unreasonable results, c) flexibility when mentally computing, [and] d) ability to move among different representations and to use the most appropriate representation.”

Still, gobble-de-gook to you? It was a little foggy to me as well till I chanced upon the key components that make up number sense. Let us discuss this a little.

Strategic Counting

Counting efficiently happens to be an important ingredient of number sense. Pundits say that efficiency in counting is strongly related to knowledge of counting principles.

A Tip to Develop Strategic Counting Skills: One of the counting principles is to adopt ‘minimum strategy’. Once a child possesses this minimum strategy, if asked “what is 8 more than 3,” she will automatically know that it is much more efficient to reverse the problem to 3 more than 8, and simply “count on” from 8. Of course minimum strategy is not rocket science for us adults but for the young ones this is like Archimedes’ Eureka. She has to know the commutative principle of addition. (And for the uninitiated, commutative principle of addition simply means, 8 + 3 is equivalent to 3 + 8.)

Magnitude Comparison

As children develop keener understanding of number and quantity, they are able to make more complex judgment of magnitude, albeit with different proficiency levels. For example, when I was in grade one I possibly knew that 8 mangoes are more than 3 mangoes but my son when he was in the same grade knew that 8 mangoes are 5 mangoes more than 3 mangoes. If you ask five kindergartners that if there is only one pizza in the kitchen and all of you race to get it, would all of them get one? They would probably give you the right answer and this will be their gross magnitude judgment. However, if you ask how many of them will not get one pizza they would probably get stumped by the question. The ability to make finite magnitude comparison is critical to the ability to calculate.

Retrieval of Arithmetic Facts

A good indicator of sound number sense is smooth transition from counting on fingers to mental calculation. When I reflect back to my early days in school, I recollect that my transition was a little painful. Indeed as the complexity of the additions increased, I wished at times that I had more fingers than ten to count with. This deficiency suggests underlying problems which experts call semantic memory.. (OK, semantic memory is an easy one. It is the ability to store and retrieve abstract information efficiently). This ability appears to be critical for students to succeed in mathematics and, ultimately, to understand mathematics

Numerical Recognition

Children begin to learn about the written symbol system for numerals before they enter school. At least, our house address and our telephone number were drilled into me again and again. The idea was, that God forbid, if I ever got lost I could blurt out ’123, Lost Valley’ efficiently and as if on reflex. This was eons before spotting lost kids through GPS became fashionable. However, this method was associated with description of our house. Things became tougher in the school settings. Here numbers are used in abstract computations. For example, working out how to solve a simple addition problem depends on a student’s recognizing the number symbols and then using other facets of his mathematical understanding, including the concepts of magnitude comparison, and counting. Here ones numerical recognition prowess was needed to be developed.

Now that I have introduced you to ‘number sense’, you have probably realized that the ideas given out here are not intuitive; some may have it some may not. It is as if  ‘number sense’ is ones sixth sense. The trick obviously is to  spot the deficit of the ingredients in a child and intervene with methods to make up the deficit. We have given an example  how to bolster a child’s strategic counting skills by adoption of the minimum strategy method. You can similarly find ways to perk up your child’s number sense.