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It Pays To Say That Your Child’s Ability Is Tops: What You Say Is What You Get!

May 28th, 2009 venkatesh No comments

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.
He introduced a concept called “Self fulfilling Prophecy”. This concept has since been bandied around a lot by a whole lot of sociologists and others. Not the least amongst them was those that made it into a rallying point. For example, invoking this concept, an American President tried to verbally buttress an ailing economy. The idea behind this concept is very simple. Let me quote, Jon Clark and Sohan Modgil from their book, Robert K Morten. Self fulfilling prophecy they say is:
The notion that a false but widely believed prediction could become true, simply because
enough people believed in it….
And continuing with their explanation:
The self-fulfilling prophecy begins, according to Merton, with the false definition of a situation,
which in turn engenders behaviour that brings the conformity with the definition.
I know, this is a little dense, but wait, I am getting to the exciting part.
Rosenthal, a researcher at Harvard, hypothetised that ‘self fulfilling prophecy’ should work at the classroom level too. Joined by Jacobson, he conducted his famous ‘Pygmalion in the Classroom’ experiment.
In Oaks School, located in an underprivileged area of San Francisco, they started their experiment. The children were administered a little known IQ test. The test had a fancy name: “Test of Inflected Acquisition”. This was in keeping with the high profile resume of the experimenters. The teachers were told that investigators from Harvard with their ‘Test of Inflected Acquisition’ could identify the potential ‘bloomers’ amongst the students; ‘bloomers’, meaning the students whose IQ was expected to shoot up substantially. The ‘bloomers’ were identified and the list was shared with the teachers. Now, this was a dummy! The list had nothing to do with the test; the children were picked randomly. Difference, if any, in the intellectual prowess of the ‘bloomers’ and the others, existed only in the minds of the teachers.
The teachers’ attitude towards the ‘bloomers’ changed. Their new attitude facilitated and encouraged the ‘bloomers’ success.
A second intelligence test was administered at the end of the year. Those students who had been identified as stars showed, on average, an increase of more than 12 points on their IQ scores, compared to an increase of 8 points among the rest of the students. The differences were even larger in the early grades, with almost half of first- and second-grade bloomers showing an IQ increase of 20 points or more.
The investigators concluded that self fulfilling prophecy was at work. But why was there less intellectual development in the higher grades? Rosenthal and Jacobson have this to say:
…. it is possible that teachers react to children of all grade levels in the same way if they believe them to be capable of intellectual gain. But perhaps it is only the younger children whose performance is affected by the special things the teacher says to them; the special ways in which she says them; the way she looks, postures, and touches the children from whom she expects greater intellectual growth.
Before you lay all the blame at the door of the teacher let us also see what Rosenthal subsequent research in 2002 has revealed. He demonstrated that “the expectations of psychological researchers, classroom teachers, judges in the courtroom, business executives, and health care providers can unintentionally affect the response of their research participants, pupils, jurors, employees and patients.” Clearly, most of us are affected by the self fulfilling prophecy; teachers, parents, almost everyone!
The trick, therefore, seems to be to reinforce our children’s intellectual development through positive self fulfilling prophecy. Tell them they are good and they will become good. What you say is what you get!

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!


Numerically Challenged? 4 Ways to Meet the Early Maths Challenge

May 8th, 2009 ashis No comments

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.

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