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Sunday, October 21, 2012

Eleven Plus Certainty

A teacher, who was very well known for gaining outstanding eleven plus successes, took a bit of a gamble by trying a fresh approach. For years the teacher would only take on children she thought would pass. Parents would do almost anything to try to entice her to tutor their children.

She asked prospective parents if they would be prepared to take part in a trial. The teacher maintained that she would take on any children for the eleven plus – whether they were eleven plus material or not. Of course the floodgates opened as playground gossip swept across the schools. All parents were asked to do was text a number with the single word `please’.

The twenty five children to take part in the trial were then drawn at random from the hundreds that applied. (The eleven plus teacher had just completed a statistics module in her further studies.) She predicted that that the probability of all 25 passing was 0.3.

This gave the intrepid teacher some food for thought. She postulated that:

F              Four or fewer would nearly pass
S              Six would pass
                More than two would fail dismally.

The teacher had to take into account that some families would have to drive long distances – and may be forced to drop out. Other children could simply leave the scheme before taking the examination. The teacher wondered that if she actually started with forty children she may land up with twenty five.  She did not know the drop-out rate for eleven plus children who were not certain to pass.

Some even plus parents may have had to re-study probability as they work with their children on exercises and papers and will recognise the nature of this problem. Essentially the chosen twenty five will either pass or fail. If more pass than those predicted is the teacher a `super teacher’? If more fail than those predicted is the teacher a charlatan and a fraud? Will the teacher build her reputation or lose it?

Is there any certainty in the eleven plus?