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Monday, April 27, 2015

The Twilight Zone: PD Day style

This illustration is wrong. Can you see why?
 
It seems Barbie should not have been ridiculed for admitting she found math class tough. The Barbie doll making the confession was yanked from the shelves and the offending words banished from her vocabulary. Now, it is clear that the Ontario Ministry of Education along with quite a number of teachers in London, Ontario, are also befuddled by math.

Professional development days, or PD Days as they are commonly called, are held by the Ministry of Education to teach teachers. A recent PD Day in London focused on improving the teaching of math in city schools. The lesson contained a glaring error. This is bad enough in itself, but how this obvious blooper slipped by numerous teachers is concerning.

The teachers were told two growing puppies both gained three kg. The first dog went from a weight of five kg to eight kg while the second went from three kg to six kg. The teachers were asked: Which puppy grew the most? For added clarity, an illustration was provided comparing the growth of the two dogs.

Unfortunately, the illustration is wrong. Rather than correcting errors in proportional thinking, the illustration promotes one of the very myths the PD Day should have been addressing. The doubling of the external dimensions of something, say a figurine, does not double its weight nor double it area. Some 26 years ago, The National Council of Teachers of Mathematics noted the surprising acceptance of this myth among math teachers.

Doubled weight? Wrong!
The second dog doubled its weight. It did NOT necessarily double in height, width and depth as well. As a former art student I know this problem well. Sculptors make small scale models, maquettes, before starting the full-sized piece.

If a small sculpture of a dog takes 1 kg of clay, the same sculpture doubled in size requires 8 kg of clay. Doubling the length, width and depth does NOT double the amount of clay required but increases it by a factor of eight.

How the little dog in the illustration only doubled its weight while expanding eight times in volume is not a riddle; It is an impossibility.

In a ministry of education publication, Paying Attention to Spatial Reasoning, the ministry reports that the National Research Council calls errors in the teaching of spacial reasoning a “major blind spot . . . locked in a curious educational twilight zone . . . "

Well, welcome to the Twilight Zone, London PD Day style.

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