Monday, August 20, 2012

Mortensen Math vs. Traditional Teaching

The Difference is Important to Your Child's Success

Parents educated by traditional math teaching, based on memorizing facts, rules, formulae and process, often do not recognize that MM is dramatically different and pass on by, overlooking the tremendous benefits to a method that is based on imagination, visualization and sets nothing less than understanding as its goal.

Our first job as MM educators is to decode this mathematical language into a spatial reality; take for example 4x3=12

All we do in math is count.

See all numbers as rectangles.

Know what one is.

From the above example, picture a rectangle that is four "over" and 3 "up," count the total unit squares.

See 12.

It's that simple.

This: 1, is not one. It is only the name of one written in arabic numerals.

What does one look like?

therefore 4x3=12 looks like this:

more at:


Saturday, August 18, 2012

The additivity of small numbers.

I consider myself liberal-minded when it comes to tolerating the opinions of others. I would rather try gently to persuade them to re-think a problem about which I think they are mistaken than to ban them from expressing their erroneous thinking out loud, after all, I too have been wrong on occasion.

However, I am losing patience with those who claim climate-change theory is a fraud, perpetrated by scientists who have a personal agenda less than scrupulous. In particular I am disturbed by those who deny the notion that human industry has had an impact on climate and will continue to do so. The nay-sayers will nit-pick about any data error and then demand that the entire enterprise be abandoned, presumably because they see nothing amiss in the world that might be prevented from worsening by doing something like say, burning less coal, or turning off unnecessary lighting.

Even those who claim to know some math have said, and are saying, that human activity is not affecting the natural cycle of climate. To them I say, there is something called the law of additivity of small numbers which goes roughly like this: no matter how large a number is, there will always be enough small numbers that, if added together, will exceed it.

What I am driving at is this, maybe one farmer cutting down a forest and planting a single crop for enough years to exhaust the field leaving it unable to absorb C02, or perhaps one coal-fired electricity generator, will not produce orchids in Greenland, but I maintain that if enough of them exist it may happen. By the way, orchids are nice but where does all the ice go?

A mere 7 Billion people burning fossil fuels, destroying forests, creating deserts, clogging rivers and harbours and fish habitat, poisoning lakes with phosphate fertilizer run-off, massacreing sharks for their fins, slaughtering lions and rhinos for aphrodisiacs, etc. may not destroy the planet today. But by 2050 there will be 9 Billion. By 3000 who knows. If you think 7 billion won't kill the planet or alter the climate, you surely must concede that there is SOME number of people who could. It took a huge number of Chinese with buckets to move a mountain to build the 3 Rivers dam, but they did it.

There used to be forests in Sudan, now there is only desert. When only a few bedouin took trees for firewood the sands were held at bay, but when millions burnt wood for cooking, and heat the desert took over. Man destroyed the local climate and he didn't need bulldozers and dynamite. They did it with their bare hands, one twig at a time. Just like the Chinese built the dam.

Kill one coyote, no problem; kill enough of them and the jackrabbits will eat the entire grazing lands leaving no food for cattle. One grasshopper, no problem; a million locusts and you have famine, it's about the additivity of small numbers.