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Monthly Archives: March 2009
Relationships – Percentages
If I ask you to count, starting at 103, for five counts, you do so by keeping track of two quantities. You keep track of them in your head, by speaking out loud and listening to what you just said, … Continue reading
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Tagged denominations, education, extending patterns, models, naming, representations, reverse engineering, unlearning
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The Whole and the Parts – Where Units Really are Arbitrary
After several posts where the entire point was to highlight situations where the whole is more than the sum of the parts, I thought it would be interesting to bring in a contrast. In this post, we will look at … Continue reading
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Tagged denominations, extending patterns, models, naming, reverse engineering, unlearning, whole vs. parts
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The Whole and the Parts – Memory and Hysteresis
Imagine I’ve got a sheet of four (square) postage stamps, like this: If I need a single postage stamp, I need to do some tearing, and that tearing takes a bit of time and effort. To tear along a single … Continue reading
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Tagged math class, models, representations, reverse engineering, unlearning, whole vs. parts
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The Whole and the Parts – Feedback Loops with Delay
In my previous post on feedback loops I promised to look at their limitations. I’ll start that in this post, but think I should say a little more about what they are good for first. In the example of a … Continue reading
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Tagged extending patterns, models, naming, representations, reverse engineering, unlearning, whole vs. parts
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The Whole and the Parts – Packaging
My earlier posts in The Whole and the Parts series may have seemed “less mathematical” to you than other posts in this blog. They didn’t involve a whole lot of arithmetic, little notation and few if any formulas. Whatever mathematics … Continue reading
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Tagged denominations, extending patterns, math class, models, representations, reverse engineering, unlearning, whole vs. parts
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Pi Day – How Big Is Pi?
In your time zone Pi Day may already be over. But here, it still is March 14, the traditional day to celebrate Pi. Most kids can rattle off that Pi has the value 3.14 (approximately) and that is used in … Continue reading
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Tagged extending patterns, math class, models, reverse engineering
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The Whole and the Parts – Feedback Loops
Imagine you live on one of the planets around one of the stars in one of these galaxies: Imagine further that you live in a society that has figured out the physics of Newton’s laws, and that this society has … Continue reading
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Tagged extending patterns, models, representations, unlearning, whole vs. parts
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Math in the Comics – part 9
In today’s Dilbert comic, another opportunity to highlight something about how math is held in society. Dilbert, rather desperately, is trying to convince his audience of something. And, somehow, he does! He invokes the Authority of Mathematical Gobbledygook, represented in … Continue reading
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Tagged math in the comics, models, representational proof, representations, unlearning
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Notes on Representation – Copying
In this blog, I’ve surveyed a number of different representation systems for quantities, including the decimal number system, the number line, tally marks, and prime bags, and I’ve tried to see and say something interesting and fresh about each. When … Continue reading
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Tagged denominations, extending patterns, models, naming, representations, reverse engineering, unlearning
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Learning and Unlearning Math 