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Tag Archives: invariants
Key Math Ideas Not Taught In School – Transactions II
This post is a continuation of the prior one, but won’t yet deliver on showing a direct connection between transactions and the kind of thinking we typically call mathematical thinking. In the previous post, I introduced the idea of a … Continue reading
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Tagged extending patterns, invariants, models, representations
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Key Math Ideas Not Taught In School – Invariants II
I want to add a bunch more examples to my prior post about invariants. I intend these examples to be relatively straightforward, and flesh out the key idea behind invariants. To this end, I’m using examples of more elaborate computation … Continue reading
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Tagged extending patterns, invariants, models, representations
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Key Math Ideas Not Taught In School – Invariants
“Counting” involves a number of different mathematical ideas If you watch really young children count, you may notice that they aren’t all doing the same thing. For some children, counting “onetwothree” is done in very much the same way as … Continue reading
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Tagged education, invariants, math class, models, reverse engineering, unlearning
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Key Math Ideas Not Taught In School
There is a shape, a progression, to the typical school curriculum from Kindergarten through High School, at least in the United States, and this progression hasn’t changed much in the last 50 years or so. We’ve gotten used to this … Continue reading
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Tagged education, extending patterns, invariants, math class, models, representations, reverse engineering, unlearning
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Quantity – Different Kinds of Numbers: Scalars
We’re used to representing quantities by numbers. In this series we’ve been looking at different kinds of quantities, and how certain actions on the numbers are meaningful for some kinds of quantities and meaningless for other kinds of quantities. It … Continue reading
Quantity – Different Kinds of Numbers: Intervals
It is useful to look closely at this graph taken from a Wikipedia article on misleading graphs: The reason given for the graph being misleading is familiar to most of us: the labels on the vertical axis don’t start at … Continue reading
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Tagged extending patterns, invariants, models, representations, unlearning
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