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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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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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 “one-two-three” is done in very much the same way as … Continue reading

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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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Quantity – Different Kinds of Numbers: Classes

Let me recap what this series of blog posts has been about.  I’ve been looking at different kinds of quantities, different kinds of numbers.  I started with observations like: it’s meaningless to add 1951 AD to 2009 AD but completely … Continue reading

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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

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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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Quantity – Different Kinds of Numbers: Keys

I introduced this series by noting that there are different kinds of numbers – more precisely, different kinds of quantities represented by numbers – and that each allows you to draw different kinds of conclusions. The most basic kind of … Continue reading

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Quantity – Different Kinds of Numbers

We’re very used to representing quantities by numbers.   The cash register will tell us how much we have to pay, and the pump at the gas station will tell us how much gasoline we poured into our tank, and the … Continue reading

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What is Multiplication – the Series

Here’s a summary of the series (thus far) of posts on multiplication, with links. This allows you to read them in order, from oldest to most recent. The series grew from a concern raised in the post Middle School Math … Continue reading

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