Monthly Archives: August 2009

Representations – Black Boxes

Posted on 2009/08/31 by Bert Speelpenning

The idea of a “black box” is common in engineering, but the idea has much wider application.  It’s a simple idea, really.  Just imagine something that has an inside that is inaccessible from the outside.   Easy, right?  For example, a … Continue reading →

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Representations – Number and Some Alternatives

Posted on 2009/08/25 by Bert Speelpenning

There are lots of ways to represent number – such as the number “ten”.  As grown-ups, we’re so used to a particular way of representing “ten” that we don’t often stop to think about what we’re doing – we just … Continue reading →

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Representations – Formulas and Some Alternatives

Posted on 2009/08/23 by Bert Speelpenning

There are systems of notation for mathematical expressions that are in wide use.  One of them is so widely used and so well-known that we often think of it as the only one, the real one, the true one and … Continue reading →

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Representations – Foreground and Background

Posted on 2009/08/14 by Bert Speelpenning

It is pretty clear that a representation of something is not the same as the something itself.  “A map is not the territory” Korzybski wrote famously, and most of us would react “well, of course!”  You would expect to encounter … Continue reading →

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Representations – Processes and Snapshots

Posted on 2009/08/10 by Bert Speelpenning

When we talk about representation in mathematics, it is surprising how often we limit ourselves to looking at formulas.   Pictures, diagrams, graphs and tables are also part of how you can represent mathematical ideas and mathematical thinking.  Most representations of … Continue reading →

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Key Math Ideas Not Taught In School – Transactions II

Posted on 2009/08/04 by Bert Speelpenning

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 – Transactions

Posted on 2009/08/02 by Bert Speelpenning

Things take time.  As the saying goes, time is God’s way to keep everything from happening all at once.  There is a sequence to solving a problem, and even the most rote-based solutions tend to involve multiple steps.  You may … Continue reading →

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