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Monthly Archives: August 2009
Representations – Black Boxes
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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Tagged black box, extending patterns, models, representations, reverse engineering, whole vs. parts
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Representations – Number and Some Alternatives
There are lots of ways to represent number – such as the number “ten”. As grownups, 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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Tagged denominations, extending patterns, invariants, representations, unlearning
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Representations – Foreground and Background
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
Representations – Processes and Snapshots
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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Tagged extending patterns, math class, models, naming, representations
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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 – Transactions
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 rotebased solutions tend to involve multiple steps. You may … Continue reading