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 Groupings, Shopping Lists, and Vectors: The Series
 Operators, Functions, and Properties  part 17
 Notes on Representation  Tally Marks
 Operators, Functions, and Properties  part 35
 Notes on Deferred Computation  the Pythagorean Spiral
 What is Multiplication  the Series
 The Whole and the Parts  Memory and Hysteresis
 Groupings, Shopping Lists, Vectors: part 17
 Math in the Comics  part 9
 A Multiplication Nomograph

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Tag Archives: unlearning
Operators, Functions, and Properties – part 30
In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out. This is a hugely important subcategory of operators, but singlein singleout operators aren’t … Continue reading
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Tagged extending patterns, models, unlearning, whole vs. parts
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Representations – Black Boxes – Equivalence 2
We ended the previous post in this series by looking at this figure: To recap, a black box is something where we have access to the behavior but not the internal organization. We can propose a model for a black … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, models, representations, reverse engineering, unlearning
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Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
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Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
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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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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: Notations
When you think of operations as having a front office component and a back office component, where the front office component provides the public face and the back office component provides the implementation, as we first introduced in the post … Continue reading
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Tagged denominations, extending patterns, models, naming, representations, reverse engineering, unlearning
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