Top Posts
 The Whole and the Parts  Packaging
 What is Multiplication  part X
 The Whole and the Parts  The Series
 "Ontogeny recapitulates phylogeny" in math education
 Notes on Deferred Computation  the Pythagorean Spiral
 Groupings, Shopping Lists, Vectors: part 18
 The Whole and the Parts  Feedback Loops
 The Whole and the Parts  The Prisoner's Dilemma
 Operators, Functions, and Properties  part 29
 Operators, Functions, and Properties  part 39

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 Mathematical Notations and Schools – 15
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 Mathematical Notation and Schools – 2
 Mathematical Notation and Schools: The Series
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Tag Archives: invariants
Operators, Functions, and Properties – part 42
In this series, we’ve been looking at black boxes, where you put something in and something comes out. From looking at its behavior, you can often propose a model for what is happening inside. If you build the model, and … Continue reading
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Tagged black box, equivalence, extending patterns, invariants, representations, reverse engineering
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Operators, Functions, and Properties – part 40
In this series, we’ve spent considerable space playing with operators, which we’ve pictured as black boxes with inputs and outputs, often as part of a machine with state. In more recent posts, e.g. this one , we’ve looked at operators … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, invariants, lookup, reverse engineering
3 Comments
Operators, Functions, and Properties – part 39
In this series, we’ve been looking at operators in various settings, and looked for ways to use them to shine a different colored light on some aspects school math. In the last four posts, we’ve explored the notions of equivalence … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, invariants, lookup, models, naming, recurrence relationship, representations
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Operators, Functions, and Properties – part 37
In this series we’ve looked at boxes that take certain inputs and then produce an output. We’ve called such boxes operators, and we’ve thought of them in many different ways. In some cases, the boxes perform arithmetic; in other cases, … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, invariants, models, representations, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 34
In the previous post in this series, we looked at some operators that take in two numbers and produce some kind of pair of numbers, an ordered pair, in a way that can be reversed. Here’s another way to produce … Continue reading
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Tagged black box, denominations, equivalence, invariants, models, representations, reverse engineering
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Operators, Functions, and Properties – part 32
In this series, we’ve been looking at a model for presenting and analyzing operators with an intention for it to have applications for students learning math in school. In recent posts, we’ve looked for interesting aspects of school math that … Continue reading
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Tagged denominations, extending patterns, invariants, models, naming, representations, reverse engineering
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Operators, Functions, and Properties – part 25
In this series, we’ve looked at operators in various ways. Recently, we’ve looked at state machines that invoke the same operator repeatedly, and generate a sequence of numbers in doing so. Conversely, sequences of numbers can often be modeled as … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, invariants, recurrence relationship, representations
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