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
 Mathematical Notation and Schools – 14
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 Mathematical Notation and Schools – 12
 Mathematical Notation and Schools – 11
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 Mathematical Notations and Schools – 7
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 Mathematical Notation and Schools – 5
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 Mathematical Notation and Schools – 3
 Mathematical Notation and Schools – 2
 Mathematical Notation and Schools: The Series
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Tag Archives: black box
Mathematical Notation and Schools – 14
Functions: Variant Notations In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning. In the prior posts, we started to explore function notation, which in middle school and … Continue reading
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Tagged black box, deferred computation, denominations, education, equivalence, math class, models, naming, notation, representations
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Mathematical Notation and Schools – 13
Functions: Standard Notation and Schools, Continued In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning. In the previous post, we started to explore function notation, which in … Continue reading
Posted in Uncategorized
Tagged black box, education, equivalence, math class, naming, notation, recurrence relationship, representations
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Operators, Functions, and Properties – part 43
In the last several posts in this series, we’ve looked at cyclical patterns of behavior of numbers and operators. For example, in the previous post we saw that when counting up, the last digit of a number consistently repeats after … Continue reading
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Tagged black box, equivalence, models, representations, reverse engineering, whole vs. parts
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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 41
In this series, we’ve pictured operators as black boxes with inputs and outputs. In the previous post we looked at rather ordinary addition from a less ordinary perspective: we imagined the number line arranged as a cylindrical spiral, like a … Continue reading
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Tagged black box, equivalence, extending patterns, models, representations, state
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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
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Tagged black box, denominations, equivalence, invariants, lookup, reverse engineering
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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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