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 What is Multiplication  part IV
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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
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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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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
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Tagged black box, equivalence, extending patterns, invariants, models, representations, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 36
In the previous post in this series, we broached the subject of equivalence classes. We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times. We drew a … Continue reading
Operators, Functions, and Properties – part 35
In the previous post of this series, we looked more closely at the mathematical notion of equivalence, through the lens of operators. Specifically, we looked at a split (pair) 213 and then looked at an operator that turns 213 into … Continue reading