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Tag Archives: representations
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 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
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 29
In this series, we’ve been looking at simple machines where pushing a button invokes an operator that changes the state of the machine. Stopwatches, coffee makers, calculators are all examples of such machines – some simpler than others. Many of … Continue reading
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Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations
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Operators, Functions, and Properties – part 28
The prior post in this series showed that we can get complex and rich behavior from combining simple operators and feeding their output back to their input (through what is called “state”, and the whole arrangement is known as a … Continue reading
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Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
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Operators, Functions, and Properties – part 26
In the previous post in this series, we linked two state machines together, weakly, by arranging to press their Start buttons at the same time and to press their Next buttons at the same time. As a result, we got … Continue reading
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Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
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