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Tag Archives: reverse engineering
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 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, look-up, reverse engineering
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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 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 33
In this series we have looked at various examples of operators, and most of our attention has been on operators where what comes out is a number, and what comes in is one or two numbers. Some examples of two-numbers … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, models, reverse engineering, whole vs. parts
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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 31
In the prior post in this series, we looked at the kind of operators typically encountered in school (K-12), whether or not they are called operators. Many of them are single number input – single number output, but not all. … Continue reading
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Tagged black box, equivalence, models, naming, reverse engineering, whole vs. parts
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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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Learning and Unlearning Math 