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A Collatz-Inspired Puzzle
This is a puzzle. In prior posts, I used the Collatz Problem, restated here: Each counting number n past 1 is assigned a successor number, as follows: The number “1″ is considered home, and when you’re...
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Operators, Functions, and Properties – part 23
In this series, we’ve been looking at operators as something that modifies the state of some machine or device, usually triggered by the pushing of a button. We’ve looked quite a bit at operators that...
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Operators, Functions, and Properties – part 24
In the previous post in this series, we started to model recurrence relationships with state machines: The idea is that we have a device with two buttons and a screen; after we press the Start button,...
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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....
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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...
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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...
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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...
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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...
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Mathematical Notation and Schools – 12
Functions: Standard Notation and Schools In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning. The focus here is modest: on...
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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...
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