Tag Archives: recurrence relationship

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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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 what teachers can do, even if their … Continue reading

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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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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

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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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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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.  Conversely, sequences of numbers can often be modeled as … Continue reading

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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, we can press the … Continue reading

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 operate on numbers, for example … Continue reading

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 home, you stop.  If … Continue reading