Tag Archives: denominations

Operators, Functions, and Properties – part 14

In earlier parts of this series, we’ve looked at operators that take a number coming in, and produce a number coming out.  We’ve looked at stringing these operators together in a chain, and we’ve looked at combinations of operators that … Continue reading

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Operators, Functions, and Properties – part 13

In this series, we have been looking at little machines that do things like “add 2”, and we’ve been chaining such machines together by connecting the output of one to the input of the next.  We’ve been exploring the behavior … Continue reading

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Representations – Black Boxes – Equivalence 2

We ended the previous post in this series by looking at this figure: To recap, a black box is something where we have access to the behavior but not the internal organization.  We can propose a model for a black … Continue reading

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First, Do No Harm

Wouldn’t that be a great stricture for Math Education to adopt, just like medical professionals do?  Whatever else you do, make sure you do no harm. You’d think that this would represent a really low standard of math education: that … Continue reading

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Groupings, Shopping Lists, Vectors: part 24

In this series of posts on the topic of vectors, I’ve been primarily interested in playing with situations in which the notion of a vector naturally arises.  Looking at shopping lists was one of those.   A shopping list is … Continue reading

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Groupings, Shopping Lists, Vectors: part 23

In this post I’m going to look at something usually referred to as linear combinations.  In the prior post, we had an occasion to look at coordinate systems where the axes are not at right angles.  We saw that you … Continue reading

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Groupings, Shopping Lists, Vectors: part 22

In the last few posts in this series I’ve examined some consequences of British values, where we have pounds and shillings (and also pence) – but then have this other value, the guinea, which equals one pound and one shilling.  … Continue reading

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Groupings, Shopping Lists, Vectors: part 21

In the previous post in this series, part 20, I showed a matrix multiplication to convert a value stated in guineas and shillings into one stated in pounds and shillings.  We were interested in the same value, expressed in different … Continue reading

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Groupings, Shopping Lists, Vectors: part 20

In England, the main currency is called the pound.  Smaller units are called shillings and pence.  A pound is 20 shillings, a shilling is 5 pence, hence a pound is 100 pence.  This system has been in place since 1971; … Continue reading

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Groupings, Shopping Lists, Vectors: part 19

In this post, I will try to connect a set of equations with matrices and vectors in a way that isn’t simply a notational shift.  In part 18 of this series, I brought up the vast preponderance of square matrices … Continue reading

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