Quantity – The Series

In this series, we take a leisurely look at quantities of different kinds.  It is rather interesting to find out that there are more than one kind of number, based on what operations make sense to perform on them.  For example, you probably have subtracted dates before: the age on their birthday of somebody born in 1951 is 2010 (current year) – 1951 (birth year).  In contrast, I doubt very much you ever had reasons to add two years like that: 2010 + 1951 is not something people commonly do with dates.  Though you can add the associated numbers (and your calculator will gladly add them for you), it is not clear what kind of real-world question 2010 A.D. + 1951 A.D. is the answer to.

Quantity – Different Kinds of Numbers – an introduction to the topic

Quantity – Different Kinds of Numbers: Keys – numbers with which you can do very little – and that is by design.

Quantity – Different Kinds of Numbers: Intervals – numbers where only differences are important.  For some reason, this post is the most popular post on the entire blog!  It doesn’t deserve to be.  I think teachers ask their students to do searches for misleading graphs.  Then this post comes up.  Or maybe it is the teachers who are doing the searching.

Quantity – Different Kinds of Numbers: Scalars – the way your calculator thinks of numbers.  You can add, subtract, multiply and divide them.  This is the way most of us think of quantities as well.   Five balloons divided by two kids – that’s 2.5 balloons per kid, right?

Quantity – Different Kinds of Numbers: Vectors – a first look at situations where one number won’t do to describe what you think of as a single thing, e.g. Jeans sizes expressed as 34×32.  They really don’t mean 1088!

Quantity – Different Kinds of Numbers: Classes – a look at (common) situations where there is an inside and an outside, a front office and a back office, an interface and an implementation.  In this post, we look at a bank and its interface to customers.  “Money” looks different to a bank than it does to me.  To me, I think in terms of $20 bills that come out of the ATM machine.  The bank thinks of bills as a bother, an expense.  The bank would much rather think in terms of megabytes of data on a disk drive or on a wire.

Quantity – Different Kinds of Numbers: Notations – a look at confusion (and amazing lack of confusion) in situations that seem ambiguous.  How come 333-60-5798 looks like a social security number and not a bunch of subtractions?  How come $2.9 is incorrect for 2 dollars and 9 cents?  And what does any of that have to do with different kinds of numbers?

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About Bert Speelpenning

http://unlearningmath.com is my blog on math learning and math teaching. My background is in the high-tech computer software industry (I've got a PhD in Computer Science from the University of Illinois) and worked for Hewlett Packard, Silicon Graphics, Borland and finally for Microsoft till I left in 2000. I have since worked in the area of math learning, with students (7-9th grade) and teachers (elementary school level). I own an independent educational consulting business called Math Partners.
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