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Q&A #10489

Teachers' Lounge Discussion: Graphing: discrete vs continuous data

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From: Chris <bell.christine54@googlemail.com>
To: Teacher2Teacher Public Discussion
Date: 2010092317:26:04
Subject: Discrete vs continuous data

	
Hi There!
I ended up on this site by pure coincidence. Actually, I was looking
for something else.

Anyway, I'm a bit baffled by the explanation. I wonder why amounts of
things on bar charts (cyclists cycling away - how many left?) and
miles vs time. Seems like apples and pears to me. I've been out of
school for a while, but my work involves a bit of maths.

Let's say you have two systems recording music.

Discrete: your system samples the music. That means it takes sort of
snapshots. For simplicity, let's say every second. That means you have
a distinct value for every second. Don't join the dots. (saying that,
in further maths you might want to do just that ... but let's leave
that)

              |
              |        |
     |        |        |
     |        |        |
 ---------------------------> t in seconds

Continuous: your system is continuously recording the music. In this
case you would have a curve as you have a value for every moment ..
err all the time ... or let's say you have no gaps.

In this case discrete is digital and continuous is analog. There are
all sorts of other topics in discrete maths. E.g. set theory,
logic,...

I don't understand why amounts of things on a bar charts are mixed
with something vs time. Surely that must be confusing for the kids.
Wouldn't it make sense to teach that separately from anything on
cartesian coordinates?

Understanding the whole concept is quite important when you move to
calculus. I didn't go to school in the UK or US and charts with
amounts in bars (you know, like amount of kids in school on Monday,
Tuesday,...) were never taught with cartesian coordinates (x and y or
something vs time). They were two very different things and I never
confused them.

Actually, another thing I don't get is why 'discrete calculus' isn't
taught before continuous. Once you work with discrete values, the
concept of integrating and differentiating really is a doddle.

A great way to teach discrete maths could be to use programming since
you can only input discrete values. Once I had to model/program a real
life maths problem the whole seemingly abstract thing became so
simple. 

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