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        riddles >> general problem-solving / chatting / whatever >> number line curio
        
(Message started by: Noke Lieu on Jan 15^th, 2009, 8:39pm)

Title: number line curio
Post by Noke Lieu on Jan 15^th, 2009, 8:39pm

At a conference, I was exposed to students failures with the concept of the "number line" and the interplay between decimals and fractions.

The biggest shock was that the "students" were final year trainee teachers.

However, there was one "failure" that got me thinking... curly.

One of the chief tests was along the lines of:

given an otherwise blank line marked
-1, 0 and 1
on a number line, place the values 1/3, 5/6, 0.253, 1/100, 0.99 and -11/13

There was an example of the student's work that had everything in the correct order, though the spacing was significantly wrong.
I wondered (quietly) whether that student was adopting a topological stand point, or genuinely had no appreciation for the scale of the fractions (which would have been countered by them getting them in the correct order).

That got me further thinking- well, couldn't you have a number line with a log scale to it?
Or couldn't it be wiggly (though without looping) and it still be legitimate.

Perhaps not as helpful, but perhaps an interesting point of discussion in a classroom?

Title: Re: number line curio
Post by pex on Jan 16^th, 2009, 12:29am

on 01/15/09 at 20:39:08, Noke Lieu wrote:

well, couldn't you have a number line with a log scale to it?

But where would you put zero?

Title: Re: number line curio
Post by towr on Jan 16^th, 2009, 1:28am

on 01/15/09 at 20:39:08, Noke Lieu wrote:

That got me further thinking- well, couldn't you have a number line with a log scale to it?

Actually, a log-scale is the natural state of the number line. If you ask hunter-gatherers to put quantities on a line they'll use a logscale. As do children that haven't been taught the linear scale yet.
(There should be some articles and research if you look for "number sense hypothesis")

Title: Re: number line curio
Post by towr on Jan 16^th, 2009, 1:31am

on 01/16/09 at 00:29:13, pex wrote:

But where would you put zero?

The same place where most people put it until the Indians came up with it: nowhere.