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*From*: "John Clement" <clement@hal-pc.org>*Date*: Sat, 19 Jan 2013 09:57:36 -0600

The mathematics of this technique serves a test of proportional reasoning in

the Doors video. They give a scenario of frogs in a pond and initially all

the caught frogs are marked. Then on the second part of the experiment a

number of frogs are caught it it is recorded how many were marked or

unmarked. Students are asked to figure out how many frogs are in the pond.

The video shows 3 different students each using different reasoning, and

only one got it right. The majority of students get it wrong and a large

number of students just add some of the figures together, while others do

some multiplications, but no ratios. Of course the students are not

bothered with figuring the STD or any uncertainties. The point of the test

is whether they can use "simple" proportional reasoning.

So before taking an ecology sequence students need to have proportional

reasoning, and I suspect most do not.

John M. Clement

Houston, TX

It happens too rarely: stumbling across a method of clever simplicity.

Take the ecologist's way of estimating populations:

catch a sample and mark the specimens then release them.

After enough time for the sample to have mixed well with the

local population, take another sample, mark them differently

and note how many were marked in the previous sample.

The population estimate can be generated from just this data

- though follow on samples would usually be taken.

The estimated population is given by the first count times

second count divided by the number

re-caught of those marked first time.

Justification: it is reasonable to suppose that the number in

the second sample includes the number previously marked in a

similar ratio to the number in the entire population

compared with the number in the first count.....

Brian Whatcott Altus OK

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**References**:**[Phys-L] Estimating animal populations***From:*brian whatcott <betwys1@sbcglobal.net>

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