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# Re: [Phys-L] teaching data analysis in high school

• From: John Denker <jsd@av8n.com>
• Date: Wed, 03 Oct 2012 06:42:11 -0700

Note that I changed the Subject: line because I strongly recommend
the terms "uncertainty" and "data analysis" rather than "error
analysis". There are some students (and others) who cling to the
idea that errors are Wrong (with a capital W) in the same way that
stealing is Wrong.

Taylor unhelpfully puts a memorable picture of a crashed train on
the cover of his book. This is /not/ the sort of "error" that we
expect in typical physics experiments.

On 09/30/2012 07:33 AM, Jeff Bigler wrote:

My question for the list is: what else would it be useful (and
practical) for kids to learn about error analysis in high school?

would be most useful for kids to learn in school?

Probability is important for all sorts of physics and non-physics
applications:
-- uncertainty and data analysis
-- thermodynamics
-- quantum mechanics
-- game design and game-playing strategy
-- military strategy
-- communication including data compression and encryption
-- pattern recognition
-- etc. etc. etc.

Despite its importance, it gets amazingly little attention in the
ordinary curriculum.

Most of my students have not taken a statistics course,

A statistics course? In high school? Yuck. That is not what I am
suggesting.

IMHO the best approach is to inculcate probability ideas gradually,
in the context of applications. It's a two-way street:
*) the applications are needed to motivate the math
*) the math is needed to understand the applications

For example, the first time a probability-related application (such as
uncertainty) comes up, one could enrich the presentation as follows:
-- here are the set-theoretic axioms of probability
-- here is a scatter plot
-- here is a histogram
-- here is a probability /density/ distribution
-- here is a /cumulative/ probability distribution
-- etc.

You don't need to make a super-big deal out of it; it's a minor
part of the overall discussion of the application.

Then the second time a probability-related application comes up,
you can continue the inculcation:
-- here again are th set-theoretic axioms of probability
-- here is a 2D scatter plot
-- here is the joint probability
-- here are the marginal probabilities
-- here are the conditional probabilities
-- note that two probability /density/ distributions will never
converge in a nice way
-- OTOH note that there is a nice natural notion of convergence
for the corresponding /cumulative/ probability distributions.
-- etc.

A lot of physics teachers are worried that teaching the math will
slow down the physics course. I guess that's a true (by a little
bit) in the short term ... but it's diametrically wrong (by a lot)
in the long term. Scrimping on the foundations is a disaster in
the long run. Perhaps the leading example of this is thermodynamics.
Thermo is all about probabilities and multi-dimensional derivatives
... yet people try to teach thermo to students who have no clue
about probabilities or multi-dimensional derivatives. The result,
typically, is a horror show.

Again: the house built upon sand is easier in the short run, but
the house built upon rock is vastly better in the long run.

============

The giant hole in my argument is this: Typically the textbook doesn't
provide much support for this approach, which leaves the teacher and
the students in a bad position.