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

[John Denker <jsd@av8n.com>]

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?

Let me answer a slightly broader question, namely: What else 
would be most useful for kids to learn in school?

Answer:  Probability.

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
 -- business and finance
 -- 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.