Re: [Phys-l] explanatory and response variables (was calibration )

[Barbara Bay <b2bay@yahoo.com>]

John Denker <jsd@av8n.com> wrote (and I put in italics):On 08/09/2007 02:09 PM, Barbara Bay wrote:  
> > When you are deciding...,you might check through the Math
> > standards for different states for terms.
 
For years, I have been keeping track of the California standards 
in physics and chemistry ... but until just now I wasn't keeping
track of the math standards.  So I learned a couple of useful
things today, thanks to phys-l contributors.

What I know of the California standards comes from here:
  http://www.cde.ca.gov/ta/tg/sr/css05rtq.asp
which points to:
  http://www.cde.ca.gov/ta/tg/sr/documents/rtqgeom.pdf
  http://www.cde.ca.gov/ta/tg/sr/documents/rtqalg1.pdf
  http://www.cde.ca.gov/ta/tg/sr/documents/rtqalg2.pdf
  http://www.cde.ca.gov/ta/tg/sr/documents/rtqchem.pdf
  http://www.cde.ca.gov/ta/tg/sr/documents/rtqphysics.pdf

Those are the released questions, (sample questions), not the actual standards themselves. They list only the standards that will be tested in this batch and how many questions will be asked for each section.
The websites for all of the applicable CA state standards:
All Math < http://www.cde.ca.gov/be/st/ss/mthmain.asp >
Algebra 1 < http://www.cde.ca.gov/be/st/ss/mthalgebra1.asp >
All 9-12 Sciences < http://www.cde.ca.gov/be/st/ss/scmain.asp >
Physics < http://www.cde.ca.gov/be/st/ss/scphysics.asp >
Investigation and Experimentation < http://www.cde.ca.gov/be/st/ss/scinvestigation.asp >
  
> >  The State of California agrees with Dr. George
> > Spagna, Jr. 

No, not really, not so far as I can tell from aforementioned
California documents.

> > In the high school Math standards, the terms "dependent
> > variable", "independent variable", "x-axis" and "y-axis" are used.

Dependent and independent variables are mentioned in item 17.0 of
the algebra I standard.  They are not mentioned in the other four
standards (algebra II, geometry, chemistry, and physics).

They are used in the context of mathematical functions, and appear
to be intimately related to the idea of domain and range.  There
does not appear to be the slightest requirement to associate them
with physics experiments or with whether a variable is "controlled" 
or not.

Which is true. But keeping terminology consistent was being discussed. None of the "Science" Standards discuss graphing or experiments at all, except the Investigative and Experimental Standards (I & E).The I & E Standards are generalizations for all the sciences and are supposed to be addressed as applicable. According to the Physics standards and the I & E Standards, my students could call the parts of a graph anything they want to. However,  every standard (science and math) in elementary school and middle school is allowed to be tested, if related to the Physics or I & E standards. And the Fifth Grade Science Standard < http://www.cde.ca.gov/be/st/ss/scgrade5.asp > #6d states: "Identify the dependent and controlled variables in an investigation", and #6e states: "Identify a single independent variable in an investigation and explain how this variable can be used to collect information to answer a question about the results of the experiment". It does not say how to
 graph these variables, but guess what shows up in the test questions?  Unfair, but reality.

Tangential remark, FWIW: the terms "horizontal axis" and "vertical 
    axis" are also used in the algebra I standard.

No, the terms "horizontal axis" and "vertical axis" are not used in any Math standard from kindergarten on up. They are used in the Math Framework once in the explanation of how the Advanced Placement Probability and Statistics Standard #12.0 (Students find the line of best fit to a given distribution of data by using least squares regression) could be addressed. The math framework can be read at < http://www.cde.ca.gov/ci/ma/cf/index.asp >. But the terms "horizontal axis" and "vertical axis" are used on the Math sample test questions (and the real test questions). Which is, again, unfair.

In the context of mathematical functions, I understand abscissa and
ordinate.  I understand domain and range.  If you want to apply the terms 
independent and dependent, that's harmless /in this narrow context/.

The terms "abscissa" and "ordinate" are never used in the Math or Science standards. "Domain" and "range" are in the Math standards but not the Science standards. "Independent variable" and "dependent variable" are used in both the Math and Science standards.

However, if we transplant the terms from math to physics, and then
overload them with the idea that independent variables are "controlled"
during the experiment ... that's just crazy.  Maybe some experiments
are done that way, but most of them aren't.  There's no reason why
they should be done that way, and many reasons why they can't be done that way.

I think your definition of "controlled" was too narrow for an informal discussion. But, "controlled" was not my word. I used the word change, which is wrong too, if we are going to be picky. I prefer the phrase "first variable measured" which would correspond to the first value in an ordered pair. For example, time is not really "controlled" (students can't make it go backwards or speed up or slow down), but many times it is used as the independent variable simply because it is usually easier to measure. The students "control" the time data only in the respect that they choose the time increments at which to measure the other variable which may, or may not, be dependent on the elapsed time.They are attempting to determine if the value of the second variable measured depends on the value of the first variable measured. That is the purpose of most high school experiments. To determine if there is a relationship between two variables and can we distill that relationship into a
 formula that can be used to make predictions and solve similar problems without having to experimental determine the answers each time. (Also to show the students that the formulas are not difficult and even they can determine the same formulas with experimentation.) The state refers to "controlled" variables in the 5th grade science standards, but never elaborates, not even in the science framework. IB refers to "controlled" variables as the variables you consciously keep the same in experiments to assure reproducibility of the experiment and the validity of the relationship (that the relationship is really between only those two variables and not some other variable).

Let's not read into the standards more than is actually there.  I 
have not seen any state standard that even pretends or attempts to 
require experiments to be done that way ... which is good, because
any such attempt would be absurd.  There are enough absurdities in
the standards already.

I totally agree with you here! And it would be nice if the standards were tested as stated, but they are not. Reading the standards is not sufficient. If you want to know what concepts will be tested, you must read the framework.  The science framework can be found at < http://www.cde.ca.gov/re/pn/fd/sci-frame-dwnld.asp >. Reading the framework fleshes out the standards (adds more). But the test questions still don't always match and you have to remember previous years knowledge may be on the test.
Barbara Bay
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