The policy distinguishes between "testing accommodations" and "testing modifications."

In short, this means that a student may use a calculator to do Algebra and Geometry, because the questions are not assessing aptitude in addition and multiplication: a calculator doesn't change the skill being assessed.

By contrast, for a question that is specifically measuring the student's aptitude in addition and multiplication, a calculator would modify the skill being assessed (i.e. from being able to do multiplication, to being able to hit the proper keys on a calculator).

The applicable passage says:

"Analysis of the constructs underlying the existing elementary and intermediate-level State tests indicates that use of certain testing modifications on certain sections of these tests change the construct of the test and yield inaccurate scores. As a result, the student may be denied appropriate and needed supports. Additionally, testing accommodations that change constructs yield scores that do not provide teachers with valid information upon which to guide instruction."  

For example, this would mean that a blind student could NOT have a "Reading Comprehension" assessment read aloud, as that would modify the skill from READING comprehension to LISTENING comprehension.

Here is the NY State document: 

NYS Policy and Tools to Guide 
Decision-Making and Implementation

http://www.p12.nysed.gov/specialed/publications/policy/testaccess

/policyguide.htm