Hello,
 
I see that you are stuck between the proverbially "rock and the hard place".  Each state varies as to what is considered "special education".  While most agree on sensory impairments (blindness, deafness, etc.) many differ as to their definition for "cognitive learning disabilities".  I have worked in a few different states and i know that each one was a bit different.
 
First, have the school make you a copy of all the testing completed.  If it was simply screening assessments, then ask for a full psycho-educational battery of tests to be conducted.  If they ask why,  indicate that screening tools are not as reliable nor valid as full assessments with a complete battery of tests.  You will need to first make a formal request for a meeting to discuss the screening results and your request for more involved testing.  This is called a multidisciplinary special education team meeting where various school professionals and yourself meet.  Go with someone to this meeting to help you write and recall information.  Also, make all requests in writing with the date.
 
Let us say that there was ONLY a screening of skills conducted and the multidisciplinaryy team has agreed to a complete psycho-educational evaluation.  What is included in this complete battery to determine if a learning disability is evident?  First a measure of cognitive skills.  This will determine your child's IQ and more importantly his ability to complete verbal and nonverbal tasks.  The examination will provide information on verbal processing (vocabulary, comprehension), memory for verbal and nonverbal learning, visual-perceptual skills and much more.  What is very useful about this testing is that your child's strengths and weaknesses should be determined.
 
Next, there should be a full battery of academic testing.  Again, not a screening or a group test, but an individualized examination.
 
In order to determine what is called processing deficits the multidisciplinary team which establishes intervention, assessment and programming (and includes yourself) may wish to have hands on/ eye-hand coordination tasks ordered.
 
The above examinations are often conducted by the school psychologist and perhaps a special educator who will complete the academic testing.
 
Also note, that receiving  1:1 instruction is usually not the norm, even within a special education setting for mild to moderate learning disabled children.  Federal laws clearly indicate that education should be conducted in the least restrictive environment if your child qualifies, so that may mean in the regular classroom with occasional support.   Having one teacher to one student  is very rare and often reserved for the most severely impaired children.
 
Since he is in high school see if there are various supports for him within the school.  Perhaps there is an academic tutoring or peer tutoring group.  Maybe there is a group of volunteers such as retired teachers, who assist in after school programs.
 
I commend you for supporting your son when he is struggling.  
 
Good luck!
 
Louise Masin Sattler, NCSP
Nationally Certified School Psychologist
Owner of Signing Families
http://www.SigningFamilies.com